Mo has some red and green sweets He eats 1/3 of the sweets ¾ of the sweets left over are green Mo buys himself 30 more green sweets. There are now 162 green sweets. How many sweets did Mo start with?

Answer:

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

(x + 6)² = 7

x + 6 = + or - [tex]\sqrt{7}[/tex]

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.

Given that the quadratic equation is x² + 12x + 36 = 7.

(x + 6)² = 7

x + 6 = ±√7

x = -6 + √7 , x = -6 - √7

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Answer:

The answer is No Solution

Answer:

No solution

Step-by-step explanation:

There is no solution to this question.

Since the x is an absolute number, the answer cannot be -4. It would have to equal 4

So if that x was a -4 it would equal 4 since it is in absolute value brackets

Answer:5000 sum

Step-by-step explanation:

The number line model that represents the expression -2/5 + 4/5 is: Option B

To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Now, in this case, the operation to solve is:

-2/5 + 4/5

Solving this gives 2/5

Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem

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Answer:

7.1

Step-by-step explanation:

d = sqrt(7^2 + -1^2)= sqrt(50)=7.1

Answer:

by using distance formula

putting values

d=√(-1-6)²+(-4--5)²

d=√(-7)²+(1)²

d=√49+1

d=√50

d=5√2=7.1

Answer:

y = -5(x) - 4

Step-by-step explanation:

Use the equation of a line and substitution.

Information given:

point 1: (-2,6)

x1 = -2 and y1 = 6

point 2: (0,4)

x2 = 0 and y2 = 4

Equation of a line: y = m(x) + b

m = slope

To find slope, you do the equation of a linear slope, which is:

m = [tex]\frac{rise}{run}[/tex]         in other words   m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]

plug in your values

[tex]\frac{6-(-4)}{-2-0}[/tex]

= -5

Great, we've found slope, now to find b

plug in the slope you found: y = -5(x) + b

Plug in and solve for each point given, aka (x,y) into the linear equation for both points.

FIRST POINT:

6 = -5(-2) + b

6 = 10 + b

6 - 10 = b

b = -4

SECOND POINT:

-4 = -5(0) + b

-4 = 0 + b

-4 - 0 = b

b = -4

We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.

Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.

Answer:

f(x)=-5x-4

Step-by-step explanation:

You are given two points (-2, 6) and (0, -4)

Find the slope: m=(-4-6)/[(0-(-2)]=-5

So you have y=-5x+b

next, find the y intercept b.

the y intercept is when x=0. in this case, the y intercept is -4

so the linear function is f(x)=-5x-4

Answer:

90/4= 12.9

1*3/4= 0.75

Step-by-step explanation:

Answer:

They are parallel because they are vertical lines, and all vertical lines are parallel.

Step-by-step explanation:

Answer:

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

95% of commuters in Boston has a commute time within 2 standard deviations of the mean

Empirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean

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Answer:

[tex]\frac{8342}{10000} \\ [/tex]

Answer C is correct

Step-by-step explanation:

[tex]0.8342 = \frac{8342}{10000} [/tex]

To check whether this correct or wrong.

[tex]0.8342 \times 10000 = 8342[/tex]

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The decimal 0.8342 expressed as a fraction is (c) 8342/10000

From the question, we have the following parameters that can be used in our computation

The decimal 0.8342

Express the decimal 0.8342 as a fraction

So, we have the following representation

Fraction = 8342/10000

When the fraction is simplified, we have

Fraction = 8342/10000

Hence, the decimal 0.8342 as a fraction is (c) 8342/10000

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Answer:

Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.

Step-by-step explanation:

Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.

Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.

The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.

By measurements and conversions processes, the features of Martian crater could be studied from images.

Answer:

D

Step-by-step explanation:

3/40 * 2.5/2.5 = 7.5/100 = 0.075

Answer:

the amount of alcohol to be added is 128 grams

Step-by-step explanation:

Given that:

The initial mass of the hand sanitizer = 480 grams

The initial strength of the hand sanitizer = 24 %

The new strength of the hand sanitizer = 40%

The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol

First; let's find the mass of alcohol in the initial hand sanitizer;

SO;

= 24  % of 480

[tex]=\dfrac{24}{100}*480[/tex]

= 115.2 grams

If y should represent the mass of the alcohol added to have 40%; we have

The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]

The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]

∴

For the new strength of sanitizer:

40 % of (480 + y) = (115.2 + y)

[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]

Thus ; we can conclude that the amount of alcohol to be added is 128 grams

Answer:

Step-by-step explanation:

2x - 3y = 9

-3y = -2x + 9

[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]

Parallel lines have same slope.So,

Slope m = 2/3

(4 , -1)

Equation: y - y1 = m(x - x1)

[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]

b = -11/3

Answer:

1/25

Step-by-step explanation:

5^-2

We know that a^ -b = 1/ a^b

5^-2 = 1/ 5^2

       = 1/25

Answer:

Figure 1

The area of circle is 452.16 inches ².

