Find the value of each of the following by using prime factorisation.
(b) 13824

Answer:

x = 2

Step-by-step explanation:

Equation: 5x = 10

--- Divide 5 on both sides

x = 2

This means that each apple can make 2 cakes.

Answer: 2

Step-by-step explanation: because  if u divide both sides by 5

Answer:

The last option

y = ⅓x-3

Step-by-step explanation:

Slope-intercept form :

y=mx+c

[tex]x - 3y = 9 \\ - 3y = - x + 9 \\ \frac{ - 3y}{ - 3} = \frac{ - x}{ - 3} + \frac{9}{ - 3} [/tex]

[tex]y = \frac{1}{3} x - 3[/tex]

Answer: $21.86 i just found this on the web buts its right

Answer:6,299,406

Step-by-step explanation:

Answer:

B)2:3

Step-by-step explanation:

the spinner has all the rainbow colors and thus two colors(blue and yellow) are 2 out of 6 possibilities. the odds against these is 4 out of six (2:3)

Answer: 3/4

Step-by-step explanation: because 12/16 simplified is 3/4

If Kevin has a total of 81 hours of service, then he volunteered for 0.48 weeks.

As per the question statement, Kevin served as a volunteer for 81 hours.

We are required to find out the number of weeks, he volunteered his service.

To solve this question, we just need to know that a week consists of how many hours ?

We can proceed with the facts that a week consists of 7 days and each day consists of 24 hours. Therefore, a week consists of [tex](24*7)=168[/tex] hours, of which, Kevin volunteered for 81 hours.

Therefore, as per the unitary method, we get that,

168 hours make 1 week, then

1 hour makes [tex](\frac{1}{168})[/tex] weeks, and

81 hours make [tex](\frac{81}{168})=0.48[/tex] weeks approximately.

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The cycle time for the company is 3.

Unitary method is a mathematical technique for first finding value of a single unit then determining the any value according to the given question.

According to the given question a company takes 4,500 hours to produce 15,000 units of a product we have to find the cycle time for the company which we can easily determine by using unitary method.

Given the company takes 4,500 hours to complete 15000 units

∴ In one hour he company can make 15000/4500 units which is

= 3 units per hour.

So the cycle time for the company is 3 units per hour.

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Between the locations S(4,-3) and T(-2,2), there are 7.81 units between them.

The length of the line segment connecting two locations serves as a measure of the distance between them. Most importantly, the distance between two points is always positive and segments with the same length are known as congruent segments.

P(x1, y1) and Q(x2, y2) are two points, and the formula for their distance is provided by: d (P, Q) = (x2 - x1)2 + (y2 - y1) 2.

The points S(4,-3) and T are given.

Therefore, the distance (d) between S(4,-3) and T(-2,2) is as follows:

⇒ d (S, T) = √

² + (2 - (-3)) ².

⇒ d (S, T) = √ (-6)² + (5) ².

⇒ d (S, T) = √ 36+25

⇒ d (S, T) = √61

D (S, T) equals 7.81 units

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The original dimensions of the piece of metal are 39 inch by 24 inches.

Let the breadth of the rectangular piece be b inches.

Hence, according to the data given in the question,

Length of the rectangular piece will be (b + 15) inches.

After 4 squares of 3 inches each are cut from the corners of the rectangular piece, the length and breadth of the piece becomes:-

Length = b + 15 - 3 - 3 = (b + 9) inches

Breadth = b -3 -3 = (b - 6) inches

The height of the subsequent open box made will be 3 inches.

We have,

Volume of the cuboidal open box = 1782 cubic inches.

