What's the GCF of 26y and 52y?

Answer:

The last number line.

Explanation:

To represent the sum of 8 + (-12), we need to represent 8 and -12 as follows:

Where 8 is represented with an arrow that goes to the right and -12 is represented with an arrow that goes to the left.

Then, if we will represent the sum of these numbers, the arrow of -12 should starts when the arrow of 8 ends. Therefore, the representation of 8 + (-12) is:

So, the answer is the last number line.

Answer:

4/10 and 16/40

Step-by-step explanation:

2/5 = 0.4(ZERO POINT FOUR NOT 0.04 ZERO POINT ZERO FOUR)

(numerator =2 x 2=4 ,denominator= 5 x 2= 10) this is how i got 4/10 (choose any number between 10 and 2 and multiply it by the denominator and numerator)

As well as 4/10  = 0.4

Also 16/40= 0.4

(Using our original fraction 2/5 we can multiply both the numerator and denominator by 8; numerator= 2 x 8 = 16  and denominator= 5 x 8 = 40

Since 4/10 and 16/40 are both equivalent to 0.4, they are equivalent fractions

(TO FIND THE DECIMAL OF THAT FRACTION DIVIDE THE NUMERATOR BY DENOMINATOR)

hope this helps, ;]

well, we know all three points are colinear, so the slope from the first two points is the same slope from either to the (c , -9) point, let's check the slope of the first two points given

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{1 +3}{10 +5}\implies \cfrac{4}{15}\)

so then, the slope from say hmmmm let's use (-5 , -3), the slope from (-5 , -3) and (c , -9) must also be the same 4/15

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{c}-\underset{x_1}{(-5)}}} \implies \hspace{5em}\cfrac{-9 +3}{c +5}~~ = ~~\stackrel{slope}{\cfrac{4}{15}}\implies \cfrac{-6}{c+5}=\cfrac{4}{15} \\\\\\ -90=4c+20\implies -110=4c\implies \cfrac{-110}{4}=c\implies -\cfrac{55}{2}=c\)

Answer: 0.4419

Step-by-step explanation:

Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.

i.e. \(\mu=6.8\ \ \ \text{ and }\sigma= 1.7\)

Let X denotes the birth weight.

Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-

\(P(6<X<8)=P(\dfrac{6-6.8}{1.7}<\dfrac{X-\mu}{\sigma}<\dfrac{8-6.8}{1.7})\\\\=P(-0.47<Z<0.71)\ \ \ [Z=\dfrac{X-\mu}{\sigma}] \\\\=P(Z<0.71)-(1-P(Z-0.47))\\\\=0.7611-(1-0.6808)\ \ \ [\text{By z-table}]\\\\= 0.4419\)

Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .

Answer:

Step-by-step explanation:

(-2 - 3)/(-5 + 3) = -5/-2 = 5/2

To the nearest cent, Eva will earn $10.50 in interest over 2 years.

What is Compound interest ?

Compound interest is a type of interest calculation where the interest earned on an initial investment or loan is added to the principal amount, and then the interest for the next period is calculated based on the new total. In other words, the interest is compounded over time, leading to exponential growth of the investment or debt.

To find the interest earned by Eva in 2 years, we can use the formula for compound interest:

B = P\((1+r) ^{t }\)

where B is the final balance, P is the principal (starting amount), r is the annual interest rate expressed as a decimal, and t is the time in years.

In this case, the principal is $50, the interest rate is 10% or 0.10, and the time is 2 years. Substituting these values into the formula, we get:

B = $50(\(1.10^{2}\))

B = $50(\(1.10^{2}\))

B = $50(1.21)

B = $60.50

The final balance after 2 years is $60.50. To find the amount of interest earned, we can subtract the initial principal from the final balance:

Interest earned = Final balance - Initial principal

Interest earned = $60.50 - $50

Interest earned = $10.50

Therefore, to the nearest cent, Eva will earn $10.50 in interest over 2 years.

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Answer:

X=y+5 is the answer because to make x the subject you need to do the opposite of the operation

Answer:

25/9

Step-by-step explanation:

x^2 + 10/3 x

Take half of the x-term coefficient and square it.

1/2 * 10/3 = 10/6 = 5/3

(5/3)^3 = 25/9

Answer: 25/9

Answer:

48 and 96

hope it's helpful ......

Answer:

48 and 96

Step-by-step explanation: each time you multiply by 2

\(\tt 2100=\dfrac{2520}{1+4e^{-0.2t}}\\\\2100(1+4e^{-0.2t})\\\\2100+2100.4e^{-0.2t}=2520\\\\8400e^{-0.2t}=420\\\\e^{-0.2t}=0.05\\\\-0.2t=ln~0.05\\\\t=15\\\\2015+15=\boxed{\bold{2030}}\)

Answer:

3y-x =-6

Step-by-step explanation:

The equation of a line in point slope form is expressed as;

y-y0 = m(x-x0)

(x0, y0) is the point = (3, -1)

Given the equation 3xs+y = 1

Get the slope

y = -3x + 1

mx = -3x

m = -3

Since the equation needed is perpendicular to the line, the slope will be expressed as;

M = -1/-3

M = 1/3

Substitute and get the equation needed

y-y0 = m(x-x0)

y - (-1) = 1/3(x-3)

y+1 = 1/3(x-3)

3(y+1) = x-3

3y+3 = x-3

3y - x = -3-3

3y-x =-6

This gives the required equation

Answer:

Step-by-step explanation:

Answer:

$450+$50= X

X=$500

Step-by-step explanation:

The sale price is $450.00, so you take that amount and $50.00 which the amount he paid less and add them both. We do this because we want to see the original price of the computer. If it mentioned the original price already and the amount $50.00 and asked the sail price instead, we would have to subtract to get the answer.

