a manager for an insurance company believes that customers have the following preferences for life insurance products: 50% prefer whole life, 20% prefer universal life, and 30% prefer life annuities. the results of a survey of 300 customers were tabulated. is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data?product number whole150universal60annuities90 step 1 of 10: state the null and alternative hypothesis.

Answer:

x = 1

Step-by-step explanation:

We are given an equation that will ultimately lead to a solution for the variable x.

To begin, we will first subtract 3 from both sides to move the constants to each side:

[tex]5=3+2x\\\\5-3=3-3+2x\\\\2=2x[/tex]

Then, divide both sides of the equation by 2 to remove the leading coefficient and isolate the variable:

[tex]2=2x\\\\\displaystyle \frac{2}{2}=\frac{2x}{2}\\\\x=1[/tex]

Therefore, x = 1.

Answer: x = 1

Step-by-step explanation: The equation is true without changing the value of x so x can only equal 1 so that the value of the numbers go unchanged. :)

Answer:

16 cookies

Step-by-step explanation:

24 cookies/1.5 cups= 16 cookies per 1 cup

The equation for a line that passes through points (2,1) and (0,7) is y-7 = -3x or y= -3x+7

To find the equation of a line passing through two points you must first find the slope of the line.

The slope can be found by using the formula: [tex]m=\frac{y2-y1}{x2-x1}[/tex]

Where m is the slope and (x1,y1) and (x2,y2) are the two points. Substituting the two points given in the problem allows us to calculate the slope as:

[tex]m=\frac{7-1}{0-2} \\m= \frac{6}{-2} \\m= -3[/tex]

Next, we have to use the point-slope formula to find the equation for the line passing through these two points.

The point-slope formula states: (y-y1)=m(x-x1)

Where m is the slope and x1, and y1 are points from which the line passes.

Substituting the value of m and x1 and y1 in the given equation,

y-7=-3(x-0)

y-7= -3x-3*0

y-7+-3x

Solving for the slope-intercept form gives:

y-7+7= -3x+7

y-0 + -3x+7

y= -3x+7

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Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

It will take 62.91 years for Kevin to make the amount  $2500 to  $7500 .

In the question ,

it is given that ,

the amount that Kevin deposited (P) in bank = $2500

the interest rate (r) = 1.75% ,

the compound interest is quarterly ,

So , n is = 4 .

let the time taken to earn $7500 be = x years ;

Substituting the values in the Amount formula for the Compound Interest ,

Amount = P(1 + r/n)ⁿˣ

7500 = 2500(1 + 0.0175/4[tex])^{4x}[/tex]

Simplifying further ,

we get ,

3 = (1.004375[tex])^{4x}[/tex]

After applying log both the sides ,

we get ,

log(3) = 4x*log(1.004375)

x = log(3)/(4*log(1.004375))

Simplifying further ,

we have ,

x = 62.91 years .

Therefore , the time taken is = 62.91 years

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The predicted strength of a weld with diameter of 51 is -503.16.

Given that diameter of weld is 51.

And we have to find predicted strength of a weld.

We know that the equation of predicted strength is,

strength = -941.6 + (8.598 × D)

where D id diameter = 51

⇒ strength = - 941.6 + (8.598 × 51)

   strength = -941.6 + 438.4

   strength = -503.2

Therefore predicted strength of a weld is -503.2 i.e option (b) -503.16.

A prediction equation predicts a value of the response variable for given values of the factors. The Delphi Survey technique is a popular method used in prediction. There are two types of prediction methods: qualitative and quantitative.

The Least square Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It is called a "least squares" because the best line of fit is one that minimizes the variance.

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The given equation 11= - 4x^2-x^3 is not quadratic. It is a cubic.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.

Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."

As highest power with the variable is 3 so it is a cubic expression not a quadratic.

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Answer:

See below

Step-by-step explanation:

This is the slope formula.  Do they give you two points?  If they give you two points like (2,3 ) and (5,7)  You subtract the y's over the subtraction of the x's

An ordered pair is in the form (x,y)  

So in the example that I give the y's are 7 and 3 and the x's are 5 and 2

[tex]\frac{7-3}{5-2}[/tex] = [tex]\frac{4}{3}[/tex]

I am thinking that they gave you two points and they want you to find the slope.

Answer:

Step-by-step explanation:

Ok so this is how to find slope of a line that passes through 2 points.

(x1,y1) and (x2,y2)

and to find the slope of the line (m) you have to do (y2-y1)/(x2-x1)

you just have to plug in the points

Answer:

-3.7%, 0.3%,7%,17%,70%

Step-by-step explanation:

The range of the function is (-6 , ∞)

What is function ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.

Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.

[tex]3^{x - 1} > 0[/tex]   for x ∈ R

Subtracting both sides by 6

[tex]3^{x - 1} - 6 > 0 - 6[/tex]

[tex]3^{x - 1} - 6 > - 6[/tex]

f (x) > -6

Range = (-6 , ∞)

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Answer:

120

Step-by-step explanation:

Don't know if this is a joke, but have a great day regardless!

The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.

Find the value of the variable that causes the equation to be true in order to solve linear equations.

Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.

To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.

So, we have the pair of linear equations:

x – y = 8 and 3x – 3y = 16

(a1/a2) = 1/3

(b1/b2) = -1/-3 = 1/3

(c1/c2) = 8/16 = 1/2

Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).

The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.

Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

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Complete question:

Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.

It is proportional because all y over x ratios are equivalent to one-third. I.e., the proportionality constant of the given table is k = 1/3.

The proportionality relationship between two variables is determined by its proportionality constant. The proportionality constant is the ratio of y over x.

I.e., k = y1/x1 = y2/x2 = y3/x3 = ... = yn/xn

The given data table is as follows:

x - 18.6, 54.3, 58.8

y - 6.2, 18.1, 19.6

So, the proportionality constant is calculated as

y1/x1 = 6.2/18.6 = 1/3

y2/x2 = 18.1/54.3 = 1/3

y3/x3 = 19.6/58.8 = 1/3

Since all three ratios are the same, then the data in the table are proportional to each other.

Therefore, option A is correct.

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Here the missing component in this study is control group.

A control group is a group of participants used to compare different groups in a test or experiment. Consists of participants who did not receive an experimental treatment. Some experiments use multiple control groups to collect more information and improve the accuracy of the results. For example, many medical studies include positive, negative, and placebo control groups to better understand the effectiveness of a treatment or drug.

Given the circumstances, the energy drink company claims that its products boost memory in students. To back up its claims, the company publishes an ad claiming that eight out of 10 people (randomly selected across the country) who tried the product reported improved memory.

But they didn't compose a control group to compare the results for test.

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The complete question is as follows:

An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a

A) control group

B) sample group

C) population

D) test group

Answer:

A. Control Group

Plato

The base of the triangle is decreasing at the rate of 1.6 cm/min.

Given

dh/dt = 1 cm/min

dA/dt = 2 cm2/min

When A = 100 cm2, h = 10 cm

We know that

A = 1/2 × b × h

b = 20 cm

Let us differentiate both sides

dA/dt = 1/2 [b dh/dt + h db/dt]

Substituting the values

2 = 1/2 [20 × 1 + 10 × db/dt]

By further simplification

4 = 20 + 10 db/dt

db/dt = -1.6 cm/min

Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.

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Answer:

53 candy

Step-by-step explanation:

Step-by-step explanation:

first thing that seems to be a given (and not mentioned in the description) : QM is a diameter (straight line) through the circle. otherwise this cannot be solved without further information.

remember, a half-circle has 180°.

so, arc angle MAP = 180 - 33 = 147°.

arc angle RMP = RM + MAP = 46 + 147 = 193°.

arc angle RSQ = 180 - 46 = 134°.

arc angle MRQ is the full half-circle = 180°.

arc angle MAP (as above) = 147°.

The temperature at Tacoma WA is -26 5/12°F.

The temperature at 5pm in Juneau Alaska: temperature at noon + total change in temperature

-20 + (-1.25 x 5)

-20 - 6.25 = -26.25°F = -26 1/4°F

The temperature in Tacoma WA = termpature in Juneau + difference in temperature

-26 1/4°F - 2/3 = -26 5/12°F

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dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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Answer:

All real numbers  are solutions

Step-by-step explanation:

Open the bracket

4(2x+3)=2(4x+6)

8x +12=8x +12

8X-8X=12- 12

=0

The equation is an identity hence, all real numbers are solutions(1,2,3,4 etc)

The equation which represent the proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

y = bx

Where,

b = constant

If y = $6 and x = 2 pairs

y = bx

6 = b × 2

6 = 2b

divide both sides by 2

b = 6/2

b = 3

In conclusion, the proportional relationship between number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

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Answer:

x^2 -10x + 41 = 0

Step-by-step explanation:

They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).

This is a working backwards problem. They gave you an answer and want the equation back again.

x = 5 + 4i

working backwards:

x - (5 + 4i) = 0

x - 5 - 4i = 0

This left side is a factor of your equation.

