In the US, 47.3% of smart phones sold are made by Apple.

Suppose that 20,465 smart phone were sold in one day.

How many of those phones would be made by Apple?

Answer:

x-intercepts:  (-1, 0) and (2, 0)

x-intercept:  (-3, 0)

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=-4x^2+4x+8[/tex]

The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0

Therefore, to find the x-intercepts of the given function, set the function to zero:

[tex]\implies -4x^2+4x+8=0[/tex]

Factor out -4:

[tex]\implies -4(x^2-x-2)=0[/tex]

Divide both sides by -4

[tex]\implies x^2-x-2=0[/tex]

Rewrite the middle term as -2x + x:

[tex]\implies x^2-2x+x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-2)+1(x-2)=0[/tex]

Factor out the common term (x - 2):

[tex]\implies (x+1)(x-2)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}[/tex]

Therefore, the x-intercepts are (-1, 0) and (2, 0).

---------------------------------------------------------------------------------------

Given quadratic equation:

[tex]-9 = x^2 + 6x[/tex]

Add 9 to both sides:

[tex]\implies x^2+6x+9=0[/tex]

Rewrite the middle term as 3x + 3x:

[tex]\implies x^2+3x+3x+9[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+3)+3(x+3)=0[/tex]

Factor out the common term (x + 3):

[tex]\implies (x+3)(x+3)=0[/tex]

[tex]\implies (x+3)^2=0[/tex]

Square root both sides:

[tex]\implies (x+3)=0[/tex]

Solve for x:

[tex]\implies x=-3[/tex]

Therefore, the x-intercept is (-3, 0).

As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.  

Answer:

E.  16y

Step-by-step explanation:

Given equation:

5(x - 6y) = 50y

Expand the brackets using
Distributive Property for subtraction:  a(b - c) = ab - ac

⇒ 5 · x - 5 · 6y = 50y

⇒ 5x - 30y = 50y

Add 30y to both sides:

⇒ 5x - 30y + 30y = 50y + 30y

⇒ 5x = 80y

Divide both sides by 5:

⇒ 5x ÷ 5 = 80y ÷ 5

⇒ x = 16y

Answer:

2,734,500

Step-by-step explanation:

27,345 × 113 - 27,345 × 13 ← factor out 27,345 from each term

= 27,345(113 - 13)

= 27,345 × 100

= 2,734,500

The ratios for the surface area, volume and width respectively are:

Ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, we are given the scale factor for this canoe is 3:14. Thus, the ratio of the surface area of the canoe model to the surface area of the original model would squared as follows:

Ratio of SA = 3²/14²

Ratio of SA = 9/196

Ratio of SA = 9:196.

For the volume, we would take the cube:

Ratio of V = 3³/14³

Ratio of V = 27/2,744

Ratio of V = 27:2,744.

For the width, we have:

Ratio of W = 3/14

Ratio of W = 3:14.

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Answer: -2

Step-by-step explanation:

When x = 0, y = -2.

So, f(0) = -2.

Answer:

236,181+150,486=386,667

Answer: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

The last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.

A few fundamental principles apply to density curves:

Following the rules above, we can see from graph B that the curve is above the horizontal axis. That shows that the probabilities are positive which is a necessity. Moreover, the area under the curve must also be 1. That is also satisfied.

Hence, the last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.

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Question 14

As we approaching from the negative side, [tex]|x-3|=3-x[/tex].

So, we have [tex]\lim_{x \to 3^{-}}=\frac{3-x}{x-3}=\frac{-(x-3)}{x-3}=\boxed{-1}[/tex]

and thus the limit exists at x=3.

Question 15

For the top part of the function, [tex](9-9)^{2}=0[/tex]

For the bottom part of the function, [tex]9-9=0[/tex]

As both one-sided limits are equal, L = 0, and thus the limit exists at x=9.

The sample standard deviation is 2.45.

Standard deviation measures the spread of a dataset around its mean. The variance measures the average degree to which each data point differs from the mean.

The standard deviation is the square root of the variance.

