This graph represents the first hypothetical described in the video. Imagine someone invests $10,000 with 7% returns compounding each year for 30 years.

Linear equations have an infinite number of solutions are-

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

c) 12.3x – 8 = 3(–6 + 4.1x)

What is  Linear equations?

A linear equation is an equation within which the very best power of the variable is usually one.

Main body:

A linear equation can be said to have an infinite number of solutions when the number of the right hand side is the same at the number on the left hand side of the equation.

For example:

2 = 2 or x = x or 0 = 0

Solving the question above:

Which linear equations have an infinite number of solutions? Check all that apply.

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

x - 3/7 = 6x/6 - 18/42

x - 3/7 = x - 3/7

Collect like terms

x - x = -3/7 + 3/7

0 = 0

The linear equation in option a has an infinite number of solutions

b) 8(x + 2) = 5x – 14

8x + 16 = 5x - 14

Collect like terms

8x - 5x = -14 - 16

3x = -30

x = -30/3

x = -10.

The linear equation in Option b has a true solution.

c) 12.3x – 18 = 3(–6 + 4.1x)

12.3x - 18 = -18 + 12.3x

Collect like terms

12.3x - 12.3x = -18 + 18

0 = 0

The linear equation in Option c has infinite number of solutions

d) 1\2(6x + 10) = 7(3\7x – 2)

6x/2 + 5 = 21/7x - 14

3x + 5 = 3x - 14

Collect like terms

3x - 3x = -14 - 5

0 = -19

The linear equation Option d has no solution

e) 4.2x – 3.5 = 2.1 (5x + 8)

4.2x - 3.5 = 10.5x + 16.8

Collect like terms

4.2x - 10.5x = 16.8 + 3.5

-6.3x = 20.3

x = -20.3/6.3

x = -3.22

Hence, the linear equation in Option e has a true solution

Therefore, the linear equations have an infinite number of solutions are:

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

c) 12.3x – 18 = 3(–6 + 4.1x)

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λ = 1 + 5i and ∨ = [ -1 + i , i ]

[tex]y(t)=e^{\lambda t}\eta^1=e^{(1+5i)t}\begin{bmatrix} -1+i\\ i \end{bmatrix}\\y(t)=e^{t}(e^{5t}\begin{bmatrix} -1+i\\ i \end{bmatrix})[/tex]

[tex]y(t) e(cos(5t) isin(5t) \begin{bmatrix} -1+i\\ i \end{bmatrix}\\\\y(t)=e^t\begin{bmatrix} (cos(5t)i+i^2sin(5t))-(cos(5t)+isin(5t))\\ cos(5t)i+i^2sin(5t)) \end{bmatrix}\\y(t)=e^t\begin{bmatrix} (-sin(5t)-cos(5t)+(cos(5t)-sin(5t))i\\ -sin(5t)+(cos(5t))i \end{bmatrix}[/tex]

[tex]y(t)=\left ( e^t \begin{bmatrix} -(sin(5t)+cos(5t))\\ -sin(5t) \end{bmatrix} \right )+\left ( e^t\begin{bmatrix} (cos(5t)-sin(5t))\\ cos(5t) \end{bmatrix} \right ) i[/tex]

[tex]y_{1}(t)= -e^t \begin{bmatrix} sin(5t)+cos(5t)\\ sin(5t) \end{bmatrix}\ and \ y_{2}(t)= e^t\begin{bmatrix} cos(5t)-sin(5t)\\ cos(5t) \end{bmatrix}[/tex]

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the othes solution in this picture: ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

The domain of the square root function is x≥0.
What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.

To find out a perfect square we need to find out square root is an integer.

Hence, The domain of the square root function is x≥0.

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The distance between -9 and 2 using ruler postulate is 11units

Ruler postulate states that the points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.

If point A is -9 and point B is 2,

therefore the distance between https://brainly.com/question/28271571 A and B is A-B= -9-2= -11 units

Therefore the absolute value of the distance is 11 units

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At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.

If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.

Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.

