If a recipe which makes 8 servings calls for 2 cups of sugar, how many cups of sugar will it take to make 18 servings?

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

Answer:

It would change to 0.04802

Step-by-step explanation:

from this question we have that n became 400

40% of 400

= 160

p* = 160/400

= 0.4

1 - p* =

= 1 - 0.4

= 0.6

at confidence level,

1 - 0.95

= 0.05

alpha/2 = 0.025

z= 1.96

margin of error. E

= 1.96 x √[(0.4 x 0.6)/400]

= 1.96 x 0.0245

= 0.04802

M.E = 0.04802

Step-by-step explanation:

Let minimum score on the final exam to earn an A be X

[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observation} [/tex]

[tex]90 = \frac{83 + 97 + 89 + 82 + x}{5} [/tex]

Further solving :

X = 99 marks

Answer:

c

Step-by-step explanation

Answer:

NOT SURE

Step-by-step explanation:

Answer:

4110

Step-by-step explanation:

One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.

2 tons*2000 lbs per ton  = 4000 lbs

1760 ounces*0.0625 lebs per ounce = 110 lbs

4000+110=4110 lbs

Answer:

Rate= 3 1/3%

Or Rate= 3.33%

Step-by-step explanation:

Final amount collected= $700

Initial amount given out= $600

Interest made= Final amount - initial amount

Interest made= $700-$600

Interest made= $100

Type of interest rate = simple

Number of years = 5

PRT/100= interest

R=(100*interest)/(PT)

R= (100*100)/(600*5)

R= 10000/3000

R= 10/3

R= 3 1/3%

Or R= 3.33%

Answer:

It is undefined.

Step-by-step explanation:

Let's take a look at the first equation- if we simplify and move the terms, it becomes sqrt of 6 = 0, which results in an undefined value of x. The second equation works with x=0 but not the first so the value of x is undefined.

Answer:

Simple Interest : $ 4400

Step-by-step explanation:

We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.

We can use the simple interest formula here, or :

I = P × r × t,

Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.

Simple Interest : 10000 × 0.055 × 8 =  $4400.00

Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.

The simple interest earned on the amount is $4,400

Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.

Simple Interest  = principal x time x interest rate

principal = amount borrowed = $10,000

time = 8 years

Interest rate = 5.5%

10,000 x 0.055 x 8 = $4,400

To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults

Answer:

The answer is 4 + 4 + 4 - 4 = 8

Step-by-step explanation:

The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.

There are many complicated problems in this book made with the intention of using logic to find a value.

The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.

Answer:

(9, -13.5)

Step-by-step explanation:

It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.

Rule for dilation is,

(x, y) → (kx, ky)

where 'k' is the scale factor.

If vertex R of the quadrilateral is (6, -9),

By the given rule of dilation,

R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]

           → R'(9, -13.5)

Therefore, Option given in bottom right (9, -13.5) will be the answer.

The answer is $12792

Explanation:

It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:

1. Write the values you know and use x to represent the value you need to find

108 = 18        

  x =   82      

3. Cross multiply

x 18 = 8856

4. Find  the value of x by solving this simple equation

x = 8856 ÷ 18

x = 492 - Amount the employer pays every two weeks for Tessa's family coverage

Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.

1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks

52 ÷ 2 = 26

2. Finally, multiply the money paid by the employer every two weeks by 26

26 weeks x $492 = $12792- This is the total the employer pays annually

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Answer:

C:750$

Step-by-step explanation:

The food expense is 15% of total income 5000$

=> food expense: (15/100) x 5000 = 750$

Answer:

[tex] X^{\frac{8}{15}} [/tex]

Step-by-step explanation:

[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]

To multiply two powers with the same base, write the base and add the exponents.

