If the probability of surviving a head on car accident at 55 mph is 0.097, then what is the probability of not surviving

Answer:

f(x) = (x + 4)(x - 4)(x + 3)

The other zeros of the function are at 4 and -3.

Step-by-step explanation:

Given function is f(x) = x³ + 3x² - 16x - 48.

Now, given that - 4 is a zero of the given function.

So, the function has a factor equals to (x + 4).  

Now, f(x) = x³ + 3x² - 16x - 48

⇒ f(x) = x³ + 4x² - x² - 4x - 12x - 48

⇒ f(x) = x²(x + 4) - x(x + 4) - 12(x + 4)

⇒ f(x) = (x + 4)(x² - x - 12)

⇒ f(x) = (x + 4)(x - 4)(x + 3)

Therefore, the other zeros of the function are at 4 and -3. (Answer)

Answer:

f(x) = (x + 4)(x - 4)(x + 3)

Step-by-step explanation:

Answer:

1.40f .

Step-by-step explanation:

One answer could be:

In March  the house had f + 40% of f

= f + 0.40f

= 1.40f

Answer:

If the February snowfall is valued as fs, the snowfall in March with an additional 40% could be expressed as:

Step-by-step explanation:

In the exercise it is mentioned that the snowfall in March was 40% higher than in February, if you wanted to express it in a mathematical function it could be mentioned that:

What could be represented as:

When calculating we would obtain:

500

Step-by-step explanation:

The median is always the middle line in the box of the data set even if the data set is uneven.

Answer: 30

Step-by-step explanation:

1:7

x:210

find x

210 is 30 times bigger than 7 so 30 is 30 times bigger than 1

30 is the answer

Answer:

30 blueberries

Step-by-step explanation:

divide the total by the 7, it's a lot simpler since it's a 1:7 but yeah so it's 30:210 blueberries to strawberries

Answer:

x = 1/4 when y = 8/3

Step-by-step explanation:

Divide both by 1/4

x = 1 when y = 32/3

When x = 1 1/8 = 9/8  

y = 32/3 x 9/8

y = 12

Answer:

31.5 hours

Step-by-step explanation:

time * speed = distance

speed=400/6=66.67 miles per hour

2100/(400/6)=31.5 hours

Answer:

[tex]a=15[/tex]

[tex]b=\frac{1}{3}[/tex]

Step-by-step explanation:

we have an exponential function of the form

[tex]y=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the base

Looking at the graph

we can see the ordered pairs (0,15) and (1,5)

(0,15) ---> y-intercept

so

The value of a is equal to

[tex]a=15[/tex]

substitute

[tex]y=15(b^x)[/tex]

with the point (1,5) find the value of b

For x=1, y=5

substitute in the exponential function

[tex]5=15(b^1)[/tex]

solve for b

[tex]5=15(b)[/tex]

[tex]b=\frac{1}{3}[/tex]

therefore

The exponential function is

[tex]y=15(\frac{1}{3}^x)[/tex]

Answer:

The value of positive integers are 21.22 and 12.11

Step-by-step explanation:

Given as :

The sum of squares of two integer = 698

Let The one positive integer be x

And The other positive integer be y

According to question

one positive integer = 3 less than twice the other positive integer

So, x = 2 × y - 3

I.e x = 2 y - 3

And x²  +  y² = 698

So, Put the value of x

I.e  ( 2 y - 3 )² +  y² = 698

or, 4 y² + 9 - 12 y +  y² = 698

Or, 5 y² - 3 y - 698 = 0

Now solving this quadratic equation

y = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

Or, y = [tex]\frac{3\pm \sqrt{-3^{2}-4\times 5\times -698}}{2\times 5}[/tex]

Or, y = [tex]\frac{3\pm \sqrt{13969}}{10}[/tex]

Or, y = [tex]\frac{3\pm 118.19}{10}[/tex]

∴ y = 12.11 , - 11.51

So , The value of y = 12.11

And the value of x = 2 × 12.11 - 3

I.e x = 21.22

Hence The value of positive integers are 21.22 and 12.11 Answer

To find the two integers, we can set up two equations based on the given information. By substituting the value of x from the first equation into the second equation, we can solve for y. Then, substituting the value of y back into the first equation, we can find the value of x.

