The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.
Find the equation for the relationship between the distance and number of seconds:A linear function containing one dependent and one independent variable.
It can be represented using the equation,
y = mx + c
where m is the slope
It is given in the question that,
Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.
After 4 seconds of driving, she was 70 meters away from the safe zone.
Let, D(t) be the distance to the safe zone (measured in meters) and t be the time (measured in seconds)
After 4 seconds of driving, she was 70 meters away from the safe zone.
⇒ This means that at t = 4 seconds, D(4) = 70 meters
Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative
⇒ m = - 24
y = mx + c
⇒ D(t) = (-24)t + c
Put t = 4,
D(4) = (-24)4 + c
70 = -96 + c ⇒ c = 166
⇒ D(t) = 166 - 24t
Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.
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Application
I
3. Ray has a stride of about 1.4 m. He runs 9 km daily to train for a marathon. Approximately
how many strides does he need to run 9 km?
He needs to run with approximately 6429 for a distance of 9 km
How to determine the number of strides?The given parameters are:
Length of stride = 1.4 m
Distance for marathon = 9 km
The number of strides needed is then calculated as:
Number of stride = Distance for marathon/Length of stride
Substitute the known values in the above equation
Number of stride = 9km/1.4m
Convert km to m
Number of stride = 9000m/1.4m
Evaluate the quotient
Number of stride = 6428.57143
Approximate the estimate
Number of stride = 6429
Hence, he needs to run with approximately 6429 for a distance of 9 km
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X
Erica works 30 hours/week for
$10/hour, but she must pay $30 in
taxes. What is her take-home income?
Answer:
$270
Step-by-step explanation:
Find her gross income....then subtract taxes:
30 hr/week * $10/hr - $ 30 = $270
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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A 12-yard-long pipe is cut into three equal sections. Two of the resulting sections are cut in half, and one of the halves is cut into thirds. If two pipe sections are chosen and combined end to end, what is the difference between the longest possible and shortest possible combinations? (Note: 1 yard = 3 feet)
Answer:
14ft
Step-by-step explanation:
12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.
Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cumulative preferred 3% stock, $20 par and 400,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $32,000; second year, $72,000; third year, $80,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00".
The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:
Cumulative Preferred Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $40,000 $36,000 $36,000
Outstanding shares 60,000 60,000 60,000 60,000
Dividend per share $0.53 $0.67 $0.60 $0.60
Common Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $0 $32,000 $44,000 $64,000
Outstanding shares 400,000 400,000 400,000 400,000
Dividend per share $0 $0.08 $0.11 $0.16
Data and Calculations:3% Cumulative Preferred Common Stock
Outstanding shares 60,000 400,000
Par Value $20 $25
Total value $1,200,000 $10,000,000
Annual dividend $36,000 ($1,200,000 x 3%)
Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $72,000 $80,000 $100,000
Cumulative Preferred $32,000 $40,000 $36,000 $36,000
Common Stock $0 $32,000 $44,000 $64,000
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question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
A
a = 10
C = 15
B
b
Find the length of b using
the Pythagorean Theorem.
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
What is the Pythagorean Theorem?The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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Armando tiene 25 chocolates en una caja y caja y cada chocolate tiene un relleno de 4 posibles fresa, mora y piña. De los 25 chocolates de la caja de armando sabes que tiene 8 tienen relleno de mora y 5 de piña si una persona torna al azar un chocolate de la caja
cuales de la posibles posibilidades se puede calcular
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
¿Como encontrar las probabilidades?
Sabemos que hay 25 chocolates en total en la caja, tal que:
8 son de mora.5 son de piñalos 12 restantes son de fresa o cereza.La probabilidad de obtener un tipo particular de sabor se obtiene como el cociente entre el número de chocolates de ese sabor y el total de chocolates.
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
Sabemos que 5 chocolates tienen relleno de piña, entonces 20 no tienen relleno de piña. es decir, la probabilidad es:
P = 20/25 = 4/5
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30% of what number is
165
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
I hope you could get this answer
Answer: -12
Step-by-step explanation: x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.
Find one possible missing coordinate so that the point becomes a solution to the given inequality. (x, 8) is a solution to 3x - 4 < y. X =
Answer:
x = 0
Step-by-step explanation:
Substituting the given "point" into the equation gives the possibilities for x.
SubstitutionUsing (x, y) = (x, 8), the inequality becomes ...
3x -4 < 8
Solving for x gives ...
3x < 12 . . . . . . . add 4
x < 4 . . . . . . . divide by 3
Any value of x less than 4 will make (x, 8) a solution to the inequality. For example, ...
x = 0 . . . . . . (0, 8) is a solution to the inequality
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
A motorist travels from town A to town B, which are 84km apart. If he has completed 7/8 of his journey, what is the distance he has travelled?
The distance that he has traveled exists 73km 500m.
What is the distance?
Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.
Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.
To estimate the distance that he has traveled
He covered 7/8 out of 84 km
So, 7/8 × 84 = 73.5 km
The distance he has traveled = 73 km 500 m
Therefore, the distance that he has traveled exists 73km 500m.
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A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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Will mark brainliest
The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.
Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.
So we have
[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]
You purchase a very basic cell phone plan that charges $24.99 a month. This plan allows for data usage but that will cost you $5 for every GB you use in a month. Write an equation below in slope-intercept form that models this situation.
The equation of this given condition in the intercept form would be
y = 5x + 24.99
The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.
