F(x)=3x^4-4x^3+x^2+6x-2

The product doubles when one of the factors in a multiplication problem is doubled

A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.

For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:

= 4 × 3 = 12

Therefore, the product doubles too.

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The correct option; B. Two irrational numbers, are the two roots found for the given quadratic equation.

For the given question;

The quadratic equation is give as;

x² + 5x + 3 = 0

discriminant D = b² -  4ac

b = 5, a = 1 and c = 3

D = 25 - 4(1)(3)

D = 25 - 12

D = 13

√D = √13

As, number is real, there will be two real roots.

As, root of discriminant √D = √13 is a irrational number, the solutions of the given quadratic equation will be two irrational number.

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The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

Given,

The population of a city can be modeled using the formula P=100,000e^(0.05t)

t is the number of years after 2012

P is the population of the city

We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.

Here,

Substitute 300000 in for P and solve for t

300000=100000e^0.05t

Divide both sides by 100000:

We get,

3 = e^0.05t

Multiply both sides by the natural log (ln)

Then,

ln(3) = 0.05t

Now, divide 0.05 on both sides to get t by its self

t = ln(3) / 0.05

Therefore,

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

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Answer:

x = 2

Step-by-step explanation:

Mr. Dunston spend is $35.

Given:

Mr. Dunston and Mr. Dolland spent $45 all together.

Mr. Dunston and Ms. Campbell spent $65 all together.

If Ms. Campbell spent 3 times as much as Mr. Dolland.

Let x , y , z be spend of dunston ,dolland and campbell.

x + y = 45

x + z = 65

z = 3*y

x + 3y = 65

on substracting x + y = 45 and x + 3y = 65 we get,

x + y - x - 3y = 45 - 65

-2y = -20

2y = 20

y = $10.

substitute y value,

x + 10 = 45

x = 45 - 10

x = $35

Therefore Mr.Dunston spend $35.

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Step-by-step explanation:

1.) The first shape is a parallelogram like prism, So we use Area of prism= Area of base shape*height

that is, Area of base shape= rectangle,L*B

35*14=490*height

490*24=11760 cm3

2.)A rectangle base prism,

Area of prism= Area of base shape*height

Area of Base shape=27*14

378cm2*21

7938cm3

3.)Square based prism,

Area of prism= Area of base shape*height

=21*21*21 (since all sides are the same)

=9261cm3

The values of the different trigonometric functions are as follows:

Now, solve using trigonometry as follows:

Now, we have:

Then, calculate as follows:

Now, we obtain:

Therefore, the values of the different trigonometric functions are as follows:

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Answer:

g(x)=−x−5, find g(1)g(1)

Step-by-step explanation:

g(x)=−x−5, find g(1)g(1)

Answer: 2012

Step-by-step explanation: biggest shift in pop

Answer:(3-i) - (2 +6i)

Combine like terms:

3-2 = 1

-i  -  6i = -7i

Combine to get 1 -7i

Step-by-step explanation:

Answer:

if D is 3/4 then it is the answer

Step-by-step explanation:

Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4

using the power rule of logarithm, the value of a is 1.1021.

In the given question we have to determine a so that [tex]A(t)=A_{0}a^t[/tex] describes the amount of nitrogen-16 left after t seconds, where [tex]A_{0}[/tex] is the amount at time t=0.

The given exponential function is [tex]A(t)=A_{0}a^t[/tex].

The amount of nitrogen-16 is approximately 7.13 seconds.

According to the question, [tex]A(t)=A_{0}/2[/tex] and t = 7.13 seconds.

Putting the value in the given function;

[tex]A_{0}/2=A_{0}a^{7.13}[/tex]

Divide by [tex]A_{0}[/tex] on both side, we get

[tex]1/2=a^{7.13}[/tex]

Taking In on both side

[tex]\text{In}(1/2)=\text{In}(a^{7.13})[/tex]

Using the power rule of logarithm

In(1/2)=7.13In(a)

Divide by 7.13 on both side

In(a)= -0.693/7.13

In(a)= -0.0972

Taking exponential on both side

[tex]e^{\text{In}(a)}= e^{-0.0972}[/tex]

a = 1.1021

Hence, the value of a is 1.1021.

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We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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The rate of gaining altitude for the hiker is 530 feet per hour.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).

Its geometric aspect is the slope of the function at a given point.

The given equation for hiker's altitude is as below,

a = 12850 + 530h

Here a is the altitude in feet and h is time in hours.

In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,

a = 12850 + 530h

Differentiate the above equation w.r.t h as,

da/dh = 0 + 530

          = 530

Hence, the rate of gaining altitude is 530 feet per hour.

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Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.

Therefore,

y=0.25 x

the initial statement is y ∝ x

to convert to an equation multiply by k  the constant of

⇒ y=k x

to find k use the given condition

y=0.5 when x=2

[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]

the equation is y = 0.25x

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The variation equation  is [tex]y=\frac{1}{5} x[/tex]

Calculation

Given, y =2 and x=10

we know the direct relation in y∝ x

so, y = kx, where k is the proportionality constant

2= k*10

k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]

Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]

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The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, based on the information we will replace m with 32. This will be illustrated thus:

1/4(32 - 4) ≤ 1/8 (32 - 16)

= 1/4(28) ≤ 1/8(16)

= 7 ≤ 2

In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.

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The depreciation expense for each year to the new delivery truck purchased by Cookie Palace would be $4, 375.