To solve this problem, we can set up two equations based on the given information. Let's say the first integer is x and the second integer is y. We are given that x is 3 less than twice y, so we can write the equation: x = 2y - 3. We also know that the sum of their squares is 698, so the equation becomes x^2 + y^2 = 698. Now we can substitute the value of x from the first equation into the second equation and solve for y.

Substituting x = 2y - 3 into the equation x^2 + y^2 = 698, we get (2y - 3)^2 + y^2 = 698. Expanding this equation, we get 4y^2 - 12y + 9 + y^2 = 698. Combining like terms, we have 5y^2 - 12y + 9 = 698. Rearranging this equation and simplifying, we get 5y^2 - 12y - 689 = 0. Now we can solve this quadratic equation to find the value of y.

Using the quadratic formula, y = (-(-12) ± sqrt((-12)^2 - 4(5)(-689))) / (2(5)). Simplifying the equation further, we have y = (12 ± sqrt(144 + 13780)) / 10. Taking the positive value, y = (12 + sqrt(13924)) / 10. Evaluating this expression, we find y ≈ 9.7394. Now we can substitute this value back into the first equation to find x.

Using x = 2y - 3, we have x = 2(9.7394) - 3. Simplifying this equation, we get x ≈ 16.4788. Therefore, the two integers are approximately 16.4788 and 9.7394.

Final answer:

It will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

Explanation:

To determine the number of weeks it will take for the stock's price to reach $20.00 per share, we need to find the number of weeks it will take for the price to decrease from $62.50 to $20.00. Since the price is declining at a rate of 5% per week, we can set up an equation:

$62.50 - ($62.50  imes 0.05  imes  ext{number of weeks}) = $20.00

Simplifying the equation, we have:

$62.50 - (0.05  imes 62.50  imes  ext{number of weeks}) = $20.00

$42.50 = (0.05  imes 62.50  imes  ext{number of weeks})

Dividing both sides by 0.05 and 62.50, we get:

ext{number of weeks} =  rac{42.50}{0.05  imes 62.50}

Calculating this, we find that it will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

The equation 6(x + 2) = 5(x + 7) simplifies to x = 23, indicating it has one unique solution. Substituting back into the original equation verifies the solution.

To classify the equation 6(x + 2) = 5(x + 7) as having one solution, no solution, or infinitely many solutions, we first simplify the equation:

This provides us with one solution for the equation, which means the equation has a single unique solution. When we substitute x = 23 back into the original equation, we get an identity, confirming that our solution is correct.

Equations with a single solution, no solution, or an infinite number of solutions are encountered often in algebra. For example, 1+x+x² = 0 may have real or complex solutions and can demonstrate the principle that an nth degree polynomial has n solutions, which can include repeated or complex roots. The equation 205+111x +4x² - 31x³ - 10x4 +5x5=0 is a higher-degree polynomial that may require numerous iterations to find a solution, emphasizing the complexity of finding solutions for polynomial equations.

Answer:

x=-1189/36, y=242/9. (-1189/36, 242/9).

Step-by-step explanation:

-8x-16y=-166

8x+7y=-76

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

-9y=-242

9y=242

y=242/9

8x+7(242/9)=-76

8x=-76-1694/9

8x=-2378/9

x=(-2378/9)/8

x=-1189/36

Answer:

Slope (m)

-0.2222

m = 2 / -9 = -0.222

Step-by-step explanation:

Answer:

ΔB D E = ΔB F K, By rule A A S similarity

Step-by-step explanation:

a right angle is congruent to a right angle, so < B D E is congruent to

< B F K

< D B F is equal to < D B F

Side B D = B F is given

Thus, creating A A S similarity

Answer:

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment of Sara during her 1st year of college = US$ 2,000

Duration of the investment = 4 years

Annual interest rate = 3%

2. Let's find the future value of this investment after 4 years, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment of Sara during her 1st year of college = US$ 2,000

number of periods (n) = 4

rate (r) = 3% = 0.03

Replacing with the real values, we have:

FV = 2,000 * (1 + 0.03) ⁴

FV = 2,000 * (1.03) ⁴

FV = 2,000 * 1.12550881

FV = 2,251.02

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.

Answer:

2240

Step-by-step explanation:

angle = 125 degree because it is Vertically Opposite to the angle 1.

