The jones family and the Connor family both bought the same boxed package of sugar cubes at the store, in which the cubes were arranged in 5 layers. After drinking of 61 cups of tea, the Joneses found that they were out of sugar. The Connors' sugar box was enough to last them thought 88 cups of tea. Both families put either 2 or 3 pieces of sugar per cup. How many sugar cubes were in the box

Answers

Answer 1

The number of sugar cubes in the box is 180

How to determine the number of sugar cubes?

The given parameters are:

Layers = 5Pieces = 2 or 3Cups of tea = 61 and 88

Multiply 61 and 88 by 2 and 3

61 * 2 = 122

61 * 3 = 183

88 * 2 = 176

88 * 3 = 264

The number of sugar cubes cannot be 122 and 264, because they are out of the range

So, we have:

183 and 176

There are 5 layers.

This means that the number of sugar cubes is divisible by 5.

The only number between 176 and 183 that is divisible by 5 is 180

Hence, the number of sugar cubes is 180

Read more about sequence at:

https://brainly.com/question/21961097

#SPJ1


Related Questions

If a and b are integers such that -6 a x b?
(A)-36
(B)-30
(C)-24
(D)-12

Answers

C is the answer for this question

Explain why statistical acceptance sampling is not an effective method for monitoring process quality.

Answers

Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.

a) Concerned with inspection of products

b) Concerned with decision making regarding products

c) One of the oldest aspects of quality assurance

The Acceptance sampling procedure is necessarily a lot sentencing procedure. It cannot be used to estimate the lot quality or lot conformity to the standard specifications.

The acceptance sampling is used when the test is destructive, or the cost of 100% inspection is quite high, or when we need a continuously monitoring program

The Acceptance sampling procedure is used for decision making of either acceptation or rejection of a lot. It can’t be used as a lot quality estimator

As Acceptance sampling is just a lot sentencing process, it can’t estimate the quality of products in the lot. But designed experiments ensure good quality of the process output before even production

To know more about Statistical acceptance visit:

https://brainly.com/question/13334231

#SPJ4

8 times the number is 200. What is 80 times the number?

Answers

Answer:

2,000

Step-by-step explanation:

⇒ 200/8 = 25

⇒ 25 * 80 = 2,000

Answer:

2000.

Step-by-step explanation:

8 * x = 200

x = 200/8

80x = 80 * 200/8

       = 10 *200

       = 2000.

 

In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz? m∠x m∠z < 90° m∠y > 90° ∠x and∠y are complementary m∠x m∠y < 90°

Answers

m∠X + m∠Y < 90° is true.

How to solve it?

XYZ is a triangle.

We have to find the option that is true about △XYZ.

By angle sum property of a triangle,

The sum of all the interior angles of a triangle is always equal to 180°.

So, ∠X + ∠Y + ∠Z = 180°

Given, m∠Z > m∠X + m∠Y.

This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.

so, ∠X + ∠Y must be less than 90°.

Hence, we can say that ∠X + ∠Y < 90°

To know more about triangles, visit:

https://brainly.com/question/1968095

#SPJ4

Answer: Option 4 or D. m∠x + m∠y∠90°

Step-by-step explanation: Trust Me! It is correct on Edge!

Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?

A: D. m∠x + m∠y∠90°

Suppose A and B are 2x2 matrices and that AB = BA =
which of the following statements is correct?

Answers

Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.

What is true on AB = BA?

If:

AB = BA = [3    0]

                 [0    3]

Then:

AB = BA = 3 [1    0]

                    [0    1]

This can be further written as:

AB = BA = 3I₂

And again as:
A (¹/₃ B) = I

This then allows us to either write this as:

A⁻¹ = ¹/₃ B

Or:

B⁻¹ = ¹/₃ A

In conclusion, option A is correct.

Find out more on matrices as https://brainly.com/question/1821869.

#SPJ1

The fit line equation for the scatterplot is y = -2.61x+152.51, where x is variable 1 and y is variable 2. according to the equation, what is the expected value of y when x-value is 45?

Answers

The expected value of y when x-value is 45 is 35.06

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. For example, y = 2x+3 and 2y = 4x + 9 are two-variable linear equations.

In the given question value of x is given and value of y is asked.

The given equation : y = -2.61x+152.51 Such questions can be solved by substituting the given value of variable in the equation which will help us find the unknown.

