You have a set of consecutive integers from (-10) to 5, inclusive. You multiply any
three of the integers. What is the greatest product you can get?

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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Answer:

  65°

Step-by-step explanation:

Short arc AC is the difference between 360° and long arc ABC:

  arc AC = 360° -230° = 130°

The inscribed angle ABC that intercepts this short arc will have half the measure of the arc:

  ∠ABC = 130°/2 = 65°

Answer:

15/7 or 2.142

Step-by-step explanation:

x=3/7×5

x=15/7

Answer: ( − 3 , − 64 )

Step-by-step explanation:

knowledge!

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

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The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

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Answer:

a=2

Step-by-step explanation:

\(area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2\)

\(\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)\)

the curve is a right parabola.

here b=0,and a=4a for x

we are finding the area between x-axis and x from 0 t0 4a.

curve is symmetrical about x-axis so we multiply by 2.

If the area of the region bounded by the curve \(y^2 =4ax\)  and the line \(x= 4a\)  is \(\frac{256}{3}\) Sq units, then the value of  \(a\) will be \(2\) .

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Area bounded by the curve  \(=\int\limits^a_b {x} \, dx\)

We have,

\(y^2 =4ax\)  

⇒ \(y=\sqrt{4ax}\)

\(x= 4a\),

Area of the region  \(=\frac{256}{3}\)  Sq units

Now comparing both given equation to get the intersection between points;

\(y^2=16a^2\)

\(y=4a\)

So,

Area bounded by the curve  \(= \[ \int_{0}^{4a} y \,dx \]\) ​

 \(\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \]\)

\(\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \]\)

 \(\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \]\)                                            

\(\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}\)

\(\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}\)

\(\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}\)

On applying the limits we get;

\(\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right]\)

\(\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }\)

\(\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}\)

\(\frac{256}{3}= \frac{4}{3} * 8 *a^{3}\)

⇒ \(a^{3} =8\)

\(a=2\)

Hence, we can say that if the area of the region bounded by the curve \(y^2 =4ax\)  and the line \(x= 4a\)  is \(\frac{256}{3}\) Sq units, then the value of  \(a\) will be \(2\) .

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Answer:

A)

Step-by-step explanation:

rise/run

down 5, left 3

Answer:

Inflation rate for 2019 is 2.5%

Step-by-step explanation:

(124/121) - 1 = 1.02479 - 1 = .02479

Change 0.02479 to percent by multiplying 100 = 2.479%

Round this up to 2.5%

Since the value is increasing from 121 in 2018 to 124 in 2019, this is an inflation.

Answer:

jus 2 ez pz broski lemon squeze

Step-by-step explanation:

Answer:

ara completar la tabla, podemos seguir el patrón de duplicar el número de granos de arroz en cada cuadrado.

Step-by-step explanation:

Podemos escribir esto en forma exponencial, donde 2^n representa el número de granos de arroz en el cuadrado n. La tabla completa es la siguiente:

Cuadrado del tablero de ajedrez Granos de arroz

1 2^0 = 1

2 2^1 = 2

3 2^2 = 4

4 2^3 = 8

5 2^4 = 16

6 2^5 = 32

7 2^6 = 64

8 2^7 = 128

9 2^8 = 256

10 2^9 = 512

11 2^10 = 1024

12 2^11 = 2048

13 2^12 = 4096

14 2^13 = 8192

Answer:

2.3%

Step-by-step explanation:

79327x + 88798x = 3890

168125x = 3890

x = 3890/168125

x = 0.023

x = 0.023 * 100

x = 2.3%

Answer:

2.3% (nearest tenth)

Step-by-step explanation:

total sales = 79327 + 88798 = 168125

percentage = \(\dfrac{3890}{168125} \times 100=2.3137546... \%=2.3\% \ \textsf{(nearest tenth)}\)

Answer: A

because slope are

Proportionately, if Lexi uses 360 g of flour, the quantity of blueberries she must use is 150 g of blueberries.

Proportion describes the two ratios equated to each other.

Proportions are fractional values between zero and one.

Recipe for making Blueberry Muffins

Ingredient  Quantity

Egg              1

Flour           120 g

Sugar         120 g

Butter          60 g

Blueberries 50 g

120 g of flour = 50 g of blueberries

The Ratio of flour to blueberries = 2.4:1

360 g of flour = 360/120 x 50

= 150 g of blueberries (360/2.4)

Thus, if Lexi uses 360 g of flour, based on the given recipe, she must use 150 g of blueberries.

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Answer:

16/20.......................

Answer:

Step-by-step explanation:

Answer: Pete is twice as old as Chris.p = 2c  Seven years ago the sum of their ages were 31.(p-7) + (c-7) = 31p + c - 14 = 31p + c = 31 + 14p + c = 45Find their ages now replace p with 2c2c + c = 453c = 45c = 45/3c = 15 is Chris's agethenp = 2(15)p = 30 is Pete's age::Check solutions in the statement"Seven years ago the sum of their ages were 31"30-7 + 15-7 = 31

Using exponential growth formula, the number of bacteria in test tube after 8 hours is  167,772,160

To calculate the approximate number of bacteria after eight hours of growth, we need to determine the number of doubling cycles that occur during that time and apply the exponential growth formula.

