The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited.

We got the mean value 4.167 and standard deviation 19.56.

In statistics, a mean value is the average value of all the available data. And it can be determined by adding all the data by dividing the amount of data.

A standard deviation is an estimation that implies how far each available data apart from the mean value.

we are given, 4% of the population has a genetic mutation

Total people in the group =600

Now, total number of people who have genetic mutation = (4/100) ×600

                                                                                              = 24

the number of randomly selected people =100= X

Mean = Number of selected people/ people who have mutation

  Mean = X/n = 100/24 = 4.167

the standard deviation = √∑(X-mean) ²/n

                                       = √∑(selected people - mean) ²/ mutation number

                                    =√(100-4.167) ²/24

            standard deviation = 19.56

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Answer:

slope = 1/4

Step-by-step explanation:

at a cafeteria the price of a salad depend on it weight in ounces. the graph shows the relationship what is the slope of the line

Find two places where the line neatly intersects the graph. For example, we will use the points: (0 , 0) and (4 , 1)

slope = change in y / change in x

[tex]slope = \frac{(y_{1} -y_{2} )}{(x_{1} -x_{2} )}[/tex]

slope = (0 - 1) / (0 - 4)

slope = -1 / -4

slope = 1/4

Answer: 1/4

Step-by-step explanation:

I just did it

The inverse function of the function f(x) = log₂(3x + 4) − 5 is y = [2^(x + 5) - 4]/3

From the question, we have the following equation that can be used in our computation:

f(x) = log2(3x + 4) − 5.

Rewrite as

f(x) = log₂(3x + 4) − 5.

Express f(x) as y

This gives

y = log₂(3x + 4) − 5.

Swap the positions of x and y

So, we have the following representation

x = log₂(3y + 4) − 5.

Add 5 to both sides

log₂(3y + 4) = x + 5

So, we have

3y + 4 = 2^(x + 5)

Subtract 4 from both sides

3y = 2^(x + 5) - 4

Divide b y3

y = [2^(x + 5) - 4]/3

Hence, the inverse function is y = [2^(x + 5) - 4]/3

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The length of diameter of the base of the cone will be 112 cm.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Equations are mathematical expressions with two algebras flanking the equal (=) sign on either side. This relationship is illustrated by the left and right expressions being equal to one another. Left-hand side equals right-hand side is a basic, straightforward equation.

By using Pythagoras's theorem,

106² = 90² + r²

simplifying the above equation, we get

r² = 106² - 90²

r = √3136

radius = 56 cm.

Then, the diameter will be,

Diameter = 2 × radius

substitute the values in the above equation,

D = 2(56)

D = 112 cm.

Therefore, the correct answer is option b. 112 cm.

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Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

[tex](x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c[/tex]

substitute b = 10 and c = 29 in this form:

[tex](x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29[/tex]

Simplify further:

[tex](x + 5) {}^{2} - 25 + 29[/tex]

[tex](x + 5) {}^{2} + 4[/tex]

c = 5, d = 4

Answer:

A)   The graph of function g(x) is V-shaped and has the following properties:

B)  Translation of 2 units down.

Therefore:

Step-by-step explanation:

The absolute value parent function, f(x) = |x|, is defined as:

[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]

Therefore:

Its graph is V-shaped and has the following properties:

Given absolute value function:

[tex]g(x)=|x+3|[/tex]

The graph of function g(x) is the parent function f(x) translated 3 units to the left.

As the graph has only been translated horizontally, the domain and range are the same as the parent function.

Therefore, the graph of function g(x) has:

Given absolute value functions:

[tex]f(x)=|x|[/tex]

[tex]h(x)=|x|-2[/tex]

The graph of function h(x) is the parent function f(x) translated 2 units down.

As the graph has been translated vertically, the domain is the same as the parent function, but the vertex and range are different.

Answer:

The graph will be a V shape

Step-by-step explanation:

The graph will be a V shape because of the absolute value

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

1. range = {-8,-6,0,8}

2. My graph is attached to this response as a photo.

Step-by-step explanation:

1. ⭐What is the "domain" of a function?

⭐What is the "range" of a function?

⭐What is the "set notation"?

Therefore, we have to find the corresponding y-values for the given x-values, and then write said y-values in set notation.

To find the corresponding y-values for the given x-values, substitute each given x-value into g(x) and solve for g(x).

