What are the solutions of this quadratic equation?

2x2 + 16x − 8 = 0

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 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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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 greatest number of cans each stack can have is 10.

What is Greatest Common Divisor (GCD)?

The number that divides two or more numbers most precisely by itself is said to be the greatest common divisor (GCD) of those numbers. It is also defined as the highest common factor (HCF).

If a and b are two numbers then the greatest common divisor of both numbers is denoted by GCD(a, b).

Given, Total number of cola cans = 150

            Total number of fruit juice cans = 260

According to the question condition, we need to find GCD (150,260)

Now, the prime factorization of 150 and 260 are:

150= 2 x 3 x 5 x 5

260 = 2 x 2 x 5 x  13

So, common factor = 2 x 5 = 10

Then, GCD (150,260) = 10

Hence, the greatest number of cans in each stack can have 10.

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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

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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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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Answer:

x = 2

Step-by-step explanation:

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

The equation of lines are (a) x - 2y + 6 = 0

                                          (b) 2x - y - 4 = 0

                                          (c) x - y + 1 = 0

                                          (d) 4x + 3y + 4 = 0

Slope-intercept form of the equation -> y = mx + c

Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]

(a) A(0,3) and B(6,6)

    m = [tex]\frac{6-3}{6-0}[/tex]

        = 3/6

        = 1/2

    Putting the value in equation,

     3 = (1/2)*0 + c

     c = 3

   Equation -> y = (1/2)x + 3

                     2y = x + 6

          x - 2y + 6 = 0  

(b) A(0,-4) and B(5,6)

    m = [tex]\frac{6+4}{5-0}[/tex]

        = 10/5

        = 2

    Putting the value in equation,

     -4 = (2)*0 + c

     c = -4

   Equation -> y = (2)x - 4

          2x - y - 4 = 0  

(c) A(-4,-3) and B(2,3)

    m = [tex]\frac{3+3}{2+4}[/tex]

        = 6/6

        = 1

    Putting the value in equation,

     3 = (1)*2 + c

      3 = 2 + c

      c = 3 - 2

      c = 1

   Equation -> y = (1)x + 1

                       y = x + 1

             x - y + 1 = 0  

(d) A(-6,4) and B(3,-8)

    m = [tex]\frac{-8-4}{3+6}[/tex]

        = -12/9

        = -4/3

    Putting the value in equation,

     -8 = (-4/3)*3 + c

     -8 = -4 + c

      c = -8 + 4

      c = -4

   Equation -> y = (-4/3)x - 4

                     3y = -4x - 4

       4x + 3y + 4 = 0  

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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)

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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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 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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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 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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The value of dy/dx is ( v du/dx - u dv/dx)/v²

From the question, we have

y = (1+x)u/(1+x)v

y = u/v

dy/dx = d/dx(u/v)

d/dx(u/v) = ( v du/dx - u dv/dx)/v²

Derivatives:

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.

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Answer:

c

Step-by-step explanation:

because the explanation its just c

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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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

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

Combine like terms:

3-2 = 1

-i  -  6i = -7i

Combine to get 1 -7i

Step-by-step explanation:

Answer:

Classification - Right Scalene

Perimeter - 30ft

Area - 30ft

Step-by-step explanation:

Classification - There's a right angle, and 3 unequal sides.

Perimeter - 5 + 13 + 12 = 30

Area = 5*12=60, 60/2 = 30

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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The Original price of barbecue grill is 96.325.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The final cost  barbecue grill is $79.95.

Discount = 25%

and Tax = 8%

let the original price be x

x- 0.25x + 0.08x = 79.95

0.83x = 79.95

x= 79.95/0.83

x = $96.325

Hence, the Original price of barbecue grill is 96.325.

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Answer:

The answer to your question is,

MEAN = 43.6

MEDIAN = 43

MODE = 43

RANGE = 5

Step-by-step explanation:

BC  I know math :)