The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.

Answer:

x=10/3

Step-by-step explanation:

isolate the variable

Answer:

1. x = 4

2. x = 10/3

Step-by-step explanation:

1. 3x - 5 = 3 + x

3x - x = 3 + 5

2x = 8

x = 4

2. x/2 + 5/9 = 2x/3

(x/2 + 5/9) * 18 = (2x/3) * 18

9x + 10 = 12x

10 = 12x - 9x

10 = 3x

x = 10/3

25/250 = 1/10

I do not know that much english. I an spanish so I might have done it wrong.

the probability that the horse is at least 25 feet away from all boundary lines is 0.5

To calculate the probability that the horse is at least 25 feet away from all boundary lines in an enclosed pasture that is 150 feet by 200 feet, we need to consider the available space for the horse to roam.

The area of the pasture is given by:

Area = Length * Width = 150 feet * 200 feet = 30,000 square feet

Now, let's consider the area where the horse must stay within at least 25 feet away from all boundary lines. We can imagine this as a rectangular strip along the inner boundary of the pasture, with dimensions reduced by 50 feet on each side.

The dimensions of this rectangular strip would be:

Length = 150 feet - 2 * 25 feet = 100 feet

Width = 200 feet - 2 * 25 feet = 150 feet

The area of this rectangular strip is given by:

Area_strip = Length * Width = 100 feet * 150 feet = 15,000 square feet

Therefore, the probability that the horse is at least 25 feet away from all boundary lines is:

Probability = Area_strip / Area = 15,000 square feet / 30,000 square feet = 0.5

The probability is 0.5 or 50%.

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Answer:

The 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two population mean is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]

Compute the value of sample means and sample standard deviations from the provided data.

[tex]\bar x_{1}=3.142\\\\\bar x_{2}=3.882\\\\s_{1}=0.4396\\\\s_{2}=0.4283\\n_{1}=n_{2}=5[/tex]

The critical value of t for 98% confidence level and (n - 1) = 4 degrees of freedom is:

[tex]t_{\alpha/2, (n-1)}=t_{0.02/2, 4}=3.747[/tex]

Compute the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities as follows:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]

     [tex]=(3.142-3.882)\pm3.747\cdot\sqrt{\frac{0.4396^{2}}{5}+\frac{0.4283^{2}}{5}}\\\\=-0.74\pm 1.0285\\\\=(-1.7685, 0.2885)\\\\\approx (-1.77, 0.29)[/tex]

Thus, the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).

Answer:

a) 17.6 + 5.4i

b) 37.6

Step-by-step explanation:

a) (9 + 9.4i) + (8.6 - 4i)

Collect like terms:

9 + 8.6 + 9.4i - 4i

= 17.6 + 5.4i

b) (9.4i)(-4i)

Expand the brackets:

9.4 * -4 * i *  i

[tex]i = \sqrt{-1}[/tex]

Therefore, i * i = -1

=> (9.4i)(-4i) = -37.6 * -1

= 37.6

Answer:

The answer is

Step-by-step explanation:

a + b + c

a = 5 b = - 1 c = - 8

Substitute the values of a , b , c into the above expression

That's

5 + ( - 1) + ( - 8)

5 - 1 - 8

Subtract the numbers

4 - 8

We have the final answer as

Hope this helps you

Answer:

-4

Step-by-step explanation:

5 + - 1 - 8= -4

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](3;\ 9)\to x_1=3;\ y_1=9\\(1;\ 1)\to x_2=1;\ y_2=1[/tex]

Substitute:

[tex]m=\dfrac{1-9}{1-3}=\dfrac{-8}{-2}=4[/tex]

Answer:

m=4

Step-by-step explanation:

Slope can be found using the following formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are points on the line.

We are given the points (3,9) and (1,1). Therefore,

[tex]x_{1}=3\\y_{1}=9 \\x_{2}=1\\y_{2}=1[/tex]

Substitute each value into the formula.

[tex]m=\frac{1-9}{1-3}[/tex]

Subtract in the numerator first.

[tex]m=\frac{-8}{1-3}[/tex]

Subtract in the denominator.

[tex]m=\frac{-8}{-2}[/tex]

Divide.

[tex]m=4[/tex]

The slope of the line is 4.