Answer:

The answer is: y = 1/2x + 2

Step-by-step explanation:

Given equation: y = 1/2x + 5

Given point: (-2, 1)

The slope of the given line is 1/2. Parallel lines have the same slope.

Use the point slope form and solve for y:

y - y1 = m(x - x1)

y - 1 = 1/2(x - (-2))

y - 1 = 1/2(x + 2)

y - 1 = 1/2x + 1/2 * 2

y - 1 = 1/2x + 1

y = 1/2x + 2

Proof:

f(-2) = 1/2(-2) + 2

= -1 + 2

= 1, giving point (-2, 1)

Hope this helps!! Have an Awesome Day!! :-)

Answer:

The measure of the diagonal is [tex]3\sqrt{6}\ units[/tex]

Step-by-step explanation:

Let

c -----> the diagonal of a square in units

a ----> the length side of a square

Remember that a square can be divided into two congruent right triangles

see the attached figure to better understand the problem

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+a^{2}[/tex]

we have

[tex]a=3\sqrt{3}\ units[/tex]

substitute

[tex]c^{2}=(3\sqrt{3})^{2}+(3\sqrt{3})^{2}[/tex]

[tex]c^{2}=54[/tex]

[tex]c=\sqrt{54}\ units[/tex]

simplify

[tex]c=3\sqrt{6}\ units[/tex]

Answer:

[tex]0.2[/tex] miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Step-by-step explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points [tex](0,3), (5,4),(10,5)...[/tex]

From these points we can find the slope of the line .

From point slope formula [tex]y-y_1=m(x-x_1)[/tex]

And assigning [tex](x,y) (0,3)[/tex] and [tex](x_1,y_1) (5,4)[/tex]

[tex]m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2[/tex]

This slope is also the speed of the bird which is [tex]0.2\ miles\ per\ minute.[/tex]

As by plugging the values of any coordinate point we can confirm this.

Lets put [tex](10,5)[/tex], y-axis is the distance so in [tex]10[/tex] minutes the the distance covered by the bird must be equal to to y-axis value which is [tex]5[/tex] miles.

[tex]y=0.2(x),y=0.2(10)=5\ miles[/tex]

Now as in [tex]t=0[/tex] the bird has started from y-intercept value [tex]3[/tex] so we can say that,the original distance of the bird from its nest is [tex]3\ miles[/tex].

So the correct choices are:[tex]B[/tex] and [tex]D[/tex]

The birds speed is [tex]0.2\ miles[/tex] per minute and is [tex]3\ miles[/tex] away from its nest.

Answer:

(d).

Step-by-step explanation:

The y-intercept (0, 3) is initial value of graph ⇒ (d). 3 miles; it represents the original distance of the bird from its nest

Answer: Line C

Step-by-step explanation: She added 12 to one side and subtracted 12 from another side when she should've added 12 to both sides.

The correct answer and work would be:

8x-3(2x+4)=10

8x-6x-12=10

2x-12=10

2x=22

x=11

Answer:9

Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.

Isolate the variable x by moving terms involving x to one side and constants to the other side. Simplify the equation step-by-step to find that x = 9.

To solve the equation 15 - 4x = 6 - 3x, we need to isolate the variable x. Follow these steps:

Therefore, the solution to the equation 15 - 4x = 6 - 3x is x = 9.

The solution to the differential equation [tex]\( \frac{dy}{dx} = \sqrt{x + 16} \)[/tex]with the initial condition y(0) = 0 is [tex]\( y = \frac{2}{3}(x + 16)^{3/2} - \frac{128}{3} \)[/tex].

To solve the differential equation [tex]\( \frac{dy}{dx} = \sqrt{x + 16} \)[/tex] with the initial condition y(0) = 0, we'll integrate both sides with respect to x.

Given:

[tex]\[ \frac{dy}{dx} = \sqrt{x + 16} \][/tex]

Integrating both sides:

[tex]\[ \int \frac{dy}{dx} \, dx = \int \sqrt{x + 16} \, dx \]\[ \int dy = \int \sqrt{x + 16} \, dx \]\[ y = \frac{2}{3}(x + 16)^{3/2} + C \][/tex]

Now, we'll apply the initial condition y(0) = 0 to find the value of the constant C:

[tex]\[ 0 = \frac{2}{3}(0 + 16)^{3/2} + C \]\[ 0 = \frac{2}{3}(16)^{3/2} + C \]\[ 0 = \frac{2}{3}(64) + C \]\[ C = -\frac{128}{3} \][/tex]

So, the particular solution to the differential equation with the initial condition is:

[tex]\[ y = \frac{2}{3}(x + 16)^{3/2} - \frac{128}{3} \][/tex]

Answer:

Step V: Transitive property of Inequality

Step VI: Subtraction Property of Inequality

Step-by-step explanation:

In Step IV, the RHS of t=both the sides are equal.

