Televisions are on sale for 40% OFF the original price of $600. After tax (8.5%) is applied, what is the final price?​

Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.5 - 0.1

P(A or B) = 0.8 - 0.1

P(A or B) = 0.7

The probability of an adult having hypertension is  0.344 and an adult having hypertension and being classified as a low level of obesity is 0.102, having hypertension given he/she is classified as a high level of obesity is 0.540. If an adult has hypertension, the probability that he/she also has a high level of obesity is  0.444.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

a)The probability of an adult having hypertension is (34 + 30 + 51) / (34 + 30 + 51 + 119 + 99 + 82) = 115 / 334 = 0.344.

b) The probability of an adult having hypertension and being classified as a low level of obesity is 34 / (34 + 30 + 51 + 119 + 99 + 82) = 34 / 334 = 0.102.

c) The probability of an adult having hypertension given he/she is classified as a high level of obesity is 51 / (30 + 51 + 82) = 51 / 163 = 0.312.

d) The probability of an adult being classified as a high or average level of obesity is (30 + 51 + 99) / (34 + 30 + 51 + 119 + 99 + 82) = 180 / 334 = 0.540.

e) If an adult has hypertension, the probability that he/she also has a high level of obesity is 51 / (34 + 30 + 51) = 51 / 115 = 0.444.

f) No, an adult's hypertension status and obesity categorization are not independent. This is because the probability of an adult having hypertension given he/she is classified as a high level of obesity (0.312) is not the same as the probability of an adult having hypertension (0.344).

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Complete question :

Put these fraction in order of size smallest to largest : 7/10, 2/3, 4/5, 11/15

Answer:

2/3, 7/10, 11/ 15, 4 /5

Step-by-step explanation:

In other to make solving the question easier, we can convert the fractions to decimal in other to make comparison easier :

7/10 = 0.7

2/3 = 0.667

4 /5 = 0.8

11 /15 = 0.733

Using the placement or how the numbers will appear to the right of a number line ;

0.667, 0.7, 0.733, 0.8

Thus we have :

2/3, 7/10, 11/ 15, 4 /5

Answer:

2. Half a lap, 0.5 or 1/2

3. 20/0.5 or 20/(1/2)

Step-by-step explanation:

Since it takes 40 seconds to skate 1 lap,

20 secs would be 20/40 laps, which is 1/2

Ratio is time/number of laps. So, 20/(1/2)

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, \(d^2=l^2+w^2+h^2\).

Plug in the values to get:

\(d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\\)

Thus d ≈ 8.3

The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.

In this problem we must use definite integrals to determine the area of the region bounded by the curves. Based on all the information given by the graph attached below, the area can be defined in accordance with this formula:

A = A₁ + A₂                                                                (1)

A₁ = ∫ [g(x) - f(x)] dx, for x ∈ [- 0.786, 0]                   (2)

A₂ = ∫ [f(x) - g(x)] dx, for x ∈ [0, 1.151]                       (3)

g(x) = x⁴ - x                                                               (4)

f(x) = x / √(x² + 1)                                                      (5)

Then, we proceed to find the integrals:

∫ g(x) dx = ∫ x⁴ dx - ∫ x dx = (1 / 5) · x⁵ - (1 / 2) · x²                          (6)

∫ f(x) dx = ∫ [x / √(x² + 1)] dx = (1 / 2) ∫ [2 · x / √(x² + 1)] dx = (1 / 2) ∫ [du / √u] = √u = √(x² + 1)                                                                                  (7)

And the complete expression for the integral is:

A = A₁ + A₂                                                                                      (1b)

A₁ = (1 / 5) · x⁵ - (1 / 2) · x² - √(x² + 1), for x ∈ [- 0.786, 0]               (2b)

A₂ = √(x² + 1) - (1 / 5) · x⁵ + (1 / 2) · x², for x ∈ [0, 1.151]                  (3b)

A₁ = 0.023

A₂ = 0.783

A = 0.023 + 0.783

A = 0.806

The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.

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Answer:

10 to the power of 2

Step-by-step explanation:

Answer: 10 to the power of 2 or 10^2

Step-by-step explanation: 10 x 10 equals 100. I used the number ten twice to get 100

The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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Answer:

e. Approximately normal with mean of $406,274 and standard deviation $3534

Step-by-step explanation:

Given,The distribution of the sales prices of these homes was as strongly right-skewed with a mean of $406,274 and a standard deviation of $49,981 & Sample of Size 200 Are Drawn .

Now, By the Central Limit Theorem, the approximately normal Mean is $406,274 .

And,

Standard deviation ⇒ s= σ / √n ⇒ $49981 / \(\sqrt{200}\)

⇒ $49981 / 10×√2 ⇒ $4998.1 / √2 ⇔ $3534.72 ≈ $3534

The tax equivalent value will be $3243. The third option is correct

Tax bracket Kent Fuller is currently in is 26 percent

Nontaxable employee benefits value: $2400

The return that a taxable benefit would need to provide in order to match the yield on a comparable tax-exempt benefit is known as the tax-equivalent value. This is very useful for investors to compare the return between a tax-free and a taxable alternative.

Finding out the tax equivalent value using the formula:

Tax equivalent value = Tax exempt value/(1 - Tax Rate)

Tax equivalent value = 2400/(1 - 0.26)

= 2400/0.74

Tax equivalent value = 3243.24 or 3243

Therefore, the tax equivalent value will be $3243. Hence, the third option is correct

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Answer:

d

Step-by-step explanation:

{x|x<-4}

The given graph is constant for the interval (-∞,-4).