Answer:

y=-2

Step-by-step explanation:

5 (y-1)+6= -9

Subtract 6 from each side

5 (y-1)+6-6= -9-6

5 ( y-1) = -15

Divide by 5

5(y-1)/5 = -15/5

y-1 = -3

Add 1 to each side

y-1+1 = -3+1

y = -2

Answer:

slope of the line through (3, 7) and (-1, 4) is

[tex]m = \frac{4 - 7}{ - 1 - 3} \\ \\ = \frac{ - 3}{ - 4} \\ \\ = \frac{3}{4} [/tex]

Hope this helps you

Answer:

3/4

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

   = (4-7)/(-1-3)

   = -3/-4

   = 3/4

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{3375} - \sqrt[4]{38416}[/tex]

Factorizing 3375 gives 15 * 15 * 15 which equals 15^3 and factorizing 38416 gives 14 * 14 * 14 * 14 which equals 14^4

=> [tex]\sqrt[3]{15^3} - \sqrt[4]{14^4}[/tex]

=> 15 - 14

=> 1

Answer:

Step-by-step explanation:

[tex] \sqrt[3]{3375} - \sqrt[4]{38416} [/tex]

Calculate the cube root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{38416} [/tex]

Calculate the root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{ {14}^{4} } [/tex]

[tex] {15}^{ \frac{3}{3} } - {14}^{ \frac{4}{4} } [/tex]

[tex]15 - 14[/tex]

Subtract the numbers

[tex]1[/tex]

Hope this helps...

Answer:

Triangle D is your answer.

Answer:

Hey there!

Triangle C is unique, as one side and two angles determine a unique triangle.

Hope this helps :)

Answer:

D

Step-by-step explanation:

It is a trinomial with a degree of 3.

This is the correct answer on the exam.

Answer:

To make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.

To make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.

To make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.

see explanation below

Step-by-step explanation:

If the ingredients to make 1 pancake is as follows:

1 1/2  cups all-purpose flour; 31/2 teaspoons baking powder; 1 teaspoon salt.

1 tablespoon white sugar.; 1 1/4 cups milk; 1 egg; and 3 tablespoons butter.

Then to make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.

cups all-purpose flour =16× 1 1/2

=  16×3/2 = 24

teaspoons baking powder = 16 ×7/2 = 56

teaspoon salt = 1×16 = 16

tablespoon white sugar= 1×16 = 16

cups milk= 16×5/4 = 20

egg= 1×16 = 16

tablespoons butter= 3×16 = 48

Then to make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.

cups all-purpose flour =4× 1 1/2

=  4×3/2 = 6

teaspoons baking powder = 4 ×7/2 =14

teaspoon salt = 1×4 = 4

tablespoon white sugar= 1×4 = 4

cups milk= 4×5/4 = 5

egg= 1×4 = 4

tablespoons butter= 3×4 = 12

Then to make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.

cups all-purpose flour =12× 1 1/2

=  12×3/2 = 18

teaspoons baking powder = 12 ×7/2 =42

teaspoon salt = 1×12 = 12

tablespoon white sugar= 1×12 = 12

cups milk= 12×5/4 = 15

egg= 1×12 = 12

tablespoons butter= 3×12 = 36

The operation applied is multiplication with each fraction.

Answer:

300

Step-by-step explanation:

A(dd): 4+5= 9

D(ivide): 540/9 = 60

T(imes): 4 x 60= 240 beads

             5 x 60= 300 beads

I hope this helped :)

Number of larger share of beads is 300 seeds

Given that;

Number of total beads = 540

Beads ratio = 4:5

Find:

Number of larger share of beads

Computation:

Number of larger share of beads = 5[540 / (4+5)]

Number of larger share of beads = 5[540 / 9]

Number of larger share of beads = 5[60]

Number of larger share of beads = 300 seeds

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Answer:

8n6

step by step explanation.

Answer:

0.31 ft/s

Step-by-step explanation:

The volume of a cone is given by the formula:

V = πr²h/3

From the question, we are given the diameter and the height to be equal, thus;

r = h/2

Putting h/2 for r into the volume equation, we have;

V = (π(h/2)²h)/3

V = πh³/12

Using implicit derivatives,we have;

dV/dt = (πh²/4)(dh/dt)

From the question, we want to find out how fast is the height of the pile increasing. This is dh/dt.

We have;

dV/dt = 35 ft³/min and h = 12ft

Plugging in the relevant values, we have;

35 = (π×12²/4)(dh/dt)

dh/dt = (35 × 4)/(144 × π)

dh/dt = 0.3095 ft/s ≈ 0.31 ft/s

Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.

