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A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400

Answer:

1 - Correct

2 - incorrect

3- incorrect

4 - incorrect

5 - Correct

Step-by-step explanation:

Notice that

3x  + 5 + 4x -1  =    3x + 4x + 5 -1 = 7x  + 4

therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore

1 - Correct

Since that is true for all numbers  

2 - incorrect

3- incorrect

4 - incorrect

The expressions are equivalent for all numbers therefore

5 - Correct

Answer: 19!!

Step-by-step explanation:

Answer:

1/2x

Step-by-step explanation:

To find the slope of a line with only 2 points we use the following formula.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex],

So we fill it in with the following points,

(7,1)

(5,0)

0 is y2 and 1 is y1 0-1 = -1

5-7 = -2

Slope: 1/2

Thus,

the slope of the line is 1/2.

Hope this helps :)

Answer:

[tex]m < C = 60[/tex]

Step-by-step explanation:

From the given right angled triangle, ∆ABC,

[tex] BC = Hypotenuse = 2\sqrt{11} [/tex]

[tex] AC = Adjacent = \sqrt{11} [/tex]

Thus, m<C can be found by applying the following trigonometric ratio formula as shown below:

[tex] cos(C) = \frac{adjacent}{hypotenuse} [/tex]

[tex] cos(C) = \frac{\sqrt{11}}{2\sqrt{11}} [/tex]

Evaluate: √11 cancels √11

[tex] cos(C) = \frac{1}{2} [/tex]

[tex] cos(C) = 0.5 [/tex]

[tex] C = cos^{-1}(0.5) [/tex]

[tex] C = 60 [/tex]

[tex]m < C = 60[/tex]

Answer: 120 ice creams total

The answer is option D

you can use the value of sin\

sin(theta) = 12/16

Now solve for theta, and do inverse sine

so theta would be 48.59037789 , or around 50 degrees

Answer:

Step-by-step explanation:

Since, it is a right triangle.

Perpendicular (p) = 12

hypotenuse ( h) = 16

now,

[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{12}{16} [/tex]

[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]

[tex]x = 48.59 \: degree[/tex]

hope this helps...

good luck on your assignment..

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

Answer:

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]

Step-by-step explanation:

Hey there!

Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.

Look at the image below ↓

By looking at the image we can conclude that the equation for the perpendicular line is,

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].

Hope this helps :)

Answer:

[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]

Step-by-step explanation:

Part 1: Finding the new slope of the line

Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.

Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].

Part 2: Using point-slope formula and solving in slope-intercept form

Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].

Then, use the point-slope equation to get b, or the y-intercept of the equation.

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

5x+8y+2z = 68

Step-by-step explanation:

Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:

The equation for the plane passing through the point is expressed as;

a(x-x0)+b(y-y0)+c(z-z0) = 0 where;

(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.

Given the point (2, 5, 9) and normal vector n =(5, 8, 2)

x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.

Substituting this values into the equation of the plane above will give;

5(x-2)+8(y-5)+2(z-9) = 0

On expansion:

5x-10+8y-40+2z-18 = 0

5x+8y+2z-10-40-18 = 0

5x+8y+2z-68 = 0

The required equation of the plane is 5x+8y+2z = 68

Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

Answer:y=Mx+b

Step-by-step explanation:

Answer:

y = 1.44

Step-by-step explanation:

What are you aiming to do here?  Please share all instructions with each problem.

If you want to solve 4.5/y = 12.5/4 for y:  Multiply both sides by 4y:

18 = 12.5y.  Then y = 1.44

Answer:

$300

Step-by-step explanation:

The couch is sold in two ways; outright payment or installment payment.

Outright payment would cost = $820

Installment payment = down payment + monthly charges

Down payment = $400

Monthly charges for a period of one year (12 months) = 12 × $60

                                         = $720

Installment payment would cost = $400 + $720

                                            = $1120

Amount saved by paying total amount at the time of purchase = $1120 - $820

                                             = $300

Thus, the outright buying the couch would save $300.

Answer: 10.246950766

Step-by-step explanation:

based on Pythagorean’s theorem:

[tex]\sqrt{19^{2}-16^{2} } =\sqrt{105} = 10.246950766[/tex]

Answer:

Time taken = 6 sec (Approx)

Step-by-step explanation:

Given:

Total distance = 1/12 mi = 0.083333

Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps

Find:

Time taken

Computation:

Time taken = Total distance / Speed

Time taken = Total distance / Speed of train

Time taken = 0.0833333 / 0.01388889

Time taken = 6 sec (Approx)

Answer:

1) Amplitude; A = 80 ft

Period = 60 ft

2)y = 80 sin ((π/30)x - 5π) + 80

3)y = 40 sin ((π/30)x - 5π) + 80

4)y = 40 sin ((π/30)x - 5π) + 40

5)y = -65sin ((π/30)x - 5π) + 80

Step-by-step explanation:

The general formula for sinusoidal wave equation is given by;

y = A sin (Bx - C) + D

Where;

A is amplitude = D_max or  D_min

Period = 2π/B

So; B = 2π/Period

Phase Shift = C/B  

So; C = B · Phase Shift

D: center

We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Thus; A = 80 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

1) From the calculations above,

Amplitude; A = 80 ft

Period = 60 ft

2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;

y = 80 sin ((π/30)x - 5π) + 80

3) In this, since the sine wave is half as tall, then after the changes, we have;

y = 40 sin ((π/30)x - 5π) + 80

4) since they have moved closer, then equation is now;

y = 40 sin ((π/30)x - 5π) + 40

5) We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;

D_min = 80 - 15 = 65. Thus; A = 65 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

The band ends down (at 15 feet) and thus A is negative

The equation is;

y = -65sin ((π/30)x - 5π) + 80

Part(1): The required values are,

Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]

Part(2):

The equation of the sine function is

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]

Part(3):

The equation of the sine curve is,

[tex]y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The equation of the  sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

The required graph is attached below,

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position

Part(1):

Amplitude=[tex]\frac{1}{2} width=80ft[/tex]

Period=[tex]2\times 30=60 sec[/tex]

Part(2):

Let the equation be,

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]

Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,

[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]

Part(3):

Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,

Amplitude=40 ft

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The graph shifts downward 40 ft then,

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]

End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]

The graph is attached below:

Learn more about the topic of Simple harmonic motion:

https://brainly.com/question/14446439

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

[tex]a^2+ b^2 = c^2[/tex]

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

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

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

Answer:

(D) -2,-3

Step-by-step explanation:

From the origin, we can find the current position of point B by counting.

B is 2 to the left of the y-axis, meaning that it's x value is -2.

B is 3 down of the x-axis, making it's y value -3.

Therefore, the coordinates of point B are -2,-3.

Hope this helped!

Answer: (D) -2,-3

Step-by-step explanation:

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Answer:

a

   [tex]P(X = 10 ) = 0.0096[/tex]

b

   [tex]P(X = 10 ) = 0.0085[/tex]

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  [tex]p = 0.35[/tex]

     The number of success we are considering is  r = 10  

Now the probability of failure is mathematically evaluated as

        [tex]q = 1- p[/tex]

substituting value

       [tex]q = 1- 0.35[/tex]

       [tex]q = 0.65[/tex]

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

    [tex]P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}[/tex]

substituting values

    [tex]P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}[/tex]

Where  [tex][\left 15 } \atop {10}} \right. ][/tex] mean 15 combination 10  which is evaluated with a calculator to obtain  

       [tex][\left 15 } \atop {10}} \right. ] = 3003[/tex]

So

      [tex]P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}[/tex]

       [tex]P(X = 10 ) = 0.0096[/tex]

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

  [tex]P(X = r ) = P( r < X < r )[/tex]

Applying continuity correction

          [tex]P(X = r ) = P( r -0.5 < X < r +0.5)[/tex]

substituting values

        [tex]P(X = 10) = P( 10-0.5 < X < 10+0.5)[/tex]

       [tex]P(X = 10 ) = P( 9.5 < X < 10.5)[/tex]

Standardizing  

         [tex]P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )[/tex]

The  where  [tex]\mu[/tex] is the mean which is mathematically represented as

        [tex]\mu = n * p[/tex]

substituting values

        [tex]\mu = 15 * 0.35[/tex]

         [tex]\mu = 5.25[/tex]

The standard deviation is evaluated as      

     [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

    [tex]\sigma = \sqrt{15 * 0.35 * 0.65 }[/tex]

    [tex]\sigma = 1.8473[/tex]

Thus  

     [tex]P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )[/tex]

     [tex]P(X = 10 ) = P( 2.30 < Z < 2.842 )[/tex]

     [tex]P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )[/tex]

From the normal distribution table we obtain the [tex]P(Z < 2.841)[/tex] as

      [tex]P(Z < 2.841) = 0.99775[/tex]

And  the  [tex]P(Z < 2.30)[/tex]

     [tex]P(Z < 2.30) = 0.98928[/tex]

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

    [tex]P(X = 10) = 0.99775 - 0.98928[/tex]

     [tex]P(X = 10 ) = 0.0085[/tex]

Looking at the calculated values for question a and b  we see that the values are fairly different.

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

Learn more about differentiation here:

https://brainly.com/question/24898810

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Answer:

144 people competed in the Chess Tournament

Step-by-step explanation:

So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.

After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

Answer:

A

Step-by-step explanation:

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