For example, suppose you plot a function.

f (x) = (x + 1) (x - 2)²

See the figure above to see how the function behaves differently for different x intercepts.

x intercept at x = -1 is the solution of the equation

x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.

x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0

The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)

coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .

thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).

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Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis on coducting a one tail test.  

A hypothesis is a theory put up to explain a phenomena. A link between two or more variables is described, and the proposition is testable. A hypothesis is an informed estimate or forecast made before undertaking any tests or research to determine its validity. A strong hypothesis should be definable, testable, and supported by prior data. It should also be stated in a way that allows it to be disproven, so that it can be tested using empirical evidence. Generally speaking, a hypothesis serves as the basis for additional research and testing in a scientific endeavour.

How to solve?

The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis if the test statistic is less than -1.96.

To calculate the test statistic, we use the formula:

z = (x - μ) / (s / √n)

x = 215, μ = 220, s = 15, and n = 64. Plugging these values into the formula gives:

z = (215 - 220) / (15 / √64) = -5 / (15 / 8) = -5 / 1.875 = -2.67

The test statistic is -2.67, which is less than the critical value of -1.96, so we reject the null hypothesis.

To calculate the p-value, we can use the z-table to look up the area under the normal curve that is to the left of -2.67. This area is approximately 0.0031, which is the p-value.

Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis.

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The difference between partitioning into a ratio of 1/2 and finding half of a line segment is that partitioning in that ratio means one part is longer than the other, whereas finding half the length means both parts are the same length.

What is the partition of the line?

Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.

When we say we want to partition a line into a ratio of say x/y, it means that the line has been divided in that ratio and as such, the total number of parts is x + y.

Similarly, when we partition a line in the ratio 1/2, it implies that the total number of parts of the line segment is 1 + 2 = 3.

This means one part of the divided segment is bigger than the other one.

In contrast, half of the line segment means that the line segment is divided into two equal parts.

Thus, the fundamental difference between partitioning into a ratio of 1/2 and finding half of the line segment is that partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.

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Because 1:2 is not a fraction while 1/2 is, you cannot assume that 1:2 is one-half of a line or anything that is being delt with in fact. The length of the line might be 18 units, and if it says that there needs to be some sort of action with a ratio of 1:2, you are not splitting that length in half, you are taking one unit from the left side, and two from the right, which does not equal the length of half of 18 units.

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y-value when x = 0).

to find the slope of the target line we use the slope of the given line : 1/2.

remember, the slope is expressed as ratio (y coordinate change / x coordinate change).

the given line increases the y- value by 1, when the x-value increases by 2.

a perpendicular slope (90°) simply turns y and x upside-down and flips the sign.

so, 1/2 turns into -2/1 = -2.

so, we see our line equation looks like

y = -2x + b

to get b we use the coordinates of the given point :

-2 = -2×1 + b

-2 = -2 + b

0 = b

so thar equation is simply

y = -2x

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-9,-6)\qquad B(-2,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:4} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{4}\implies \cfrac{A}{B} = \cfrac{3}{4}\implies 4A=3B\implies 4(-9,-6)=3(-2,1)[/tex]

[tex](\stackrel{x}{-36}~~,~~ \stackrel{y}{-24})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{3}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-36 -6}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-24 +3}}{3+4} \right)} \\\\\\ C=\left( \cfrac{ -42 }{ 7 }~~,~~\cfrac{ -21}{ 7 } \right)\implies \boxed{C=(-6~~,~~-3)}[/tex]

the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.

How to solve?

The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

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The correct option is that Undergraduate is assigned to the purchaser group.

P ( purchase | Undergraduate ) = [tex]\frac{70}{70 + 30}[/tex] = 70 / 100 = 0.70 ,

                                         ⇒   P ( y = 0 | Undergraduate ) = 0.3

P ( purchase | Graduate ) = [tex]\frac{100}{100 + 110}[/tex] = 0.476

                                         ⇒   P ( y = 0 | Graduate ) = 0.524

Therefore,

    as P ( y = 1 | undergraduate ) = 0.707 >  0.30 and

                                                       0.476  > 0.524,

Undergraduate group is assigned to the purchase group.