Step-by-step explanation:

Complete question is provided in the attachment below.

Formula: The average rate of change for this function y=f(x) for the interval from  x= a to x= b :

[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]

Let y= f(x) for the given table:

At x= 3 , f(3)=8 and f(5)=32

Then, the average rate of change for this function for the interval from x=3 to x=5:

[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]

Hence, the average rate of change for this function for the interval from x=3 to x=5  is 12.  (Option A is correct.)

Answer:

Beryllium, 2 times

Step-by-step explanation:

1.12×10⁻¹⁰ has a higher exponent than 5.6×10⁻¹¹.

-10 > -11

The ratio between them is:

(1.12×10⁻¹⁰) / (5.6×10⁻¹¹)

(1.12 / 5.6) (10⁻¹⁰ / 10⁻¹¹)

0.2 × 10¹

2

Answer:

[tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex]

Step-by-step explanation:

Let be [tex]f(x) = \frac{3}{5}-\frac{8}{x}[/tex] and [tex]F[/tex] is the antiderivative of [tex]f(x)[/tex] such that:

1) [tex]F = \int {\left(\frac{3}{5}-\frac{8}{x} \right)} \, dx[/tex] Given.

2) [tex]F = \frac{3}{5} \int \, dx -8\int {\frac{dx}{x} }[/tex] ([tex]\int {[f(x)+g(x)]} \, dx = \int {f(x)} \, dx + \int {g(x)} \, dx[/tex])

3) [tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex], where [tex]C[/tex] is the integration constant. ([tex]\int {k} \, dx = k\cdot x[/tex]; [tex]\int {\frac{dx}{x} } = \ln|x|[/tex], [tex]\int {k\cdot f(x)} \, dx = k\int {f(x)} \, dx[/tex]) Result.

Answer:

It takes the crew 12 days to clear the bush.

Step-by-step explanation:

Given clears 2/3 acres / 2 days, or 1/3 acre per day

Time to clear 4 acres

= 4 / (1/3)

= 4 * (3/1)

= 12 days

Answer:

The answer is option C

Step-by-step explanation:

To find the length of AB we use sine

sin∅ = opposite / hypotenuse

From the question

The hypotenuse is AB

The opposite is AC

So we have

sin 54 = AC/AB

sin 54 = 16 / AB

AB = 16/sin 54

AB = 19.777

Hope this helps you

Answer:

AB = 19.78

Step-by-step explanation:

From the diagram (Right-angle triangle):

AC = 16

AB = ?

Angle = 54°

Applying trig ratio:

Tan 54° = 16/BC

1.376381920 = 16/BC

Therefore;

BC = 16/1.376381920

BC = 11.62

To solve the length AB:

Cos 54° = BC/AB

0.587785252 = 11.62/AB

Solving AB gives:

AB = 11.62/0.587785252

AB = 19.78

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

cosΘ = - [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Given that Θ is in the third quadrant then cosΘ < 0

Given

tanΘ = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13

Thus

cosΘ = - [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{12}{13}[/tex]

Answer:

Step-by-step explanation:

In algebra, we always need to follow a set of steps that involve undoing the operations that led to the equation to reveal the value of x.

e < -12

(Since we divided by a negative number, we must reverse the inequality sign.)

(-1/6)(-12) > 2

2 > 2 ✅

Now we check a number less than -12, such as -14.

(-1/6)(-14) > 2

2 1/3 > 2 ✅

Answer:

There will be $4450 left at the end of the year.

Step-by-step explanation:

We first take 11% and multiply it by $5,000. We get 550. This means that the account will lose $550. Next, we take our original amount, $5,000, and subtract $550 from it. We will get $4450.

Correct question:

A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given

approximately by the function H(t) = - 0.0004.x2 + 2.582 + 700, where H is measured in

feet above the river and is the horizontal distance from his launch ramp.

How high above the river was the launch ramp?

What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?

Answer:

A) 700 feet ; 4866.7025 feet above the river

3227.5 Feets from the ramp

Step-by-step explanation:

Given the Height function:

H(t) = 0.0004x^2 + 2.582x + 700

H = height in feet above the river

x = horizontal distance from launch ramp.

How high above the river was the launch ramp?