The linear equation written in the form
y = mx + b
is in slope-intercept form where: m is the slope, and b is the y-intercept.
In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.
Thus the equation of this given condition in the intercept form would be
y = 5x + 24.99
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A college class is made up of f freshman and s sophomores. If 5 freshmen drop this class would be 3 times the number of freshman. Which of the following equations represents a in terms of f ?
Answer:
The answer is G.
f-5 drop the class while s class is 3(f-5)
therefore, s=3(f-5)
I need help ASAP PLS HELP MEE I'll mark brainlist if correct and ill add 50 points I NeED The answer 5 mins AFTER PLS DO IT BEFORE 5 MIn (with explanation)
On which number line do the points represent negative seven and one over two and +1?
Answer list (below)
Answer:
Second number line
Step-by-step explanation:
This second line is the only line on which
[tex]-7\frac{1}{2} \text{ appears to the left of } 0 \text{ on the line (Point R)}\\+1 \text{ appears to the right of } 0 \text{ on this number line (Point T) }\\[/tex]
Answer:
○B (second option)
Step-by-step explanation:
In the second option, we can see that the point T is at +1. The point R is between -7 and -8, therefore we understand that it is at a value of [tex]\bf -7\frac{1}{2}[/tex].
All the other options have the points R and T at values not asked for in the question.
For the function f(x)=3x²-7, find the value of f(x) when x=3.
Answer:
Step-by-step explanation:
Simply plug in a 3 where you see an x in the function:
[tex]f(3)=3(3)^2-7[/tex] so
f(3) = 3(9) - 7 and
f(3) = 27 - 7 so
f(3) = 20
3a²+ab²-b² x a²-2ab²-3b²
/a+b
Answer:
It might be - c² or b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)
Step-by-step explanation:
I agree with the person above ^^^
A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Astrid is looking for a job at a call center. Call center A offers her $15 per hour and call-center B offers her $.25 per minute.
Which place offers a higher wage?
Answer: They are the same
Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.
Ali’s ate 1/3 of a pizza for lunch. Later, she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
What is the ratio of my lawn if it is 4 meters by 4.5 meters
Answer:
The 1:n ratio is= 1 : 1.125
The n:1 ratio is= 8/9 : 1
Just the simple ratio is= 4 : 4.5
In a certain school 70% of the students in first-year chemistry have had algebra. If there are 290 students in first-year chemistry, how many of them have had algebra?
The number of the students in the school that have had algebra is 203
How to determine the number of students?The given parameters in the question are
Proportion of students taking algebra, p = 70%Number of students in the school, n = 290The number of students that had algebra in the school is calculated as:
Algebra = Proportion of students taking algebra * Number of students in the school
The above equation can be represented as:
Algebra = np
Substitute values for n and p in the above equation
So, we have
Algebra = 290 * 70%
Express 70% as decimal i.e. 0.70
So, we have
Algebra = 290 * 0.70
Evaluate the product i.e. multiply 290 and 0.70
So, we have
Algebra = 203
Hence, the number of the students in the school that have had algebra is 203
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Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6
The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
What are Equivalent Equations?Equations that are equivalent to each other have the same value when evaluated or simplified.
Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.
8x - 6y = 12
Subtract 8x from both sides of the equation
8x - 8x - 6y = -8x + 12
-6y = -8x + 12
Divide both sides of the equation by -6
-6y/-6 = -8x/-6 + 12/-6
y = 4x/3 + (-2)
y = 4x/3 - 2
Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
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The coefficient of 8 • 2N is
Answer:
16
Step-by-step explanation:
when we multiply we have 16n so thats is d coefficient
HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Write each expression in the standard form for the complex number a + bi.
1. [ 4 ( cos (7pi/9) + i sin (7pi/9))]^3
2. The complex fifth roots of 5 - 5 sqrt(3)i
1. By de Moivre's theorem,
[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]
2. First write the given number in exponential/trigonometric form.
[tex]z = 5-5\sqrt3\,i[/tex]
has modulus
[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]
and since it lies in the second quadrant of the complex plane, its argument is
[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]
So, we have
[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]
Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are
[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]
[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]
[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]
[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]
[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]
SOLVE THE FOLLOWING PROBLEMS.
A) IN HOW MANY WAYS CAN THE LETTERS OF THE WORD “TRACK” BE ARRANGED?
B) A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM. IN HOW MANY WAYS CAN THIS BE DONE?
C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE
The answers to the question are:
12021038760How to solve for permutations and combinations1. The letters of the word track can be arranged in 5! ways
These are 5 x 4 x 3 x 2 x1
= 120
2. The way that the student would be able to select 6 out of 10 questions would be by 10C6
= 210 ways
C)This teacher would be able to make the decision of the prices to the students using =20C6= n!(n-r!r!)
= 38760
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What is the solution to x2 – 9x < –8? x < 1 or x > 8 x < –8 or x > 1 1 < x < 8 –8 < x < 1
In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.
x²− 9x < − 8Let's find the critical points of the inequality.
x² − 9x = − 8x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)
x² − 9x + 8 = 0(x − 1)(x − 8) = 0 (Factor left side of equation)
x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)
x=1 or x=8Check intervals in between critical points. (Test values in the intervals to see if they work.)x < 1 (Doesn't work in original inequality)
1 < x < 8 (Works in original inequality)
x > 8 (Doesn't work in original inequality)
Answer:1 < x < 8
The third option is the correct one.
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