Figure 2

The area of circle is 615.44km².

Figure 3

The area of circle is 132.665 km².

4) The radius of circle is 9 cm and diameter is 18cm.

Answer:

Step-by-step explanation:

The growth rate of the coin is exponential. We would apply the formula for exponential growth which is expressed as

y = ab^x

y = b(1 + r)^ t

Where

y represents the value of the coin after x months.

x represents the number of months.

a represents the initial value of the coin.

b represents rate of growth.

From the information given,

a = 243

b = 1 + 15/100 = 1 + 0.15 = 1.15

Therefore, the exponential expression to determine the number of months, x it will take for the coin to attain a certain value, y is expressed as

y = 243(1.15)^x

If y = 1000, it means that

1000 = 243(1.15)^x

1000/243 = 1.15^x

4.115 = 1.15^x

Taking log of both sides, it becomes

log 4.115 = xlog1.15

0.614 = 0.061x

x = 0.614/0.061

x = 10 months

It will take 10 months

Answer:

The hydro-static force [tex]F=245000N[/tex]

Step-by-step explanation:

given data

base = 3 m

height = 5 m

density of water = 1000 kg/m3

Acceleration due to gravity = 9.8

The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION

Answer:

25.75 %  interest rate

Step-by-step explanation:

Given:

Amount was invested = r% per quarter  

Amount invested = P

Rate of interest = r %  per quarter

Time (n) = 4  Quarters

Computation:

A = P(1 + r/100)ⁿ

According to question.

⇒ A = P + 1.5P  = 2.5P

⇒ 2.5P = P(1 + r/100)⁴

⇒ 2.5  = (1  + r/100)⁴

⇒ 1 + r/100  =  1.2575

⇒ r/100 = 0.2575

⇒ r = 25.75

25.75 %  interest rate

Answer:

0.5 or C on edge2021

Step-by-step explanation:

The multiplicative rate of change of the function will be:

The multiplicative rate of change is the common factor that the numbers can be multiplied with to get the succeeding figures.

For instance, if 0.25 is multiplied by 0.5, the result will be 0.125. Also, if 0.125 is multiplied by 0.5, the result will be 0.0625.

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Use the chain rule to compute the second derivative:

[tex]f(x)=\ln(\sin(2x))[/tex]

The first derivative is

[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]

[tex]f'(x)=2\cot(2x)[/tex]

Then the second derivative is

[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]

[tex]f''(x)=-4\csc^2(2x)[/tex]

Then plug in π/4 for x :

[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]

Answer:

7000

Step-by-step explanation:

If the hundreds place is higher than 5, then add 1 to the thousands place.

Multiply her savings by the percent spent:

850 x 0.35 = 297.50

The tv cost $297.50

Answer:

the price of TV is = 297.5$

Step-by-step explanation:

all money= 850$

purchased money= 35% of all money ==> 850 ( 35%) = 297.5$

Answer:

2/33

Step-by-step explanation:

Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)

Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)

8/22 = 4/11

Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11

= 4/66

= 2/33

Answer:

6 pretzels and 8 crackers

Step-by-step explanation:

Since his mom told him to give her the remaining, 6*4= 24 giving to his mom 2 pretzels and 8*4=32 so he has to give his mom 3 crackers. This way him and his friends have the same amount of snacks.

Hope you find it useful.  Good night

To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.

The equation would be y = 40x + 25

Answer:

Poisson distribution

Step-by-step explanation:

Given that :

There is an average of 0.1 flaws per square meter of cloth

So X = the number of flaws in a bolt of 2000 square meters of cloth.

The objective is to deduce how is X distributed.

Well, we can say X undergoes Poisson distribution.

Because, the flaw can be randomly positioned on the cloth and also dictate  how many times the event is likely to occur within a specified period of time.

Most time Poisson distribution is majorly used for independent events.

An independent is an event which contains two types of events occuring at a time say event [tex]E_1[/tex] and event [tex]E_2[/tex] and the event [tex]E_1[/tex] does not in any way affects the occurrence of the event [tex]E_2[/tex] .

Answer:

work is shown and pictured

Answer:

12.0

Step-by-step explanation:

d(pi)=37.7

d=12.0