Substituting x = 45 in the given equation , we get

y = -2.61 x 45 + 152.51

y =  -117.45 + 152.51

y = 35.06

Thus the expected value of y when x-value is 45 is 35.06

Learn more about Linear equations in two variables here :

https://brainly.com/question/24085666

#SPJ4

An exponential growth function represents a quantity that has a constant doubling time true or false

Answers

False, An exponential growth function represents a quantity that has a constant doubling time.

It might always be having time,  Or 13 times, where I would not double but be unable to receive 2/3. Because the quantity is bigger than one, exponential growth would have a constant time between doublings. The halving time for any exponential decay function is A = Ao * kt1/2 x = x * kt1/2 = ktln(1/2) = t * ln kt = ln(1/2) / ln k.Because the quantity is bigger than one, exponential growth would have a constant time between doublings.

What does an exponential growth function represent?

The base b is a constant when describing an exponential function. When the domain is the collection of real numbers, the exponent x is the independent variable. Exponential growth and decay are the two different kinds of exponential functions. When b > 1, the function f (x) = bx represents exponential development.

Learn more about exponential growth function brainly.com/question/11811611

#SPJ4

Does this graph show a function? Explain how you know.
• A. Yes; the graph passes the vertical line test.
• B. No; there are y values that have more than one x-value.
• C. No; the graph fails the vertical line test.
• D. Yes; there are no y-values that have more than one x-value.

Answers

The graph doesn't show a function as C. No; the graph fails the vertical line test.

What is a graph?

It should be noted that a graph is the diagrammatic representation of data.

In this case, the graph doesn't show a function as the graph fails the vertical line test.

The vertical line test is a visual way that's uses to determine if the curve is a graph of the function.

Learn more about graph on:

brainly.com/question/19040584

#SPJ1

What is the slope of the line represented by the equation y=x/6 −5 ?
−5
1/6
5/6
6

Answers

Answer:

slope is the gradient(coefficient of (x) in the equation .We have [tex] \frac{x}{6} [/tex]which can also be written as [tex] \frac{1}{6} x \: therefore \: the \: slope \: is \: \frac{1}{6} [/tex]

Answer:

1/6

Step-by-step explanation:

Solution:

The given equation is:y=x/6 -5

arranging the equation :x/6-y=5

Given,

Coefficient of x=1/6

coefficient of y=-1

So,

Slope(m)=-(Coefficient of x/coefficient of y))

= -(1/6 / -1) {minus divided by - becomes plus }

1 by 6 whole divide by 1

= 1/6 ans✓

55. TECHNOLOGY
If f is a linear function, f(0.1) = 11.5, and f(0.4) = -5.9, find an equation for the function.

Answers

Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

Linear equation o line

A linear equation o line can be expressed in the form y = mx + b.

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Equation for the function in this case

In this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:

(x1, y1)= (0.1, 11.5) (x2, y2)= (0.4, -5.9)

So, the slope m can be calculated as:

[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]

Solving:

m= -58

Considering point 1 and the slope m, you obtain:

11.5= -58×0.1 +b

11.5= -5.8 + b

11.5 + 5.8= b

17.3= b

Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

Learn more about the equation of a line having 2 points:

brainly.com/question/12851029

brainly.com/question/19496333

#SPJ1


[tex]x + 6 = 10 \\ x = 10 - 6[/tex]
simultaneous equations

Answers

Answer:

False.

These are not simultaneous equations.

Step-by-step explanation:

Simultaneous equations are equations involving two or more unknowns that are to have the same values in each equation. In the equations given there is only one unknown value.

Mathew rolls a number cube labeled with the numbers 1−6. he then flips a fair coin. what is the probability that he rolls a 4 and flips a head? write your answer as a fraction.

Answers

The probability that he rolls a 4 and flips a head is 1/12

What is the probability?

Probability determines odds that a random event would happen. The odds of the random event happening lie between 0 and 1.

The probability that he rolls a 4 and flips a head = (number of sides that is a 4 / total number of sides) x (number of sides that is a head / total number of sides)

(1/6) x (1/2) = 1/12

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

Answer: 1/12

Step-by-step explanation:

just say the answer

Checking number 2( Solving inequalities)

Answers

1. x < 20

x - 7 < 13

x < 20

2. x > -7

-3(x + 4) < 9

-3x - 12 < 9

-3x < 21

x > -7

Hope this helps!

