x = 3 / 5 (cb+k)
Solve for b

Answer:

[tex]\Huge \boxed{{x=-1\pm \sqrt{7}}}[/tex]

Step-by-step explanation:

x² + 2x = 6

Subtract both sides by 6.

x² + 2x - 6 = 0

ax²+bx+c=0

a=1, b=2, and c=-6

We can apply the quadratic formula.

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Plug in the values.

[tex]\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)(-6)}}{2(1)}[/tex]

Evaluate.

[tex]\displaystyle x=\frac{-2\pm\sqrt{4-(-24)}}{2}[/tex]

[tex]\displaystyle x=\frac{-2\pm\sqrt{28}}{2}[/tex]

[tex]\displaystyle x=\frac{-2\pm 2\sqrt{7}}{2}=-1 \pm \sqrt{7}[/tex]

Answer: Edmentum and Plato

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The excel function that will gibe the p-valur for overall significance of a regression has 75 observations and 5 predictors and gives an F test statistic FCal = 3.67 is given below:

F.DIST.RT(3.67,5.69)

Answer:

27720

Step-by-step explanation:

So let's assume that in any arrangement we are not able to distinguish the balls having the same colour, so only different orders of the colours involved are counted.

If we number these balls we have 12 different numbers, 3 of which belong to the white balls, 4 belong to the blue balls and the final 5 belong to the red balls. They could be arranged in 12! different ways. Pick any of these arrangements.

The white balls in this arrangement are now ordered because I gave these balls a number. But I specifically stated in the first alinea that we were not interested in all these possible orders of the white balls within a sequence of 12 balls. So we must correct for these orders, there are 3! of these, each one leading to exactly the same visual order of white balls. The other colours lead to a correction of 4! and 5!. Moreover, these corrections are independent of each other. I can change the position of the white balls without interrupting the order of the colours of the remaining balls. So we should divide by the product of 3!,4! and 5!.

Total number of arrangement = 3,628,800

Given that;

Number of red ball = 5

Number of white ball = 2

Number of blur ball = 3

Find:

Total number of arrangement

Computation:

Total number of balls = 5 + 2 + 3

Total number of balls = 10

Total number of arrangement = 10!

Total number of arrangement = 3,628,800

Find out more information about 'Total arrangement'

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Answer:

[tex]\huge\boxed{f(-9) = 184}[/tex]

Step-by-step explanation:

[tex]f(x) = 3x^2 +5x-14[/tex]

Put x = -9

[tex]f(-9) = 3(-9)^2+5(-9)-14\\f(-9) = 3(81) -45-14\\f(-9) = 243-45-14\\f(-9) = 198-14\\f(-9) = 184[/tex]

Steps to solve:

f(-9) = 3(-9)^2 + 5(-9) - 1

~Solve using PEMDAS

f(-9) = 3(81) - 45 - 1

f(-9) = 243 - 45 - 1

f(-9) = 198 - 1

f(-9) = 197

Best of Luck!

Answer:

$240

Step-by-step explanation:

50% = 0.5

$120 ÷ 0.5 = $240

The original price without the discount is $240.

Hope that helps.

Answer:

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.

Step-by-step explanation:

There are several ways to solve this, I like using proportions.

(You could also find 3/4 of every ingredient since 12 is 3/4s of 16)

We can do this by temporarily naming the amount of each ingredient a variable, and then using the proportion to find the variable.

Note that in a given proportion such as:

a/b=c/d

will always equal

a*d=b*c

This is known as cross multiplying.

For each ingredient I'm going to set up the following proportion:

[tex]\frac{amount of given ingredient in 16 brownies}{16 (number of brownies)} = \frac{variable (amount of given ingredient in 12 brownies}{12 (new number of brownies)}[/tex]

Now we can start setting up proportions for every ingredient.

Butter:

(2/3)/16=b/12

(2/3)(12)=16b

8=16b

b=1/2

Chocolate:

5/16=c/12

60=16c

c=60/16

c=15/4

Sugar:

(3/2)/16=s/12

(3/2)(12)=16s

18=16s

s=18/16

s=9/8

Vanilla:

2/16=v/12

24=16v

v=24/16

v=3/2

Eggs:

2/16=e/12

24=16e

e=3/2

Flour:

1/16=f/12

12=16f

f=3/4

Therefore, the ingredients for 12 brownies would be:

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.