Given:

Initial number of bacteria (N₀) = 50 (given as the inoculum)

Doubling time (t) = 20 minutes

Let's first calculate the number of doubling cycles that occur in eight hours (480 minutes):

Number of doubling cycles = (8 hours * 60 minutes per hour) / 20 minutes

Number of doubling cycles = 24 cycles

Now, we can apply the exponential growth formula to calculate the final number of bacteria (N) after eight hours:

N = N₀ * (2 exp (number of doubling cycles))

N = 50 * 2²⁴

Using a calculator or computational tool, we can evaluate this expression:

N ≈ 1.6777216 * 10^8

Therefore, after eight hours of growth, the test tube should contain approximately 167,772,160 bacteria.

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

2 dollars

Step-by-step explanation:

5 % of 40 is 2

Then change to dollars

Answer:

The age of Noelle  =  20 years

Age of Noelle's dad   = 54 years

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

i will trun on the light and see what color the socks are

please write complete question

Answer:

Step-by-step explanation:

xy = 864

x + y = 60                     Solve for y in the second equation

y = 60 - x                      

x * (60 - x) = 864          Remove the brackets.

60x - x^2 = 864           Put in order of powers and subtract 864

-x^2 + 60x - 864 =0    Multiply through by -1

x^2 - 60x + 864 = 0

This factors

(x - 36)(x - 24) = 0

Either

x - 36 = 0    in which case

x = 36

or

x - 24 = 0

x = 24

The two numbers are x = 36 and y = 24

of x = 24 and y = 36

F(x) = 2x³ - x² + 5x − 3 is the polynomial that is in standard form. Thus, option D is correct.

Algebraic expressions called polynomials can include exponents that are multiplied, divided, or added. Different types of polynomials exist. specifically, monomial, binomial, and trinomial. A polynomial with only one term is referred to as a monomial. A polynomial with two unlike terms is referred to as a binomial. An algebraic expression with three terms is known as a trinomial.

Monomials - The term "monomial" refers to algebraic expressions with a single term. In other words, it is an expression that includes any number of similar terms. Hence the name "Bi"nomial," binomials are algebraic expressions with two unlike terms. Trinomials - Trinomials are algebraic expressions with three dissimilar terms, hence the name "Tri"nomial.

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The error in the expression 4 + 2x - 1/2(10 - 4x) is the missing parentheses.

Parentheses are a sort of punctuation mark that is used to separate or distinguish content inside a phrase. They frequently assist to clarify the meaning of a statement by adding information. Parentheses can also be used to denote a break or to divide items in a list.

Error in the given question: Missing parentheses

Corrected expression: 4 + 2x - 1/2(10 - 4x)

The problem may be fixed by ensuring that the proper syntax is used when declaring variables. If the variable is a string, for example, it should be stated as "var myVariable ='string value';". If it is an integer, define it like "var myVariable = 42;".

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The equatiοn fοr the parabοla is  y= (- 21/2 )x²

A parabοla is a mirrοr-symmetrical, rοughly U-shaped planar curve that is used in mathematics. It cοrrespοnds tο a number οf mathematical explanatiοns that appear tο differ οn the surface but which all define the same curves.

A line and a pοint (the fοcus) are twο ways tο describe a parabοla (the directrix). Nοt the directrix is the main fοcus. The lοcatiοn οf pοints in that plane that are equally spaced apart frοm the directrix and the fοcus is knοwn as the parabοla. Cοnic sectiοns, which are fοrmed when a right circular cοnical surface and a plane perpendicular tο anοther plane that is tangential tο the cοnical surface intersect, are anοther way tο describe parabοlas.

Vertex is at (0,0) ,  directrix is at y=1/42

Equatiοn οf parabοla is y = a(x-h)² + k---------(1)

(h,k ) is the vertex, (h,k )= (0,0)

(1)=> y = a(x-0)² + 0

=>  y= ax² ----------(2)

Directrix is abοve the vertex. sο parabοla οpens dοwnwards and

'a' is  negative

The distance οf directrix frοm vertex is  1/42

D= 1/4|a| =>  1/42 =  1/4|a|  =>  |a| = 21/2

=> a = - 21/2

(2)=>  y= (- 21/2 )x²

The equation for the parabola is  y= (- 21/2 )x²

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The value of the expression given as 1045 + (834 − 612) is 1267

The expression is given as

1045+(834−612)

Evaluate the brackets in the above expression

So, we have the following equation

1045 + (834 − 612) = 1045 + 222

Evaluate the sum in the above expression

So, we have the following equation

1045 + (834 − 612) = 1267

The above equation/expression cannot be solved further

So, we make our conclusion

Hence, the solution to the expression is 1045 + (834 − 612) = 1267

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Answer: 13,668 i think.

Answer:

17.40

Step-by-step explanation:

no