4. Use the triangle congruence postulates to prove congruence.
Part I: Fill in the blanks to name each triangle congruence postulate.
a. SSS:
b. SAS:
c. ASA:
AAS:
In the triangle

Answers

The triangle congruence postulate is illustrated below

How to illustrate the triangle?

It should be noted that two triangles are congruent if they have the same shape and size.

AAS: The angle-angle-side theorem illustrates that two triangles are congruent if the two angles and a side note between the two angles are identical to that of another triangle.

SSS: This illustrates that the three sides of a triangle are congruent to the corresponding three sides of the other triangle.

ASA: This illustrates that the triangles are congruent when the two angles and the side are the same as the corresponding angles and sides of the other triangle.

SAS: When two sides and the included angle of a triangle are congruent to the corresponding sides and the included angle if a second triangle then it follows the side-angle-side theorem.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Identify the 8th term of the given geometric sequence. 1/2, 2, 8, 32,...

Answers

Geometric sequence.

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

We have:

[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]

Find the common ratio:

[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]

The formula of the n-th term of a geometric sequence:

[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]

Substitute:

[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]

Method step by step:

[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]

find the value of 7 + 15 + 23 +...+ 767 + 775 + 783

Answers

Answer:

38,710.

Step-by-step explanation:

This is an arithmetic series  with common difference  8 , first term a = 7 and last term L = 783.

The number of terms n = (783 - 7) / 8 + 1 = 98

Sum of 98 terms = (n/2)[a + L)

= (98/2)(7 + 783)

= 49 * 790

= 38,710.

(01.04 LC)Multiply negative 1 over 6 multiplied by negative 1 over 5. negative 1 over 11 negative 1 over 30 1 over 30 1 over 11

Answers

The expression is -1/6 x (-1/5) = 1/30.

What is expression?

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given:

negative 1 over 6 multiplied by negative 1 over 5.

As per the data,

if -1/6 is multiplied with -1/5 then the resultant value will be

=-1/6 * -1/5

= 1/5*6

=1/30

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

HEEEELPPP MEEEEEEE FRRRRRR!!!!!!! 30POINTS!!!!!

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Circumference of a circle: }[/tex]

[tex]\bullet\ \large\boxed{\mathsf{2\pi r}}}\\\rightarrow\large\boxed{\textsf{Whereas, } \pi \large\textsf{ is your pi and it is approximately equal to 3.14}}\\\rightarrow\large\boxed{\textsf{ And \underline{r} is the radius of the circle.}}[/tex][tex]\huge\textbf{Area of a triangle:}[/tex]

[tex]\bullet\ \large\boxed{\mathsf{\dfrac{1}{2}bh}}\\\\\rightarrow\large\boxed{\textsf{Whereas, }\mathsf{\dfrac{1}{2}} \large\textsf{ is half your triangle, \underline{b} is your \underline{b}ase, and b is your \underline{h}eight}}[/tex]

[tex]\huge\textbf{Surface area of a rectangular prism: }[/tex]

[tex]\bullet \ \large\boxed{\textsf{2(wl + hl + hw)}}\\\rightarrow\large\boxed{\textsf{Whereas, l is your \underline{l}ength, h is your \underline{h}eight, and w is your \underline{w}idth.}}[/tex]

[tex]\huge\textbf{Volume of a rectangular prism:}[/tex]

[tex]\bullet\ \large\boxed{\textsf{whl = v}}\\\rightarrow\boxed{\large\textsf{Whereas, v is your \underline{v}olume, w is your \underline{w}idth, h is your \underline{h}eight, l is}}\\ \ \large\boxed{\textsf{your \underline{l}ength}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Kevin earned $80. Out of his earnings, he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi. Find the remaining amount.

Answers

The amount remaining out the money earned is $37.5

Sum of values and proportion

Given the following parameters

Amount earned by kevin = $80

If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;

Total money spent = 51/2 + 68/5 + 22/5

Total money spent = 51/2 + 90/5

Total money spent = 25.5 + 18

Total money spent = 43.5

Amount remaining = 80. - 43.5

Amount remaining = 37.5

Hence the amount remaining out the money earned is $37.5

Learn more on difference here: https://brainly.com/question/148825

#SPJ1

Rectangle ABCD is congruent to rectangle URST.

Rectangles A B C D and U R S T are congruent. The length of sides A B is 9 millimeters and the length of sides R S is 15 millimeters.