Step-by-step explanation:

-2a4 - 3a2 + 7a + 6 - 6a3 + a4 + 7a2 - 6

Solving like terms

-a4 - 6a3 + 4a2 + 7a

Option A is the correct answer

Answer:

16.64

Step-by-step explanation:

Distance between any two points (x1,y1) and (x2,y2) is given by

Distance = [tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]

Given point

X(-3, 8) and Y (6, -6).

The distance XY will be

[tex]XY = \sqrt{(-3-6)^{2} + (8 - (-6)^{2} }\\XY = \sqrt{(-9)^{2} + (8 +6)^{2} }\\XY = \sqrt{81 + 196 }\\XY = \sqrt{277 }\\XY = 16.64[/tex]

Thus, distance between X(-3, 8) and Y (6, -6) is 16.64  , rounded to nearest tenth.

The travel of the spring is it’s amplitude, which is a cosine function.

The lowest y value is -5

Multiply that by cosine of pi x time

The formula is d = -5cos(pi t)

The equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t.

We know the cosine equation for distance d:

d = acos(bt+c) + d

From the graph: a = -5, b = π

Assume the phase and vertical shift are zero.

c = 0 and d = 0

Plug all values in the function, the equation becomes:

d = -5cos(πt)

Thus, the equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.

Learn more about trigonometry here:

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Answer:

0.027

Step-by-step explanation:

The p-value for Jane's chi-square test for goodness of fit is computed by using value of test statistic and degree of freedom.

Using Excel function CHISQ.DIST.RT(7.24,2) for computing p-value for chi-square goodness of fit test. 7.24 is the value of test statistic and 2 is degree of freedom. The resultant value is 0.026783. By rounding off to three decimal places the required p-value is 0.027.

Answer:

The  probability is  

        [tex]P(Z>1.3793 ) = 0.083901[/tex]  

Step-by-step explanation:

From the question we are told that

   The  proportion proportion is  [tex]p = 0.30[/tex]

    The sample size is [tex]n = 1000[/tex]

    The  sample  proportion [tex]\r p = 0.32[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{p (1 - p)}{ n} }[/tex]

       [tex]SE = \sqrt{\frac{ 0.30 (1 - 0.30 )}{ 1000} }[/tex]

      [tex]SE = 0.0145[/tex]

The probability that more than 32% of the respondents say they prefer the Laurier brand is mathematically represented as

        [tex]P(X > 0.32 ) = P( \frac{X - p }{ SE} > \frac{\r p - p }{ SE} )[/tex]

 Here  [tex]\frac{X - p }{SE} = Z (the \ standardized \ value \ of \ X)[/tex]

            [tex]P(X > 0.32 ) = P(Z>1.3793 )[/tex]

From the z -table   [tex]P(X > 0.32 ) = P(Z>1.3793 ) = 0.083901[/tex]

  [tex]P(Z>1.3793 ) = 0.083901[/tex]  

Using the normal distribution and the central limit theorem, it is found that there is a 0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Then, the mean and the standard error are given by:

[tex]\mu = p = 0.3[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{1000}} = 0.0145[/tex]

The probability that more than 32% of the respondents say they prefer the Laurier brand is 1 subtracted by the p-value of Z when X = 0.32, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.32 - 0.3}{0.0145}[/tex]

[tex]Z = 1.38[/tex]

[tex]Z = 1.38[/tex] has a p-value of 0.9162.

1 - 0.9162 = 0.0838

0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

Answer:

Option E - sigma greater than or equal to $327

Step-by-step explanation:

In this question, we are testing whether the standard deviation of the base price of a certain type of all-terrain vehicle is at least $327.

Now, standard deviation is denoted by the symbol sigma(σ). Since the test is saying it should be at least $327, it means it should either be equal to $327 or greater than $327.

Thus, we would use the symbol ≥ which means "greater than or equal to".

Thus, the claim as a mathematical statement would be;

sigma greater than or equal to $327

Answer:

3.14159

Step-by-step explanation:

This number is pi. Pi goes on for millions of digits on end.

Answer:

The answer is pi. Pi goes on forever and irrational nunbers go on forever.