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Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.

Create a point F' on ray AC such that BF' is equal to DE.

Angle BAF' = angle BAC, which equal to

angle EDF, AB = DE (given), so ∆ DEF

= ∆ ABP

Point F' has two possibilities: F' is equal to point C please.

If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.

Therefore, F' = C must be true.

∆ABC = ∆ABF' = ∆DEF.

The reasonwe only need some parts to

prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.

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Answer:

4 , 12 , 14

Step-by-step explanation:

1) We are told that the median (middle number) is 12 and that the mean is 10

This means that the numbers added together, divided by 3 which equals to ten. From this we can understand that the numbers should add up to 30 as 30 divided by 3 is 10

2) We already know one of the middle numbers which is 12 so the next step would be to subtract 12 from 30 which would be 18.

3) We are also told that the range is 10 meaning that the difference between the smallest and biggest number is 10. If the difference between the smallest and biggest is 10 and the number that they can add to is 18, all we have to do to get our numbers subtract 10 from 18 which is 8 and divide it by 2 which is 4. We have to divide it because we need to find two more numbers

4) From the information we have so far we know that one of our numbers is 4 and the other is 12. To get the final number, add 12 and 4 together which is 16, and subtract that from 30 which is 14. Meaning our numbers are 4 , 12 and 14

5) To check if this is right we can see that the range is 10 (14 - 4 = 10) the mean is 10 (4 + 12 + 14 = 30) and the median is 12!!

Hope this helps, have a great day!

The area of the given triangle is 20 square kilometers.

Here, we are given a triangle as shown in the figure below.

There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-

area of triangle = 1/2 × sinФ × side 1 × side 2

where, Ф = angle formed by side 1 and side 2

Here, Ф = 35

Sin 35 = 0.5736

Thus, the area of the triangle will be-

1/2 × 0.5736 × 7 × 10

= 35 × 0.5736

= 20.076

20.076 rounded off to nearest hundredth is 20

Thus, the area of the given triangle is 20 square kilometers.

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Your question was incomplete. Check for the missing figure below

The total cost for buying 10 packs of paper and 30 notebooks is $87.50.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Mr. Imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modelled by 1.25p + 2.50n. evaluate for p = 10 and n=30

Putting p = 10 and n = 30, we get,

1.25*10+2.50*30 = 87.50

Hence, The total cost for buying 10 packs of paper and 30 notebooks is $87.50.

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The length of the bracket after 1 iteration is 100%.

Let  f(x) = x³-15x² + 50x

a = 0, b=10.

Let the golden ratio be  

GR=√5-1 / 2=0.618

Now, d = GR (b-a)

= 0.618 (10-0) = 6·18

[tex]x_{1}[/tex]= a+d = 0 + 6·18 = 6.18

[tex]x_{2}[/tex] = b-d = 10- 6·18 = 3.82

f([tex]x_{1}[/tex]) = (6·18)³ - 15 (6·18)² + 50(6·18) = -27.887  

f([tex]x_{2}[/tex]) = (3.82)³-15(3.82)²+50(3.82)=27.857

so, f([tex]x_{2}[/tex]) > f([tex]x_{1}[/tex]) new interval is [a,x,]

i.e., maximum lies in [0, 6·18]

so, Xmax = [tex]x_{2}[/tex]= 382

Uncertainty in measurement will be,

∈= [tex]\frac{1-GR) (b-a)}{Xopt}[/tex] =[tex]\frac{((1-0.618) X (10-0)}{382}[/tex] × 100%

∈ = 100%

In arithmetic, quantities are within the golden ratio if their ratio is the same as the ratio in their sum to the larger of the 2 portions. Expressed algebraically, for quantities a and b with [tex]a > b > 0[/tex], [tex]\frac{(a+b)}{a}[/tex] = [tex]\frac{a}{b}[/tex]= φ

The golden ratio turned into known as the acute and suggest ratio by way of Euclid, and the divine proportion using Luca Pacioli, and also is going through numerous other names. The golden ratio seems in some patterns in nature, such as the spiral association of leaves and different elements of plants.