What is the area of rectangle URST?
24 mm
48 mm
135 mm2

Answers

The area of the rectangle URST is 135 mm². so the option C is correct.

What are Congruent rectangles?

Congruent rectangles have the same lengths of sides, same measures of angles and same areas and same perimeters

The Rectangle ABCD is congruent to rectangle URST

Given; Rectangle ABCD ≅ rectangle URST

AB = UR , BC = RS , CD = ST , AD = UT

AB = 9 millimeters

UR = 9 millimeters

We know that, The area of any rectangle = l × w,

In rectangle URST

∵ UR = 9 millimeters

∵ RS = 15 millimeters

- Assume that UR = l and RS = w

The area of rectangle URST = UR × RS

The area of rectangle URST = 9 × 15 = 135 millimeters²

Hence, The area of rectangle URST is 135 mm²

Learn more about rectangle here;

https://brainly.com/question/13307509

#SPJ1

30 points plus brainliest if answered right!

Answers

Answer:

The second choice.

Step-by-step explanation:

The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.

Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.

Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.

Therefore, we are left with the second option.

Answer:

AC = 5, BC = √17, AB = √32

Explanation:

Given points: A(-3, -2), B(1, 2), C(2, -2)

Use distance between two points formula:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2} = \sqrt{25+ 0} = 5[/tex]

BC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]

AB length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

2x2 – 9x + 2 = –1 discrimiant

Answers

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

How to determine the discriminant of a quadratic equation

For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:

2 · x² - 9 · x + 2 = - 1

2 · x² - 9 · x + 3 = 0

d = (-9)² - 4 · (2) · (3)

d = 81 - 24

d = 57

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

To learn more on quadratic equations: https://brainly.com/question/2263981

#SPJ1

-10 -8 -6 -42
10
8
6
41
2
-2
-4
-6
-8
+10
y
2
4 6 8 10
x
Study th
to find its
The equ

Answers

Answer: [tex]y=x+2[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{0-2}{-2-0}=1[/tex]

since the y-intercept is 2, the equation is [tex]y=x+2[/tex]

suppose g(x)=f(x+2)-3 wich statement best compares the graph of g(x) with the graph of f(x)

Answers

Answer:

xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8

Step-by-step explanation:

q+++

porfaaaaaaa ayudaaaaaaa
Determine el dominio y el rango de la siguiente función.
f(x)=-25-x+50

Answers

The domain and the range of f(x) = -25x + 50 are the set of all real numbers

How to determine the domain and the range?

The function is given as:

f(x) = -25x + 50

The above function is a linear function.

All linear functions have their domain and range to be the set of all real numbers

Hence, the domain and the range of f(x) = -25x + 50 are the set of all real numbers

Read more about domain and range at:

https://brainly.com/question/1632425

#SPJ1

pls help me answer this

Diagram 3 shows a composite solid, formed by joining a half m-cylinder with a right prism. ABKJ is the cross - section of the right prism. MK is the diameter of the half - cylinder Given BK 28 cm, AJ = 14 and AE = 20 cm, The volume of the composite solid is 17000 cm³
Using
[tex]\pi = \frac{22}{7} [/tex]
calculate the value of h

Answers

Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of  [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.

write the equation for the graph given below

Answers

Answer: Option (1)

Step-by-step explanation:

The slope of the line is

[tex]\frac{9-6}{4-(-4)}=\frac{3}{8}[/tex]

This eliminates all the options except for (1).

GEOMETRY HELP ME PLS PLS!!!! THE FOLLOWING ROMBUS!!

Answers

Answer:

12

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.

Using the Pythagorean theorem, it follows that KN = 12.

GIVING BRAINLEST!
Linda collected 1/2 of a stamp album. Becky collected 7 1/3 times as many stamps as Linda. How many
stamp albums were collected by Becky?

O 3 1/3
O 2 1/3
O 3 2/3
O 1 1/3
*

Answers

Answer:

3 2/3

Step-by-step explanation:

To do this question, you would need to multiply 7 1/3 with 1/2. The answer is 3 2/3.