If 5+4i is a root then 5-4i is also a root. So do the same thing:

x = 5 - 4i

x - (5 - 4i) = 0

x - 5 + 4i = 0

x - 5 + 4i and

x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.

Answer:

x² - 10x + 41 = 0

Step-by-step explanation:

complex roots occur as a conjugate pair.

given x = 5 + 4i , then x = 5 - 4i is also a root

the corresponding factors are

(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is

(x - 5 - 4i) and (x -5 + 4i)

the quadratic equation is then the product of the factors, that is

(x - 5 - 4i)(x - 5 + 4i) = 0

multiply each term in the second factor by each term in the first factor.

x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms

x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]

x² - 10x + 25 + 16 = 0

x² - 10x + 41 = 0 ← in standard form

15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

A process involving numerous stages, multiplication or division, especially a conversion factor, can be referred to as Unit Conversion. Additionally, rounding and determining the number of significant digits may be necessary steps in the procedure.

For measuring various properties, including length, weight, capacity, and temperature, many units of conversion are employed. We can change the units of measurement in mathematics to better understand.

Unit conversions are used to represent an amount in a different unit.

We have to convert 15 nm into km.

1 nm = [tex]10^{-12}[/tex] km

15 nm = 15 × [tex]10^{-12}[/tex] km

          = 1·5 × [tex]10^{-11}[/tex] km

Thus, 15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

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Answer:

formula: Tn=a+(n-1)d

Step-by-step explanation:

Tn=2+(n-1)2

Answer: 42 is a 19.231% decrease of 52.

gg against the jags yesterday

The values that make v ≥ 1 inequality true are 2, 3, 4, 5....

What is inequality in mathematics?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The inequality is given as:

v ≥ -1

The values of c for which the given inequality → v ≥ -1 is true will belong to the set (say A) -

A = [-1, - ∞)

Therefore, we have to select all numbers which fall in this set. The numbers are

-1, 0, 1, 2, 3,....

Rewrite properly as:

v ≥ 1

The above means that the true values of v are values greater than 1.

Hence, the values that make v  ≥ 1 inequality true are -1, 0, 1 , 2, 3, 4, 5....

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All of the given numbers are irrational numbers.  

A real number that can't be stated as a ratio of integers is said to be an irrational number. In simple words, an Irrational number is a number that cannot be represented as p/q where q ≠ 0.  

An irrational number's decimal expansion is neither ending nor recurrent i.e the decimal expansion of an irrational number will be a Non-terminating decimal number.  

Here are some examples of Irrational Numbers

Here we have

[tex]1.7 \overline {3}[/tex] ,  π, ∛90, and √60    

If we observe the given numbers

[tex]1.7 \overline {3}[/tex] = 1.73333333..... is a Non -terminating decimal number  

π is an example of an irrational number

∛90  cannot be represented as a p/q form

√60 = √4 × 15 = 2√15  where √15 is an irrational number

From above information

The given numbers  π, √90, and √60 all are irrational numbers

Therefore,

All of the given numbers are irrational numbers

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Answer: y=-15/6x+6

Step-by-step explanation:

Find slope using slope equations y2-y1/x2-x1

16-(-14)/-4-8

30/-12

slope equals to -15/6

y=-15/6x+b

-14=-15/6(8)+b

b=6

y=-15/6x+6

Order of Operations: BPEMDAS

Functions

Compounded Interest Rate Formula:
[tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^t[/tex]

Let's compile what we know (what we are given).

An investment of $500 means that our principle amount P equals 500.

2.8% nominal yearly interest means that our rate r equals 0.028.

Compounded quarterly means that our compounded rate n equals 4.

So, we have:

[tex]\displaystyle\begin{aligned}P & = 500 \\r & = 0.028 \\n & = 4 \\\end{aligned}[/tex]

In order to find an equation that models the final amount A in terms of t years, we can simply substitute in our known variables:

∴ our equation that models the amount A the investment is worth t years after the principle has been invested is:

[tex]\displaystyle \boxed{ A = 500(1.007)^t }[/tex]

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Topic: Algebra I

Unit: Interest Rate Formulas

According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.

The equation is a mathematical statement or model that shows that two mathematical expressions are equal.

In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.

Cost of the new car = $25,000

Depreciation rate per annum = 20%

Value of the car = V

The price paid initially = P = $25,000

The annual rate of depreciation = r

Depreciation period = 4¹/₂ years

Equation model: V=P(1-r)^t

Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂

= $9,158.93

= $9,200

Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.

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