A few twentieth-century artists and architects, together with Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing them to be aesthetically appealing. these uses often appear in the form of a golden rectangle.

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The system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, so the daily demand is 2700 units / day.

In the given question, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks.

We have to find the daily demand.

The figure is given below:

Total operating time of the facility = 8 hours - 2 breaks of 15mins each

Total operating time of the facility = 480 mins - (2*15 mins)

Total operating time of the facility = 480 mins - 30 mins

Total operating time of the facility = 450 minutes.

Time taken for 1 output = Cycle time of system = Bottleneck of the supply-demand matched process = 10 seconds.

Total output = Total operating time / Time taken for 1 output

Total output = 450 minutes / 10 seconds

Total output = 2700 units / shift.

Since the market's demand and operational time are in balance, all production is created using the pull principle.

That means; Supply = demand.

Therefore the market demand for the product = 2700 units / day.

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16 weeks would pass before any further dogs need to be bathed.

The parameters being:

From the formula;

Profit = Sales - Expenses.

Weekly profit is $124 - $8 = $116.

Total revenue generated:

Number of weeks Profit per week.:

= $116 × 8

= $928

Total ownership is total revenue plus initial investment.

Owned in total:

$928 + $32 = $960.

The number of weeks until the entire amount owned is spent can be computed as follows:

Total amount owned weekly spending

=  ($960 / $60) = 16

Thus, 16 weeks would pass before any further dogs need to be bathed.

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The percentage tip did they give is 18%

If their food and beverage cost $25. 30

There i an 8% meal tax

The tax will be

$25.30(0.08) = $2.024.

Then we add the tax to the price such that

The bill will be

$25.30 + 2.024 = $27.32

Tip = 32.24 - 27.32 = 4.92

percentage tip did they give

= tip given /total amount of the bill x 100

= 4.92/27.32 x 100

= 18%

Therefore, If their food and beverage cot $25. 30 and there i an 8% meal tax and after adding a tip, the total lunch cot wa $32. 24.the percentage tip did they give is 18%

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Step-by-step explanation:

9÷3=3 so when beth is 30 you need to do 30-6 which is 24

When beth was 9, paul was 3 times younger = 9/3 = 3 years old.

Beth has gained 21 years since, so the age of paul is 3 + 21 = 24 years old.

You work an average of 39 1/8 hours per week.

The given can be used to calculate the average.

(36 3/8 + 41 1/4 + 40 1/2 + 38 3/8) / 4 =

36 + 41 + 40 + 38 = 155

3/8 + 1/4 + 1/2 + 3/8 = 3/8 + 2/8 + 4/8 + 3/8 = 12/8 = 1 1/2

155 + 1 1/2 = 156 1/2

(156 1/2) / 4 =

313/2 * 1/4 = 313/8 = 39 1/8

average weekly hours are 39 1/8.

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The diagram of adiabatic and isochoric process on a pv diagram is given below.

In the given question we have to suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped the draw the adiabatic and isochoric processes on a p-v diagram.

The Adiabatic Process

A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy. The adiabatic process is mathematically represented by the expression ∆Q=0.

The Isochoric Process

A thermodynamic process known as an isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, occurs when the volume of the closed system undergoing the process remains constant.

The diagram of adiabatic and isochoric process on a pv diagram is given below:

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Solution of the equation 3x - 14 =  4 will be x=6

What are Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

3x - 14 =  4

⇒3x = 4 +14 (adding 14 on both side)

⇒x = 18 / 3 (dividing 3 from both sides)

⇒x = 6

Hence, Solution to the equation 3x - 14 =  4 will be x=6

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The inequality to represent the number of album and song Jorge can download is 2s + 12a ≤ 50

It cost 2 dollars to download a song and 12 dollars to download an entire album. Jorge has 50 dollars to spend on downloading music.