Answer:

3 2/3 albums

Step-by-step explanation:

Let's say that the stamp album has 12 stamps (12 is just an arbitrary number used to make calculation easier). If Linda collects half of the album, it means she has 6 stamps. If that is the case, Becky has 6 * 7 1/3 stamps. Since 7 1/3 is equivalent to 22/3, we can determine that Becky has collected 44 stamps (6*22/3). There are 12 stamps in one album, which means there are 44 stamps in 3 2/3 (11/3) albums:

[tex]\frac{12}{1}=\frac{44}{y} \\12y=44\\y=11/3[/tex]

Since the ratio of stamps to albums is constant, the calculation above demonstrates that the number of albums it takes to have 44 stamps is 3 2/3. Please note that the numbers I used are arbitrary. If you substitute 12 for a variable x, you will get the same result.

I need your help :))
Question is:
Make a pattern and explain the rule the pattern follows. Use a minimum of 3 terms within your pattern.

Answers

The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:

[tex]a_n = 1 + 2(n - 1)[/tex].

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:

[tex]a_1 = 1, d = 2[/tex]

Hence the rule for the pattern is given by:

[tex]a_n = 1 + 2(n - 1)[/tex].

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

#SPJ1

Other Questions
Ted wants to become a writer and often asks more competent and experienced writers to critique his stories. Chad was the only student in his class who persisted on a difficult puzzle until the bell rang. He gave up his lunch break for the opportunity to ask the professor how to solve the puzzle. What is implied here Compare the early Roman Empire to the empire conquered by Alexander the Great. Why did the Roman Empire hold together for so much longer than Alexander's? 5 Quick algebra 1 questions for 50 points! Only answer if you know all 5, Tysm! :) Question 4 of 5Use the drawing tools to form the correct answer on the number line.Graph the solution set to this inequality.-4(1 + 3) -21Drawing ToolsSelectPointOpen PointRay>Click on a tool to begin drawing.A+++-10-8-6-4-20Delete24Undo620.8Reset10?os The gradual expansion of project requirements, specifications and priorities during the execution of project is known as ____________. 4The theme in the Odyssey most clearly evidenced by the suitors early in the reader's acquaintance with them inthe story isO coming of agedesire for the good lifeO temperance and restraintO marriage and fidelityO gods and humansO leadership and decision-makinghospitalitytemptationO heroism Which equation has infinite solutions?3(x 1) = x + 2(x + 1) + 1x 4(x + 1) = 3(x + 1) + 12x + 3 = 2 x plus 3 equals StartFraction one-half EndFraction left-parenthesis 4 x plus 2 right-parenthesis plus 2.(4x + 2) + 2StartFraction one-third EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals 3 left-parenthesis x plus 1 right-parenthesis minus x minus 2.(6x 3) = 3(x + 1) x 2 Which of the following linesfrom "True Stories of Historyand Biography" uses a tonethat reveals Hawthorne'sattitude toward IsaacNewton?A. All that he had learned only made himfeel how little he knew in comparison towhat remainedB. Just as the destruction was completedNewton opened the chamber doorC. There stood little Diamond, the author ofall the mischief paragraph on right to education Which heart rate zones are generally anaerobic in nature? Zones 1 and 2 Zones 4 and 5 Zones 2 and 3 Zones 3 and 4 Please help! I don't understand how to do this. Dwight Donovan, the president of Finch Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of five years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $103,000 and for Project B are $41,000. The annual expected cash inflows are $34,441 for Project A and $12,522 for Project B. Both investments are expected to provide cash flow benefits for the next five years. Finch Enterprises desired rate of return is 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) An object moving with a speed of 1 m/s accelerates uniformly at 9 m/s2 in the direction of its motion for a distance of 7 meters. What is the final speed of the object A company is looking for an employee to design and test connections in itscomputer systems. Which field includes this job? What are some other ways that people can express a commitment to their country? A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible Phenylketonuria (PKU) is a disease in humans where the function of the enzyme phenylalanine hydroxylase is impaired by mutation of the human PAH gene. Untreated, individuals with PKU can have intellectual disability, behavioral problems, and seizures. However, people who eat a diet low in phenylalanine can lead a normal life. What terms describe PKU as a trait During the 1960s, some civil rights leaders had different views on combating racial injustice. where would you think the sea floor is the oldest and why? Explain.a) near the divergent plate boundary (Mid-oceanic ridge).b) directly between the divergent and convergent boundaries.c) in the area of the subduction zone near an ocean trench. Which expressions are equivalent to 1,120y? Select three options.2-2-2-2-5-7-y-y2 2 2 5 72 2 2. 5.17.7.SY02.2.y2-5-7-y4y70y