So, they equated the LHS of both the sides.

This is the transitive property of equality which states that if a = b and c = b then a = c.

In this case, a = [tex]$ \angle {m_1} + \angle {m_2}  $[/tex]

b = 180⁰

c = [tex]$ \angle {m_2} + \angle {m_3} $[/tex]

Consequently, [tex]$ \angle {m_1} + \angle {m_2} = \angle {m_2} + \angle {m_3} $[/tex]

In step VI, [tex]$ \angle {m_2} $[/tex] is subtracted on both the sides. So, this is called as Subtraction Property of Equality.

Answer:

Divide by 13, you will get 10x - 1

To factor the expression 130x - 13, find the greatest common factor, which is 13, and factor it out. The factored form is 13(10x - 1).

To factor the expression 130x - 13, you need to look for a common factor in both terms. In this case, both terms can be divided by 13, which is the greatest common factor of the two numbers. By factoring out 13, you get:

13(10x - 1)

This process is known as factoring by common factor or GCF factoring. It simplifies the expression to a product of a constant (13) and a binomial (10x - 1). This method is very useful in solving equations, simplifying expressions, and can be a first step in more complex factoring processes.

The equation of the line that parallel to x = -3 and passes through the point (4, -7) is y = -3x + 5

Solution:

The two forms of writing a point and slope in equation are point slope form and standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

The given point is (4,-7) and the slope is -3.

The slopes of parallel lines are always equal.

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The equation of line in point slope form is given as:

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

[tex]\begin{array}{l}{y-(-7)=-3(x-4)} \\\\ {y+7=-3(x-4)} \\\\ {y+7=-3 x+12}\end{array}[/tex]

y = -3x + 5

Now, let us convert this equation to standard form

3x + y = 5

Thus the equation of line in point slope and standard form is found out

Answer: 20/27

Step-by-step explanation:

multiply numerators and denominators

1/3 x 20/9 = 20/27

you can not simplify further

Answer:

1,187 bu/hr

Step-by-step explanation:

4.8 mi/hr

240 inches

Efficiency: 85% (0.85)

120 bushels/acre

1 acre = 6 272 640

1 mile = 63 360 inches

4.8 miles = 304 128 inches

120/6 272 640 x 240 = 5/1089 (bushels/inch)

5/1089 x 304 128 x 85% = 1 186.9 = 1187 bu/hr

Wow, that's hard for me :) Hope it's helpful

Answer:

- 0.183

Step-by-step explanation:

Given that [tex]\sin \theta = \frac{1}{3}[/tex]

and [tex]\frac{\pi }{2} < \theta  < \pi[/tex]

We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

Now, [tex]\sin \theta = \frac{1}{3}[/tex]

⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]

Now, since  [tex]\frac{\pi }{2} < \theta  < \pi[/tex],

So, [tex]\theta  = 180 - 19.47 = 160.53[/tex]

{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]

Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]

Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

= [tex]\sin 190.52[/tex]

= - 0.183 (Approximate) (Answer)

Answer:

The second city is 54 miles behind the first city

Step-by-step explanation:

The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.  

The speed of the second bus is then 54/0.6 = 90 mph

When 1 and a half hour has passed, the first bus has moved a distance of

[tex]X_1=54\times 1.5[/tex] = 81 miles

The second bus (behind the first bus) has moved

[tex]X_2=90\times 1.5[/tex] = 135 miles

The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city

So, the second city is 54 miles behind the first city

Answer:

w(-15-w)= 0

w= 0 or (-15-w) = 0

Now,

-15-w =0

w= -15

So,The solution of w(-15-w) = 0

w= 0, -15

Answer:

w=-15,0

Step-by-step explanation:

w(-15-w)=0

-15w-w^2=0

-(w^2+15w)=0

w(w+15)=0

w=-15,0