The inequality that represents the number of songs(s)  and album(a) that Jorge can download can be represented as follow:

Therefore,

Hence, the inequality is as follows:

2s + 12a ≤ 50

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Using p-hat formula and probability,

we get

a) Sampling distribution of p-hat = 0.02029286

b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is

=0.3121

c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635

We have given that

29% of adults do not own a credit card according to creditcard.com.

a) Sample size (n) = 500 of adults have own credit card

sample proportion, for the adults do not own a credit= 29% = 0.29

Normal distribution exits here with p

= 1-0.29=0.71 and

Standard error (p-hat) =sqrt(p(1-p)/n)

=sqrt(0.71× 0.29/500)

p-hat = 0.02029286

b) Now, more than 30% do not have own credit card.

P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))

=P(Z>0.49) =0.3121 (from standard normal table)

c) Sample size (n) = 500 and p-hat lies between 25% to 30% .

P(0.25<phat<0.3)

= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))

=P(-1.97<Z<0.49)

=0.6635 (from standard normal table)

Hence, we calculated all the required probabilities.

a) p-hat = 0.02029286

b) P(p-hat>0.3) =0.3121

c) P(0.25<phat<0.3) =0.6635

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Complete question:

According to creditcard.com, 29% of adults do not own a credit card.

a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.

b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?

c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?

The solution to the equation 8^x/2=2^3/8×4^3/4 is x = 15/14

To simplify an expression: to remove brackets, unnecessary terms and numbers

[tex]8^{x/2} = 2^{3/8} * 4^{3/4}[/tex]

[tex]2^{3x/2} = 2^{3/8} * 2^{2 (3/4)}[/tex]

using law of Indices

[tex]2^{3x/2} = 2^{3/8 + 6/4}[/tex]

[tex]\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}[/tex]

[tex]\frac{3x}{2} = \frac{3+12}{8}[/tex]

[tex]\frac{3x}{2} = \frac{15}{8}[/tex]

cross multiply

24x =30

Divide both sides by 24

[tex]\frac{24x}{24} = \frac{30}{28}[/tex]

x = 15/14

Therefore, the solution to the equation is x = 15/14

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A linear function is represented by the graph straight line.

In the given question we have to explain which parent function is represented by the graph straight line.

As we know that;

The simplest function in a family of functions, a parent function maintains the definition of the entire family.

There are several basic functions that we run with frequently in math. These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.

A linear function with a degree of one that is linear and expressed as f(x)=x. f(x) = x, where the function's graph passes through the origin, is referred to as a linear function.

Hence, a linear function is represented by the graph straight line.

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The required annual premium rate for the given term life policy is $50,850.

Term life insurance  covers you for a particular measure of time - basically, the strategy's term. The length of the term can change to suit your specific conditions. You can likewise look over two changed sorts of term disaster protection: diminishing term protection and level term protection.

Annual Premium Rate implies, if pertinent, the exceptional rate so determined on the Statements Page of this Strategy to be utilized in processing a premium to be transmitted yearly.

Jacob needs to purchase a $500,000 15-year term life strategy, and the yearly superior rate (per $1000 of presumptive worth) for his age bunch is $6. 78.

Number of 1000 of every 500000 will be 500000/1000 = 500

the yearly superior rate (per $1000 of assumed worth) for his age bunch is $6. 78.

Absolute premium is 500 x 6.78 = 3390

The premium each year is 3390

For quite some time, the all out premium is

15 x 3390 = 50850

Thus, over all premium jacob have paid $50850.

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The equation that can be used to find the width, w, of the rectangle with the given area is 2w² - w - 91 = 0

To determine the equation that can be used to find the width we use the following formula; Area of a rectangle = length × width

Since the area of the rectangle is 91 square inches and the length of the rectangle is 1 less than twice its width, this can be represented as;

Length of the given rectangle = 2w - 1

Using the area formula the equation to find the width would be:

(2w - 1)(w) = 91

2w² - w - 91 = 0

Hence 2w² - w - 91 = 0, is the equation that can be used to find the width.

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