Step-by-step explanation:

Hope it helps u mate

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Answer:

derivative of the vector function given = ( -16-22t, 14-36t, -2-16t )

Step-by-step explanation:

given data:

vector function : r(t) = ta*(b+tc)

a = ( 2,-3.4) .   b = (-4,5,-1).  c = ( -2,-1,5)

to find the derivative of the vector function we will differentiate with respect to x attached below is the detailed solution

Answer:

Here we have the case where:

"one chip is eaten in 1/4 mins."

(that means unit rate, the amount of a given variable that we need to do a unit of another variable)

Then the unit rate would be:

4 chips per minute.

Or, in a more mathematical way to write this:

4 chips/min.

Now we could write this in other units, for example.

We know that 1 min = 60s.

Then we have that (1/4) min = 60s/4 = 15s.

Then we have the unit rate:

1 chip every 15 seconds, or:

(1/15) chips/second.

Now, the variable in this case is time, t  = time, let's multiply bot our unit rates by the same amount of time, and see if we have the same outcome.

Let's use t = 2 min.

1) (4chips/min)*2min = 8 chips.

2) ((1/15) chips/second)*2min

First, 2 min = 120 seconds.

((1/15) chips/second)*2min = ((1/15) chips/second)*120seconds = 8 chips.

So both unit rates are equivalent.

Answer:

Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehension, such as quadratic equations and interval notation.

Step-by-step explanation:

Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehensions, such as quadratic equations and interval notation. With one, you could pick up such skills just by living life. With the other, there is a higher chance that attending an educational institute would bestow such skills and understanding.

Answer:

???

Step-by-step explanation:

???

Answer:

1246 2/3 feet

Step-by-step explanation:

17 miles/hour * 5280 feet/1 mile * 1 hour/60 minutes * 1 minute/ 60 seconds =

24.93 feet/second * 50 seconds = 1246 2/3 feet

Answer: about 25 feet

Step-by-step explanation:

( the exact number for the problem would be 24.933.... so round )

convert 17 miles into a # of feet

convert 1 hr into a # of secs

# of feet=89760

# of secs=3600

divide 89760/3600

you get 24.9333..........

Round to the nearest tenth and get 25

Answer:

22

Step-by-step explanation:

The volume of a cube is given as:

Cube volume = length × length × length

Since the edges of the cube measure 3 inches, this means that the length of the cube is 3 inches, therefore:

Cube volume = 3 inches × 3 inches × 3 inches = 27 in³

The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.

The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³

The number of pine trees that can be made = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees = 22

Answer: X=-12

Right ain’t it ?

Answer:

The first equation can be multiplied by 3 and the second equation by 2.

Step-by-step explanation:

We are given the following system of equations:

[tex]\boxed{\left \{ {{2x+3y=25} \atop {-3x+4y=22}} \right.}[/tex]

To eliminate a variable in the equation, they must cancel out. For instance, if x = 1, in order to cancel out the numbers, you must add -1.

To multiply an equation, you must apply the constant that you are multiplying by to all constants and coefficients of the equation. For example, to multiply 2x + 4y = 8 by 3, you must multiply 2x by 3, 4y by 3, and 8 by 3.

Therefore, using this information, you can attempt each answer set and test the possibilities.

Answer Choice A

If you multiply the first equation by -3, you will get -6x - 9y = -75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -6 + -6 gives you -12, so these do not cancel out.

Answer Choice B

If you multiply the first equation by -4, you will get -8x - 12y = -100. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -8 + -6 gives you -14, so these do not cancel out.

Answer Choice C

If you multiply the first equation by 3, you will get 6x + 9y = 75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding 6 + -6 gives you 0, so these do cancel out.

Answer Choice D

If you multiply the first equation by 4, you will get 8x + 12y = 100. If you multiply the second equation by -3, you will get 9x - 12y = -66. Adding 8 + -9 gives you -1, so these do not cancel out.

Answer:

Step-by-step explanation:

Let the original trail be x

From the question 150% of the trail is

12 mile

That's

150% of x = 12

So we have

[tex] \frac{150}{100} x = 12 \\ \\ \frac{3}{2} x = 12[/tex]

Multiply through by 2

That's

[tex]2 \times \frac{3}{2} x = 12 \times 2[/tex]

We have

3x = 24

Divide both sides by 3

We have the final answer as

x = 8

Therefore the length of the original trail is

Hope this helps you

Answer:

Non-answer

Step-by-step explanation: Don't like my answer? Let me know!