Here we have to add.

450+50=500

(add the dollar sign)

$450+$50=X

X=$500

Answer:

false

Step-by-step explanation:

pretty sure the equation is x=-b2a

Answer:

The absolute value of +98 is simply 98. So, | +98| = 98.

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

The absolute value of a number is its POSITIVE distance from 0, so as +98 is 98 away from 0, then |+98| = 98.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t\)

the area is simply the product of its width and length, so hmmm before doing so, let's change all the mixed fractions to improper fractions and then multiply.

\(\stackrel{mixed}{4\frac{1}{5}}\implies \cfrac{4\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{21}{5}} ~\hfill \stackrel{mixed}{4\frac{2}{7}} \implies \cfrac{4\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{30}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{5}\cdot \cfrac{30}{7}\implies \cfrac{21}{7}\cdot \cfrac{30}{5}\implies \cfrac{3}{1}\cdot \cfrac{6}{1}\implies \text{\LARGE 18}~in^2\)

The area of the rectangle is 18 \(inch^{2}\) and the perimeter is  \(16\frac{34}{35}\) inches.

We know that, Area of a rectangle = l * b

        and Perimeter of a rectangle = 2(l + b)

 Where, l = length of the rectangle

             b = breadth of the rectangle

According to the question, l = \(4\frac{1}{5}\) inch = \(\frac{21}{5}\) inch

                                             b = \(4\frac{2}{7}\) inch = \(\frac{30}{7}\) inch    

Area of the given rectangle = l* b

                                              =   \(\frac{21}{5}\) * \(\frac{30}{7}\)

                                              = 18 \(inch^{2}\)

The perimeter of the given rectangle = 2(l + b)

                                                              = 2( \(\frac{21}{5}\) + \(\frac{30}{7}\))

                                                              = 2 (\(\frac{297}{35}\))

                                                              = \(\frac{594}{35}\)

                                                              = \(16\frac{34}{35}\) inch

Hence, the area of the rectangle = 18 \(inch^{2}\)

and the perimeter =  \(16\frac{34}{35}\) inch

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The value of the vehicle 13 years after purchase is $13,695.24.

What is exponential decay?

Exponential decay is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decay also decreases.

We can use the formula for exponential decay to find the approximate value of the vehicle 13 years after the purchase:

\($V = V_0 e^{-rt}$\)

where V0 is the initial value of the vehicle, r is the annual depreciation rate (as a decimal), t is the number of years since purchase, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

\($V \approx 29800 e^{-0.06*13}$\)

\($V \approx 29800 e^{-0.78}$\)

V ≈ 29800 x 0.4593

V ≈ 13695.24

Therefore, the approximate value of the vehicle 13 years after purchase is $13,695.24.

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The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Step-by-step explanation:

Let x and y denote the cost of one hot dog and the cost of one hamburger.

ATQ,

Five hot dog(s) and four hamburger(s) cost $16.75 and four hot dog(s) and five hamburger(s) cost $17.00

So,

5x+4y = 16.75 ....(1)

4x + 5y = 17 ....(2)

Multiply equation (1) by 4 and equation (2) by 5.

20x+16y = 67 ....(3)

20x+25y= 85 ....(4)

Subtract equation (3) and (4).

20x+16y-(20x+25y) = 67-85

16y-25y = -18

-9y = -18

y = 2

Put the value of y in equation (2).

4x + 10 = 17

4x = 7

x = 1.75

So, the cost of one hot dog is $1.75 and that of cost of one hamburger is $2.

Answer:

4 minutes, because in 3 minutes, the slower copier has done 1/4 of the job (at a 12 minute pace ). That means that during the same 3 minutes, the faster copier did 3/4 of the job.

So the faster copier is on pace to complete the entire job in 4 minutes (3 X 4/3).

Step-by-step explanation:

Answer:

cos(49) = x/50

Step-by-step explanation:

(The answer to the equation is 32.8)

If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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The requried measures of the arc in the given circle are shown below.

From the figure,
(a)

Following the complementary angle theorem,

mEF = 90°-mGE
mEF=90-65 = 35°

(d)

Arc mGBD consist of mGB and mBD.

mGBD = mGB+mBD
           = 90 + 30
           = 120°

Similarly,
(b) mDE= 150°
(c) mBEF= 125°
(e) mBGF= 155°
(f) mBFD= 330°

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Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

Probability of selecting first black card is

\(\text{Probability}=\dfrac{26}{52}\)

\(\text{Probability}=\dfrac{1}{2}\)

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

\(\text{Probability}=\dfrac{25}{51}\)

So, the probability that both cards selected for black is

\(\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}\)

\(\text{Probability}=\dfrac{25}{102}\)

Therefore, the required probability is \(\dfrac{25}{102}\).