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

Given the graph,

The value of y in the coordinate plane represents the value of the graph so to be constant the value of y must be constant.

Since the line is coming from negative infinite is horizontal till x = -4.

Hence "The given graph is constant for the interval (-∞,-4)".

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

C

Step-by-step explanation:

Hope it helps :)

The percentage value of 7 is 140% of the number 5

Given data ,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

To find the percent of one number in relation to another, we can use the following formula:

Percent = (Part / Whole) * 100

In this case, we want to find what percent 7 is of 5.

Percent = (7 / 5) * 100 = 1.4 * 100 = 140

So, when we divide 7 by 5, we get a ratio of 1.4. Multiplying this ratio by 100 gives us the percentage value of 140%. This means that 7 is 140% of 5.

Hence , 7 is 140 percentage of 5.

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The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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Step-by-step explanation:

12 months with $60 every 3 months is $240

then add $28 "per month after that"

Answer:

− 8 x ^2  +  10 x

Step-by-step explanation:

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  \(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

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Answer: 100

Step-by-step explanation:

Sub in 5 for b in the expression

\(4b^2\\4(5)^2\)

You must do the exponent first as it comes before multiplication in the order of operations

\(4(5)^2\\4(25)\)

Now multiply

\(4(25)\\100\)

The domain is the set of all values in the set (- ∞, ∞).

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a quadratic function as follows -

ax² + bx + c

For any quadratic equation (with vertex at origin), the value of [y] or the range is either the set of all positive values from 0 to infinity when the quadratic function open upwards and  the set of all negative values from 0 to -infinity when the quadratic function open downwards. The domain is the set of all values in the set (- ∞, ∞).

Therefore, the domain is the set of all values in the set (- ∞, ∞).

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{Question in english language is as follows -

How the domain of the quadratic function is determined.}

Answer:

(c) and (e) are true

Step-by-step explanation:

Given

\(P(d) = 10. (1.08)^d\)

See attachment for complete question

Required

Which of the options is true

(a) 1080 insects on day 1

This implies that d = 1

So, we have:

\(P(1) = 10* (1.08)^1\)

\(P(1) = 10* 1.08\)

\(P(1) = 10.8\)

(a) is incorrect because \(P(1) \ne 1080\)

(b) 10800 insects after a week

This implies that \(d = 7\)

So, we have:

\(P(7) = 10* (1.08)^7\)

\(P(7) = 10* 1.71382426878\)

\(P(7) = 17.14\)

(b) is incorrect because \(P(7) \ne 10800\)

(c): Growth factor per day is 1.08

An exponential factor is represented as:

\(y = ab^x\)

Where

b is the growth factor

By comparison:

\(b = 1.08\)

Hence, (c) option is true

(d): Growth factor per week is 1.08*7

In (c), we have:

\(b = 1.08\) as the daily growth factor

So, the growth factor for n days is:

\(Factor = 1.08^n\)

Substitute 7 for n i.e. 7 days

\(Factor = 1.08^7\)

So, the growth factor for 7 days is: \(1.08^7\) not \(1.08*7\)

Hence, (d) option is true

(e): Growth factor per week is 1.08*7

In (c), we have:

\(b = 1.08\) as the daily growth factor

For hourly rate, we have:

\(Factor = 1.08^\frac{1}{24}\)

Hence, (e) option is true

The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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The population to which it would be most reasonable to generalize the results of the observational study is women who are students at Midwestern colleges in the United States.

This population is well-defined and can be used to make generalizations about the results from the study.

This population can be calculated by taking the total number of college students in the United States and subtracting the number of college students in other regions, as well as the number of male students in the Midwestern region.

The total population of women college students in the Midwestern region of the United States can then be calculated by multiplying the total population by the percentage of female students in the region.

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Answer:

7x8+10

Step-by-step explanation:

Drag the numbers and symbols till it matches 7x8+10 because the pruduct means multiplication, and more than means addition. If there needs to be a letter, than it's x=7x8+10

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The function that represent the function g(x) is g(x) = f(x) + 4.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

The graph of the function f(x) is given.

We know that, a linear function in slope intercept form can be represented as, y = mx + d, where m is slope and d is the y intercept.

y intercept is the y coordinate of the point where the line touches with the Y axis. At this point x coordinate is 0.

From the graph, we have f(x) = y = -1 when x = 0.

So y intercept, d = -1

Take two points from the graph (1, 0) and (0, -1).

Slope, m = (-1 - 0) / (0 - 1) = -1 / -1 = 1

f(x) can be represented in slope intercept form as f(x) = x - 1

We have a second function g(x) from the transformation of f(x).

y intercept of g(x) = 3

f(x) + 4 = x - 1 + 4 = x + 3 which can be g(X), since y intercept is 3.

Hence g(x) = f(x) + 4 is the function that represents the transformation of f(x) with y intercept 3.

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Answer:

154 square inches of parchment paper will cover his baking pan.

Step-by-step explanation:

Since Kevin is baking crescent rolls for his dinner guests, and his rectangular baking pan measures 11 inches by 14 inches, to determine how many square inches of parchment paper will cover his baking pan, the following calculation must be performed:

11 x 14 = X

154 = X

Therefore, 154 square inches of parchment paper will cover his baking pan.