✦ When x = -3

[tex]g(x) = 2x-2[/tex]

[tex]g(-3) = 2(-3) -2[/tex]

[tex]g(-3) = -6 -2[/tex]

[tex]g(x) = -8[/tex]

✧ y = -8

________________________________________________________

✦ When x = -2

[tex]g(-2) = 2(-2) -2[/tex]

[tex]g(-2) = -4-2[/tex]

[tex]g(-2) = -6[/tex]

✧ y = -6

________________________________________________________

✦ When x = 1

[tex]g(1) = 2(1) -2[/tex]

[tex]g(1) = 2-2[/tex]

[tex]g(1) = 0[/tex]

✧ y = 0

________________________________________________________

✦ When x = 5

[tex]g(5) = 2(5) -2[/tex]

[tex]g(5) = 10 -2[/tex]

[tex]g(5) = 8[/tex]

✧ y = 8

________________________________________________________

Next, we have to write the y-values in set notation. Make sure to write it from least to greatest.

range = {-8, -6, 0, 8}

The perimeter of the figure with the varied side length is 52 cm

From the question, we have the following parameters that can be used in our computation:

Shape = composite figure

Smaller shapes = squares and rectangles

Side lengths = varied values

The perimeter of the figure is calculated as

Perimeter = Sum of the sides lengths of the shape

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 12 + 7 + 3 + 4 + 3 + 7 + 6 + 10

Evaluate the sum in the above equation

Perimeter  = 52 cm

Hence, the perimeter is 52 cm

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Answer:

9 ( x + 9 )

Step-by-step explanation:

81 = 9 × 9

9x = 9 × x

9x + 81 = 9 ( x + 9 )

Answer:

A.) y=6x+2

Step-by-step explanation:

I got this answer by first finding the slope. To find the slope you use the slope formula which is y2-y1 over x2-x1. When I set up the equation I got -10-26 over -2-4 and I got -36/-6 which is 6. So your slope is 6. So then you would mark out answer c and d because their slope is negative and the slope I got is positive. To find the y-int I put in two points online and I put in the slope. I did this twice with four different points just to make sure that it was right and then it gave me that the y-int is 2. So then you would mark out b because the y-int is not negative but positive. (Hope this helps in some way...if not then I'm sorry..)

By using the given scale, we will see that the real distance is 240km

We know that the scale of the map is 1 cm to 12km, so we just need to take the distance in centimeters on the map, and multiply that number by 12 km.

We know that on the map, the distance between Cardiff and London is 20cm, then the real distance is 12km times that, so we will get:

real distance = 20*12km = 240km

The real distance between Cardiff and London is  240 kilometers.

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25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given

Expression

(5x⁻⁵ y³)⁻²

25x¹⁰ y⁻⁶

25x¹⁰/y⁶

25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².

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Answer:

x > 2

Step-by-step explanation:

8x - 5 > 13 - x             Add x to both sides

8x + x - 5 > 13 - x + x

9x - 5 > 13                   Add 5 to both sides

9x - 5 + 5 > 13 + 5

9x > 18  Divide both sides by 9

[tex]\frac{9x}{9}[/tex] > [tex]\frac{18}{9}[/tex]

x > 2

Answer:

x>2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The congruency proofs that can be used for each of the triangles are;

1) SSS Congruency

2) None

3) HL Congruence

1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.

Thus, we conclude that the congruency can be proved using SSS Congruency postulate.

2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.

3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem

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Answer:

x = 44

Step-by-step explanation:

Given that line m is parallel to line n, the angles that we see are same-side exterior angles, meaning that these two angles add up to 180°.

Set up the equation: [tex]112 + (2x - 20) = 180[/tex] and solve for x.

. . . . . . . . . . . . 112 - 112 + 2x - 20 = 180 - 112

. . . . . . . . . . . . 2x - 20 + 20 = 68 +20

. . . . . . . . . . . . 2x /2 = 88 /2

. . . . . . . . . . . .  ∴ x = 44

The value of the expression f(x) + g(x) - h(x) will be 2x² + 7x + 2. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = 3x² + 5

g(x) = 4x - 2

h(x) = x² - 3x + 1

The expression is given as,

⇒ f(x) + g(x) - h(x)

⇒ (3x² + 5) + (4x - 2) - (x² - 3x + 1)

⇒ 3x² + 5 + 4x - 2 - x² + 3x - 1

⇒ 2x² + 7x + 2

The value of the expression f(x) + g(x) - h(x) will be 2x² + 7x + 2. Then the correct option is B.

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Answer: 55000 grams

Step-by-step explanation:

With the help of Geometry We would make Australia 200 miles more wider.

What is geometry?

Geometry is a branch of mathematics that is concerned with the study of shapes, sizes, and relative positions of figures and the properties of space. It is one of the oldest branches of mathematics that has been around for centuries and is still relevant today. Geometry is used to explain many aspects of our lives, from the size of buildings and bridges to the path of a baseball in flight. It is a powerful tool for problem solving and understanding the world around us. Geometry is based on axioms, or accepted truths, that are used as the basis for forming logical proofs. These proofs are used to develop theorems and formulas which help us to understand and explain our world.

We would make Australia 200 miles more wider too or just give 200 miles long US to some other country to make their sizes equal.

Hence, we would make Australia 200 miles more wider

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With the decimal point in the proper place, dividing decimals is equivalent to dividing entire numbers.

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The slope of a line that is perpendicular to the x-axis is undefined, so we cannot use the standard form of the equation of a line, y = mx + b, where m is the slope of the line. Instead, we can use the point-slope form of the equation of a line, which is given by y - y1 = m(x - x1). In this case, m is undefined, so we can simplify the equation to y = x1 - y1, where x1 and y1 are the coordinates of the point that the line passes through. In our case, this gives us the following equation:

y = 6 - (-2)

 = 8

Therefore, the equation of the line that is perpendicular to the x-axis and passes through the point (6,-2) is y = 8.