Also, we know that,

Volume of cuboid = l*b*h

Where,

l is the length,

b is the breadth, and

h is the height

Hence,

(b+9)(b-6)(3) = 1782 cubic inches

(b+9)(b-6) = 1782/3 = 594

We can write 594 as 33*18

Hence,

(b+9)(b-6) = 33*18

b+9 = 33 or b-6 = 18

b = 33-9 = 18+6 = 24

Hence, the original dimensions are :-

b + 15 = 24 + 15 = 39 inches, and

b = 24 inches

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The points ( 3. 125, 0) represents the time intervals for which the rocket reaches a height of - 312. 5 feet

Given the function;

h(t)= -16t^2+50t

Where;

The time interval to reach the height of the rocket is ( 3. 125 , 0)

Time interval, t = 0 - 3. 125

Time interval, t = -3. 125

Substitute the value into the formula

h(t) = - 16(-3. 125)² + 50(-3. 125)

h(t) = -16(9. 765) - 156. 25

h(t) = - 156. 25 -  156. 25

h(t) = -312. 5 feet

Thus, the points ( 3. 125, 0) represents the time intervals for which the rocket reaches a height of - 312. 5 feet

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The function rules for each of the given tables are;

11) f(x) = 4x

12) f(x) = x - 3

13) f(x) = x + 12

14) f(x) = x/10

15) This doesn't have a function rule.

16) Function rule here is non existent

11) In this table, we can observe that the output values are all four times the input value. Thus, the function rule here is;

f(x) = 4x

12) In this table, we can observe that the output values are all 3 units less than the input value. Thus, the function rule here is;

f(x) = x - 3

13) In this table, we can observe that the output values are all 12 units more than the input value. Thus, the function rule here is;

f(x) = x + 12

14) In this table, we can observe that the output values are equal to the input value divided by 10. Thus, the function rule here is;

f(x) = x/10

15) This doesn't have a function rule as the values don't match a pattern

16) Function rule here is non existent

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Although part of your question is missing, you might be referring to this full question: The stadium has 15400 seats and it is to be renovated with a new seating capacity of 20790 seats. After renovation what will be the percentage increase in the number of seats?

The initial capacity of the stadium  = 15400 seats

Planned new capacity = 20790 seats

Increment in the number of seats = 20790 - 15400 = 5390 seats

Percentage increase in the number of seats = (Increment in seats/Initial capacity of the stadium)*100

Therefore,

(5390/15400)*100 = 0.35*100 = 35%

So the percentage increase in the number of seats after renovation will be 35%

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I am the fraction 28/40.

It is given in the question that my numerator and denominator are even numbers. Also, the sum of the numbers is 68 and the fraction I am is equivalent to 7/10.

We have to find the fraction which I am.

Let the fraction I am be 7x/10x.

According to the data given in the question, we can write,

7x + 10x = 68

17x = 68

x =68/17

x = 4

Hence, both the even numbers are :-

7x = 7*4 = 28, and

10x = 10*4 = 40

Hence, the fraction which I am is 28/40.

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The cumulative frequency distribution indicates the total number of data items with values below the class's upper limit.

Cumulative frequency analysis examines how frequently values of a phenomena occur that are less frequent than a reference value. The phenomenon could depend on time or place. Another name for cumulative frequency is frequency of non-exceedance. Each frequency from a frequency distribution table is added to the total of its predecessors to determine the cumulative frequency. Since all frequencies will have previously been added to the prior total, the final result will always be equal to the sum of all observations. The quantity of an element in a set is referred to as the element's frequency. The accumulation of all earlier frequencies up to the present time is another definition for cumulative frequency.

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Answer:

-65

Step-by-step explanation:

Given ~

[tex] \tt \: f(x) = - 4 {x}^{2} + 7x[/tex]

[tex] \: [/tex]

put x=5 in given function ~

[tex] \: [/tex]

[tex] \tt \: f(5) = - 4(5) ^{2} + 7(5)[/tex]

[tex] \: [/tex]

[tex] \tt \: f(5) = - 4(25) + 7(5)[/tex]

[tex] \: [/tex]

[tex] \tt \: f(5) = -100 + 35 [/tex]

[tex] \: [/tex]

[tex] \underline{\boxed{\red{ \tt f(5) = - 65}}}{\green✓}[/tex]

[tex] \: [/tex]

hope helps ~

The area of the semicircle with the given diameter is 189.97 mm^2

The given parameters are

Diameter, d = 22 mm

The area of the semicircle is calculated as

A = 1/2 * pi * (d/2)^2

So, we have

A = 1/2 * 3.14 * (22/2)^2

Evaluate the expression

A = 189.97 mm^2

Hence, the area of the semicircle with the given diameter is 189.97 mm^2

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The rewritten form of the equation as given in the task content such that it has no fraction is; 10x + 60 = 6.