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(a*x^2+b*x+c)=0  

STEP

1

:

Equation at the end of step 1

 y - ax2 - xb - c  = 0  

STEP

2

:

Solving a Single Variable Equation

2.1     Solve   y-ax2-xb-c  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Answer:

12

Step-by-step explanation:

4y - 6 + 5y = y

place 2 in the spot of y

4(2) - 6 + 5(2)= y

keep that last y the way it is

4•2=8     5•2=10

8-6+10=y

Simplify

2+10=y

12=y

Answer:

A; ?; Line 3

Step-by-step explanation:

Question 1:

-30 divided by -6 is 5.

The negatives cancel each other out.

And 30 divided by 6 is simply 5.

Question 2:

[tex]62\div(3+9)[/tex]

Do the operation inside the parenthesis first:

[tex]62\div12[/tex]

Divide. 12 does not go into 62 evenly. 12 times 5 is 60, so the answer is 5 remainder 2:

[tex]62\div12=5\text { R}2[/tex]

Or in fractions:

[tex]31/6[/tex]

(Was there a typo? From what you've given me, the correct answer is not listed.)

Question 3:

So we have to following steps:

[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+11(2)\\\text{Line 4: }21+22\\\text{Line 5: }43[/tex]

The mistake is in Line 3. Danny cannot just combine 5+6(2) into 11(2). Instead, he should multiply 6(2) and then add. Thus, the correct solution is:

[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+5+12\\\text{Line 4: }26+12\\\text{Line 5: }38[/tex]

Answer:

Not a function

Step-by-step explanation:

Answer

p/q = 8/6

Make p the subject

p = 8q/6........equation 1

This year the price was reduced by 4

p-4/q-4 = 7/5

Cross multiple

5(p-4) = 7(q-4)

5p-20 = 7q-28

5p - 7q = -8 .......equation 2

Sub 8q/6 for p in equation 1

5(8q/6) - 7q = -8

Multiply through by 6

40q-42q=-48

-2q=-48

q=24

Sub 24 for q in equation 1

p= 8(24)/6

p= 192/6

p= 32.....

Check the answer for confirmation.

Thanks.

Answer:

B. (0, 5]∪(15,30] only (15,30] contains viable rates for the hoses.

Step-by-step explanation:

The question is incomplete. Find the complete question in the comment section.

For us to meet the pool maintenance company's schedule, the pool needs to fill at a combined

rate of at least 10 gallons per minute. If the inequality represents the combined rates of the hoses is 1/x+1/x-15≥10 we are to find all solutions to the inequality and identifies which interval(s) contain viable filling rates for the  hoses. On simplifying the equation;

[tex]\frac{1}{x} + \frac{1}{x-15} \geq \frac{1}{10}\\\\ find\ the \ LCM \ of \ the function \ on \ the \ LHS\\\\\frac{x-15+x}{x(x-15)} \geq \frac{1}{10}\\\\\frac{2x-15}{x(x-15)} \geq \frac{1}{10}\\\\10(2x-15)\geq x(x-15)\\\\20x-150\geq x^2-15x\\\\collect \ like \ terms\\-x^2+20x+15x - 150\geq 0\\[/tex]

[tex]-x^2+35x-150 \geq 0\\\\multipply \ through \ by \ minus\\x^2-35x+150 \leq 0\\\\(x^2-5x)-(30x+150) \leq 0\\\\x(x-5)-30(x-5) \leq 0\\\\[/tex]

[tex](x-5)(x-30) \leq 0\\\\x-5 \leq 0 and x - 30 \leq 0\\\\x \leq 5 \ and \ x \leq 30[/tex]

The interval contains all viable rate are values of x that are less than 30. The range of interval is (0, 5]∪(15,30]. Since the pool needs to fill at a combined  rate of at least 10 gallons per minute for the pool to meet the company's schedule, this means that the range of value of gallon must be more than 10, hence (15, 30] is the interval that contains the viable rates for the hoses.