When given the residual value, depreciation can be found using the straight - line method which has the formula:

= (Cost of delivery truck - residual value) / Number of years in estimated life

Solving for the depreciation expenses each year gives:

= (20, 000 - 2, 500) / 4

= 17, 500 / 4

= $4, 375

In conclusion, the depreciation to the delivery truck every year would be $4, 375.

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Answer:

c

Step-by-step explanation:

because the explanation its just c

Answer: y = -x - 8

Step-by-step explanation:

    Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.

    We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).

    For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.

    Now, we will write the full equation:

y = -x - 8

Answer:

The answer to your question is,

MEAN = 43.6

MEDIAN = 43

MODE = 43

RANGE = 5

Step-by-step explanation:

BC  I know math :)

Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).

Given,

Factor sipping distributive property,

For the numbers 28 and 49

GCF:

28 + 49

7(4) + 7(7)

7(4+7)

7(11)

77

Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

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The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x

The definitions of the functions are given as

f(x) = √4x and g(x) = √16x

Evaluate the square roots in the above equations

This gives

f(x) = 2√x and g(x) = 4√x

To find the composition (f - g)(x), we make use of

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation So, we have the following equation

(f - g)(x) = 2√x - 4√x

Evaluate the like terms

This gives

(f - g)(x) = -2√x

Hence, the value of the composition is (c) (f - g)(x) = -2√x

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The total cost to be in the team will be $1192. He must earn an average of $119.2 per week for 10 weeks. If Ralph is paid at a flat rate of exactly q dollars each week, so the standard deviation will $0.

Total cost is the sum of all expenditures made to produce a certain level of output; when this total cost is divided by the quantity produced, average or unit cost is discovered. The sum of the fixed and variable costs is the total cost. For instance, if a company has a fixed cost per unit of $30 and a variable cost per unit of $5 that increases as output increases, the total cost will be $35. Total cost is equal to the sum of all fixed and variable costs. Total Cost = (Average Fixed Cost + Average Variable Cost) x Number of Units is another way to express it. All of this had to do with the total cost formula, which is a crucial idea for figuring out the total cost of production.

Here,

The expenses of team is,

Uniform=$67.00

Registration=$50.00

Tournaments=$775.00

Travel =$300.00

Total cost=sum of all expense

=67+50+775+300

=$1192

Average cost=Total cost/number of weeks he worked

=1192/10

=$119.2

Deviation of distribution cost,

If Ralph is paid at a flat rate of exactly q dollars each week then there will be $0 deviation.

It will cost $1192 in total to join the team. For ten weeks, he must make an average of $119.2 per week. If Ralph receives a fixed weekly salary of exactly q dollars, the standard deviation will be zero.

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Answer:

8 people=24 minutes

Step-by-step explanation:

(1,10)(5,18)=18-10/5-1= 8/4 =2

y-8=2(x-4)

The Sample proportion for the data to construct a 95% confidence interval is 0.1351.

The percentage of red candies is  (24.5%,  2.52%)

What do you mean by sample proportion?

The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Sample proportion [tex]=\frac{5}{37}=0.1351[/tex]

For 95% confidence interval, z = 1.96

Hence,

95% confidence interval will be:

[tex]0.1351 \pm 1.96\times \sqrt{0.1351\times(1-0.1351)/37}[/tex]

[tex]0.1351\pm0.1099[/tex]

(0.245, 0.0252)

(24.5%,  2.52%)

Since the confidence interval only contains values less than 30%.

The result is not consistent with 34% rate reported by the candy maker.

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The Claire's principal balance at the beginning of November is 32516.

Given that,

Vehicle purchase by Claire Russell. Her interest rate for the month of November was 210 percent at 7 3/4%. Employ 360 days. When calculating, do not round the numerator; instead, round your result to the nearest dollar.

We have to find how much was left on Claire's principal at the start of November.

We know that,

Principal= Interest / time× rate of interest

Here,

Interest is 210

Time is 30/360

Rate of interest is 0.0775

Principal = 210/(30/360)×0.0775

Principal= 210/ 0.00645833

Principal =32516

Therefore, The Claire's principal balance at the beginning of November is 32516.

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The percentage of shaded grid is 45% and the number of squares is 5.

a. Percentage of shaded grid

The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.

Percentage of shaded grid = Shaded grid /Total grid

Percentage of shaded grid = 9/20 × 100

Percentage of shaded grid = 45%

b. Number of squares to be shaded

Number of squares = 20 grid × (70% - 45%)

Number of squares = 20 grid × 25%

Number of squares =  5 squares

Therefore the percentage is 45% .

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The value of the test statistic of the given problem is; -17.969

In statistics, hypothesis testing is simply a method used to test a claim about a population.

We are given;

Sample size; n = 1160

Sample proportion; p^ = 88% = 0.88

The percentage of 97% represents the proportion of a population and this tells us that we are making a claim about the population proportion (p) in the hypotheses.

We claim "fewer then 97%", which indicates less than 97% or 0.97:

p<0.97

The null hypothesis states that the population proportion is equal to the value mentioned in the claim.

H₀: p = 0.97

The claim is either the null hypothesis or the alternative hypothesis. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

Hₐ: p < 0.97

The value of the test-statistic is gotten from the formula;

z = (p^ - p)/(√(p(1 - p)/n))

z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))

z = -17.969

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