In order words, when the equation " 2/3x+4=2/5" is rewritten such that it does not have fractions, it is rewritten as 10x + 60 = 6.

It follows from the task content that the equation given be rewritten such that it has no fraction.

Given:

(2/3)x + 4 = 2/5

Hence, we multiply all terms in the equation by the lowest common multiple of 3 and 5.

Multiply both sides by 15 so that we have;

10x + 60 = 6.

Ultimately, the rewritten form is as indicated above.

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Answer:122 days

Step-by-step explanation:

Answer:

$8.50

Step-by-step explanation:

This is a division problem.

You need to divide $25.50 by 3.

25.5/3 = 8.5

Answer: Each sister pays $8.50.

Answer:

$8.50

Step-by-step explanation:

Since the gift is $25.50, including tax, and there are three sisters, divide the cost of the gift ($25.50) by the number of sisters (3) to find how much each one of them has to pay.

25.50 ÷ 3

= $8.50

Each sister should pay $8.50.

Have a lovely rest of your day! :)

Answer:

Step-by-step explanation:

False, the left side is not equal to the right side

Answer:

-15+13i

Step-by-step explanation:

Distribute the negative to get (-10+6i)

Combine both parenthesis and the answer is -5-10=-15 and 7i+6i=13i

Final answer is -15+13i

Answer:

the question should have something in between 6 and x

Answer:

what give a pasia what do in

Answer:

A. 8500

Step-by-step explanation:

All the other asnwers are correct!

The simplest expression that represents the total number of beads in her bracelet design is 2b + 7.

Expression:

An expression is the  sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

The structure of an expression is:

Expression = (Number/variable, Math Operator, Number/variable)

Given,

Jewelry Marena is using a certain number of blue beads in a bracelet

design. she will use 7 more red beads than blue beads.

Here we need to write an expression in simplest form that represents the total number of beads in her bracelet design.

Assign a variable for the unknown value.

Let b be the number of blue beads for the bracelet.

The number of red beads will be represented as b + 7.

Determine the expression for the total number of beads.

Then we can written it as,

=> b + (b +7)

=> 2b + 7.

Therefore, the total number of beads can be written as 2b + 7.

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The values of r and s is -1 and -4 respectively.

Given that:-

coordinates of j are (-8,-5)

coordinates of l are (6,-11)

coordinates of k are (r-4,2s)

Also, k is the mid-point of jl.

We have to find the values of r and s.

We know that, for  (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).

Here,

(x,y) = (-8.-5)

(z,w) = (6,-11)

(r-4,2s) = ((x+z)/2,(y+w)/2)

Hence,

(r-4,2s) = ((-8+6)/2,(-5-11)/2)

(r-4,2s) = (-1,-8)

Comparing the coordinates, we get:-

r - 4 = -1

r = -1+4 =3

2s = -8

s =-8/2 = -4

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Answer:

a)  5.9

b)  4.2

Step-by-step explanation:

Plot the data points on the number line (see attached).

Part (a)

[tex]\begin{aligned}\textsf{Distance between Ben and Kloee} & = \sf \left| Ben - Kloee \right|\\& = \sf \left|-2.65-3\frac{1}{4}\right|\\& = \sf \left|-2.65-3.25\right|\\& = \sf \left|-5.9\right|\\& = \sf 5.9\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}\textsf{Distance between Middle school and Football field} & = \sf \left| Middle\:school-Football\:field\right|\\& = \sf \left| 1.5-5.7\right|\\& = \sf \left| -4.2 \right|\\& = \sf 4.2\end{aligned}[/tex]

False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.

What does the term "echelon form" mean?

What purpose does echelon matrix serve?

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