Answer:

3.  $42,540

4.  $53,480

Step-by-step explanation:

Income

Gross income = $61,840

Allowances

Head of household (2009) = $8,350

Single with 2 dependents = $3,650 + $3,650 · (2) = $10,950

Total allowances = $8,350 + $10,950 = $19,300

Taxable Income

Gross income - total allowances = $61,840 - $19,300 = $42,540

Income

Gross income = $79,480

Allowances

Married filing jointly (2009) = $11,400

Married with 2 dependents = $7,300 + $3,650 · (2) = $14,600

Total allowances = $11,400+ $14,600 = $26,000

Taxable Income

Gross income - total allowances = $79,480 - $26,000 = $53,480

The surface area increases when the radius of the sphere is 160π cm^2/s

Given that dt/dr =10 cm/s and r=15 cm

Find out dt/ds=?

We know that the surface area of sphere S=4πr^2

dt/ds=4π(2r)

dt/dr=8π(2)(10)

=160π cm^2/s.

Let r, V, and S be respectively the radius, volume, and surface area of the spherical balloon at time t.

∴V=4/3 πr^3 and S=4πr^2

Rate of change of surface area with respect to t

⇒ dt/dS=2

⇒ d/dt=(4πr^2)=2

⇒8πr dt/dr =24

⇒ dr/dt=1/4πr.... (i)

Rate of change of volume of the balloon with respect to t

=dV/dt

=d/dt(4/3πr^3)

= 4/3π⋅3r^2dr/dt

​=4πr ^2⋅ dr/dt

=4πr^2.1/4πr ....[From (i)]

r=10

Hence, the volume of the spherical balloon is increasing at the rate of 10cm^3/sec.

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Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with [tex]\frac{dollars}{student}[/tex]:

[tex]\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}[/tex]

The rate is 5 dollars per student.

Cos W as a fraction in the simplest terms is 2/3  

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle.

From a Right-angled triangle with an angle θ

sin θ = Opposite side/Hypotenuse

cos θ = Adjacent side/Hypotenuse

tan θ = Opposite side /Adjacent side

Here we have

A triangle UVW

where VW = 10 units

And WU = 15 units

As we know

cos θ = Adjacent side / Hypotenuse  

cos W = VW/WU = 10/15

cos W = 2/3    [ divided by 5 ]  

Therefore,

Cos W as a fraction in the simplest terms is 2/3  

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95% confident the population mean is between (9.1,9.9).

We are given the following data set:

9.3, 9.7, 9.2, 9.7

What is Standard Deviation?

Standard Deviation [tex]$=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}$[/tex]

where[tex]$x_i$[/tex] are data points, [tex]$\bar{x}$[/tex]is the mean and [tex]$\mathrm{n}$[/tex] is the number of observations.

Mean [tex]$=\frac{\text { Sum of all observations }}{\text { Total number of observation }}$[/tex]

Mean [tex]$=\frac{37.9}{4}=9.475$[/tex]

Sum of squares of differences [tex]$=0.2075$[/tex]

S.D[tex]$=\sqrt{\frac{0.2075}{3}}=0.262$[/tex]

[tex]$95 \%$[/tex] Confidence interval:

[tex]$\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}$[/tex]

Putting the values, we get,

[tex]$t_{\text {critical }}$[/tex] at degree of freedom 3 and[tex]$\alpha_{0.05}=\pm 3.182$[/tex]

[tex]$9.475 \pm 3.182\left(\frac{0.262}{\sqrt{4}}\right)=9.475 \pm 0.416842=(9.058158,9.891842) \approx(9.1,9.9)$[/tex]

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The correct answer is m√5 + m√2 = 180°.

Parallel lines are those in a plane that are regularly spaced apart from one another. There is no crossing of parallel lines.

Given, k and p are parallel lines.

In an expression or equation, one value can be substituted for another and the result will still be the same. This is known as the substitution property of equality. If the values of x and y are the same, then x and y can be substituted for one another.

And we have,

m√1 + m√2 = 180°

And  m√5 =  m√1

So,  m√5 + m√2 = 180°

Therefore, in the proof, the missing term is  m√5 + m√2 = 180°.

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324 Miles

If you divide 189 by 7, you get 27. If you then multiply 27(miles per hour) by 12(hours) you get 324.

The probability that one has a dog allergy when tested positive will be 0.3311.

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to the given question,

We have the given information:

1% of the population has an allergy to dogs.

This will be:

= 1% × 100000

= 1000

So, 1000 people have an allergy to dogs.

The number of people who doesn't have allergy to dogs will be:

= 100000 - 1000

= 99000

Those that have allergies = 2% × 1000 = 20

So, the probability that one has dog allergy will be:

= P(has allergy and test positive)

= (0.01 × 0.98) + (0.098 + 0.0198)

= 0.0098/0.0296

= 0.3311

Therefore, the probability is 0.3311.

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