Standard deviation = √6 = 2.45

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Answer:

D

Step-by-step explanation:

Converting percent to decimal : 2.2/100 = 0.022

Finding 2.2$ of $75k : 75,000 x 0.022 = $1,650 (also the increase in one year)

Finding how much it was worth after 11 years :

(75,000 x 0.022) x 11 = $18,150 or 1,650 x 11 = $18,150

Now add the product to the regular amount to find out the answer:

75,000 + 18,150 = $93,150 (which is how much it increased after 11 years)

The future value of the annuity after the end of 5 years is $552.56.

Given that, r =5%= 0.05, 5 years  = 5 yearly payments, so n = 5, and P = $100.

The formula to find the annuity formula [tex]FV=\frac{P \times ((1+r)^{n}-1 )}{r}[/tex].

Now, [tex]FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}[/tex]

⇒FV = 100 × 55.256

⇒FV = $552.56

Therefore, the future value of the annuity after the end of 5 years is $552.56.

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Answer:

Step-by-step explanation:

y = mx + b is the formula to figure out your question

Now, the equation ( y = 28x + 8)

Already shows the m and b

m = 28

b = 8

Hope this helps! :)

If not ask me in the comments about your question and I’ll answer

Answer:

100

Step-by-step explanation:

10^2 is 100 therefore it is 100

The inverse of the function f(x) = 2x + 5 is; f⁻¹(x) = (x - 5)/2

An inverse function in mathematics is function which reverses the another function.

We want to find the inverse of the function; f(x) = 2x + 5

Thus;

Step 1; y = 2x + 5

Step 2; Subtract 5 from both sides to get;

y - 5 = 2x

Step 3;  Since we want to find the inverse of f(x), then we now have;

x - 5 = 2y

Step 4: Divide both sides by 2 to get;

(x - 5)/2 = y

Step 5; Thus, we have;

f⁻¹(x) = (x - 5)/2

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Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.

En esta situación, Julio debe pagar por 29 fotocopias de los apuntes de un  compañero suyo. El monto a pagar es el producto del número de copias y el coste unitario de cada fotocopia, es decir:

x = (0.30 PEN) · (29)

x = 8.70 PEN

Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.

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There are 8,709,120 ways to arrange the people around the table

The given parameters are:

People = 13

Actors = 9

If the actors must seat together, then the actors must be grouped as 1.

The 9 actors can be arranged in 9! ways

Now, we have 1 group + 4 individuals.

This equals 5 people (in theory)

The 5 people can be arranged in 5! ways

So, the number of ways is

Ways= 9! * 5!

Evaluate

Ways = 8,709,120

Hence, there are 8,709,120 ways to arrange the people around the table

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Answer:

b

Step-by-step explanation:

15/8

All the options are incorrect. the required average is (3x-9)/2.

Thermometer A reads xº.
Thermometer B reads 2° below the reading on thermometer A = x-2
Thermometers C and D each read 4° less than twice the reading on thermometer  = 2(x-2)-4

Average of the values is the ratio of total sum of values to the number of values.

As per question,
A=x
B = x-2
C.D = 2(x-2)-4= 2x-8
Average = A + B + C + D /4
= x+x-2+2x-8+2x-8/4
= 6x-18/4
= 3x-9/2

Thus, the required average of temperature = 3x-9/2.

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Answer:

Whats the question then?

Step-by-step explanation:

Answer:

x>=2 so B

Hope this helps :)

if the perimeter=s+s+s+s

=x+x+x+x

Answer:

B. 30

Step-by-step explanation:

3x + 2x + x = 180 (angle sum of a triangle is 180)

6x = 180

x = 30

Answer:

B. 30

Step-by-step explanation:

3x + 2x + x = 180

             6x = 180

               x = 180/6

               x = 30

In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.

a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.

b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.

c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.

d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.

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From the given options A and option D are the possible equations will be;

                x² + (y – 3)² = 36

      or,      x² + (y + 8)² = 36

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

Here, General equation of circle

   (x - a)² + (y - b)² = r²

where, (a, b) are the coordinates of center

           and r is the radius of circle.

Now, given data; Diameter = 12 units

                                 Radius  = 6 units

center lies on y-axis so coordinates will be (0, b)

   Equation of given circle

                    x² + (y - b)² = 6²

                     x² + (y - b) = 36

where, b may be any value on y-axis.

Thus, from the given options A and option D are the possible equations will be;

                x² + (y – 3)² = 36

      or,      x² + (y + 8)² = 36

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