H(t) = - 0.0004x^2 + 2.582x + 700

To find height of launch ramp above the river, we set the horizontal distance to 0, because at this point, the motorcycle stunt rider is on the launch ramp and thus the value of H when x = 0 should give the height of the launch ramp above the river.

At x = 0

Height (H) =

- 0.0004(0)^2 + 2.582(0)+ 700

0 + 0 + 700 = 700 Feets

B) Maximum height abive the river and how far the rider is from the ramp when maximum height is reached :

Taking the derivative of H with respect to x

dH'/dx = 2*-(0.0004)x^(2-1) + 2.582x^(1-1) + 0

dH'/dx = 2*-(0.0004)x^(1) + 2.582x^(0) + 0

dH'/dx = - 0.0008x + 2.582

Set dH'/dx = 0 and find x:

0 = - 0.0008x + 2.582

-2.582 = - 0.0008x

x = 2.582 / 0.0008

x = 3227.5 feets

To get vertical position at x = 0

Height (H) =

- 0.0004(3227.5)^2 + 2.582(3227.5)+ 700

- 4166.7025 + 8333.405 + 700

= 4866.7025 feet

4866.7025 feet above the river

3227.5 Feets from the ramp

Using quadratic function concepts, it is found that:

The height after x seconds is given by the following equation:

[tex]H(x) = -0.0004x^2 + 2.582x + 700[/tex]

Which is a quadratic equation with coefficients [tex]a = -0.0004, b = 2.582, c = 700[/tex]

The height of the ramp is the initial height, which is:

[tex]H(0) = -0.0004(0)^2 + 2.582(0) + 700 = 700[/tex]

Thus, the launch ramp was 700 feet above the river.

The maximum height is the h-value of the vertex, given by:

[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

Then, substituting the coefficients:

[tex]h_{MAX} = -\frac{(2.582)^2 - 4(-0.0004)(700)}{4(-0.0004)} = 4866.7[/tex]

The maximum height is of 4866.7 feet.

The horizontal distance is the x-value of the vertex, given by:

[tex]x_V = -\frac{b}{2a} = -\frac{2.582}{2(-0.0004)} = 3227.5[/tex]

The ramp was 3227.5 feet along when he reached maximum height.

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Answer:

62

Step-by-step explanation:

Turn 4 and 1/2 into a decimal.

4.5

Divide 279 by 4.5

279/4.5=62

You can cut 62 4 and 1/2 inch pieces.

Answer: (x^2-1)(x^2+1)=(x-1)(x+1)(x^2+1)

Step-by-step explanation:

(x²+1)(x²-1) are factors of polynomial x4-1 and  x=1,-1, i are the roots of x⁴ − 1.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

The given polynomial is Q(x) =  x⁴ − 1.

We can write it as (x²)²-1²

We have a algebraic formula which is

a²-b²=(a+b)(a-b)

Similarly

(x²)²-1²=(x²+1)(x²-1)

Now let us find the roots of factors (x²+1) and (x²-1)

x²+1=x=√-1=i,-i

x²-1=x=1,-1

The multiplicity of the roots is always one.

Hence (x²+1)(x²-1) are factors of polynomial x4-1 and  x=1,-1, i are the roots of x⁴ − 1.

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Answer:

ΔV = 865.51 mm^3

Step-by-step explanation:

In order to calculate the difference in volume between both baseballs you use the following formula for the volume of a sphere:

[tex]V=\frac{4}{3}\pi r^3[/tex]       (1)

where r is the radius of he sphere.

You calculate the volume of each sphere:

First baseball:

radius = 23.2mm/2 = 11.61mm

[tex]V_1=\frac{4}{3}\pi (11.61mm)^3=6555.18\ mm^3[/tex]

Second baseball:

radius = 24.2mm/2 = 12.1mm

[tex]V_2=\frac{4}{3}\pi (12.10)^3=7420.70\ mm^3[/tex]

Then, the difference in the volumen of both spheres is:

[tex]\Delta V=V_2-V_1=7420\ mm^3-6555.18\ mm^3=865.51\ mm^3[/tex]

Answer:

SOHCAHTOA

Step-by-step explanation:

Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.

Answer: SOHCAHTOA

Step-by-step explanation:

The pneumonic I learned is SOH-CAH-TOA.  it says that Sin = opposite/hypotenuse.  Cos = adjacent/hypotenuse.  Tan = opposite/adjacent.

Hope it helps <3