[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]

[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]

[tex] = X^{\frac{8}{15}} [/tex]

Answer:

Mean= $21.5067

Median = $15.8

Standard deviation= $19.02

Coefficient of skewness= $0.8991

Step-by-step explanation:

Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8

+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15

Mean =$ 322.6/15

Mean= $21.5067

Median= middle number

Median = $15.8

Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15

Variance=$ 5424.79/15

Variance=$ 361.65

Standard deviation= √ variance

Standard deviation= √361.65

Standard deviation= $19.02

Coefficient of skewness

=3( mean-median)/standard deviation

= 3(21.5-15.8)/19.02

= 3(5.7)/19.02

= 17.1/19.02

Coefficient of skewness= 0.8991

Answer:

2.5 meters

Step-by-step explanation:

Answer:

exact form: x=-56/3

mixed number form: -18 2/3

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

False

Step-by-step explanation:

the answer is false because

year 1 to 2 is $18

year 2 to 3 is $17

year 3 to 4 is $18

year 4 to 5 is $17

false because simple interest always has the same money not a pattern

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

Answer:

2:3

Step-by-step explanation:

It’s easy

Answer:

2.5

Step-by-step explanation:

i think

Let [tex]\mu[/tex] be the average number of televisions per household in the United States .

As per given ,

[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]

Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.

For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]

T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]

Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]

This means we cannot reject null hypothesis.

We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.

Answer:

The median is 1.84 and the difference between the first and third quartile is 0.34

Step-by-step explanation:

When you write them out 1.84 is the median (middle number). To find the difference I just subtracted the third quartile (2.09) by the first quartile (1.75)

========================================================

Explanation:

Original data set = {1.96, 2.09, 1.79, 1.61, 1.75, 2.11, 1.84}

Sorted data set = {1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11}

Notice that 1.84 is in the middle of the sorted set. Three values are smaller than it, and three values are larger than it.

Therefore, 1.84 is the median.

The values {1.61, 1.75, 1.79} are smaller than the median. We'll call this set L for lower set.

The values {1.96, 2.09, 2.11} are larger than the median. We'll call this set U for upper set.

From set L = {1.61, 1.75, 1.79}, the median here is 1.75. This is the value of the first quartile Q1

The value of Q3 is 2.09 as it is in the direct middle of set U = {1.96, 2.09, 2.11}

The interquartile range (IQR) is the difference of Q3 and Q1

IQR = Q3 - Q1

IQR = 2.09 - 1.75

IQR = 0.34

Answer:

Hope this helps :)

Step-by-step explanation:

A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.

My conclusion,

They help organize important data for future occurences.

Answer:

The percentage increase in the production cost of the printer is 3%.

Step-by-step explanation:

We are given that the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$.

Also, the cost of raw materials and overheads are increased by 11% and 20% respectively while wages are decreased by 15%.

Cost of raw material = $100

Cost of overheads = $80

Cost of wages = $120

So, the total cost of the printer = $100 + $80 + $120

                                                   = $300

Now, the increase in the cost of raw material = $100 + 11% of $100

                                                                           = [tex]\$100 + (\frac{11}{100} \times \$100)[/tex]

                                                                           = $100 + $11 = $111

The increase in the cost of overheads = $80 + 20% of $80

                                                                = [tex]\$80 + (\frac{20}{100} \times \$80)[/tex]

                                                                = $80 + $16 = $96

The decrease in the cost of wages = $120 - 15% of $120

                                                          = [tex]\$120 - (\frac{15}{100} \times \$120)[/tex]

                                                          = $120 - $18 = $102

So, the new cost of a printer = $111 + $96 + $102 = $309

Now, the percentage increase in the production cost of the printer is given by;

      % increase =  [tex]\frac{\text{Net increase in the cost of printer}}{\text{Original cost of printer}} \times 100[/tex]

                         =  [tex]\frac{\$309- \$300}{\$300} \times 100[/tex]

                         =  3%

Hence, the percentage increase in the production cost of the printer is 3%.

Answer:

measure

Step-by-step explanation:

The collection of quantitative or numerical data that describes a property of an object or event is called a measured/measurement.

The SI Unit is a metric system. An example of an SI Unit is the kilogram, centimeter, second, etc.

Measurements are made by comparing a particular quantity with an SI unit or assigning numbers to certain objects in a way that reflects its value.

Answer:

[tex]\large \boxed{\$10000.00}[/tex]

Step-by-step explanation:

We can use the formula for continuously compounded interest.

[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Answer:

Step-by-step explanation:

Hello,

[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]

So if we take

[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

12/27

Step-by-step explanation:

Step 1

We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.

Where

R = Red

B = Blue

Y = Yellow

RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR

We have 27 Total outcomes for this 6 faced die

Step 2

The event that exactly one of the colors that appears face up is red.

RBY, RYB, YBR, YRB, RBB, RYY, BBR,

BRB, BRY, YRY, BYR, YYR

Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12

The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes

= 12/27