Answer:
16 KMH is the correct answer
Step-by-step explanation:
which of the following sequences are convergent
Answer:
option A and E
Step-by-step explanation:
Arithmetic sequence converge, only in the case only when r=0
otherwise , arithmetic sequence goes increasing or decreasing at a constant rate.
So we ignore second and fourth option
If |r|<1 then geometric sequence converge
if |r|>1 then geometric sequence diverge
In option A, r= 1/5 that is less than 1 so it converge
In option C, r= -2 , |r| > 1 so geometric sequence diverge
In option E, r= 2/3 that is less than 1 so it converges
Answer is option A and E
what should the following equation be multiplied by in order to eliminate the fractions? x over 2 + x over 3 = 25 over 3
A. 5 B. 9 C. 25 D. 6
Final answer:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to multiply the entire equation by 6.
Explanation:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to find a common denominator for both fractions. The common denominator for 2 and 3 is 6. Therefore, we need to multiply the entire equation by 6 to eliminate the fractions.
Multiplying the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3)
Simplifying further, we get: 3x + 2x = 50
Combining like terms, we have: 5x = 50
Finally, dividing both sides of the equation by 5 gives us: x = 10
Final answer:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, one must multiply each term by 6, which is the least common multiple of the denominators 2 and 3, making option D correct.
Explanation:
The equation x/2 + x/3 = 25/3 should be multiplied by a number that is a common multiple of the denominators 2 and 3 to eliminate the fractions. To find the least common multiple (LCM) of 2 and 3, we can list out the multiples of these numbers (2,4,6,8,... for 2 and 3,6,9,12,... for 3) and identify the smallest multiple they have in common, which is 6. Therefore, multiplying the entire equation by 6 will eliminate the fractions and give us an equation with whole numbers.
Multiplying each term of the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3). Simplifying each term results in: 3x + 2x = 50 which is an equation without fractions.
The correct answer to the question is D. 6.
An object is thrown upward at a speed of 171 feet per second by a machine from a height of 17 feet off the ground. The height h of the object after t seconds can be found using the equation h = − 16t^2 + 171t + 17
When will the height be 307 feet?
When will the object reach the ground?
Answer:
Step-by-step explanation:
a) When will the height be 307 feet?
h = − 16t^2 + 171t + 17
307 = − 16t^2 + 171t + 17
Solving the quadratic equation by the general formula (find the plot attached). It reaches 307' twice as it is a parabolic shot.
t=2.1141s
t=8,5734s
b) When will the object reach the ground?
h = − 16t^2 + 171t + 17
0 = − 16t^2 + 171t + 17
t=-0.0985s (not real as there exists no negative time)
t=10.786s
The object will be at a height of 307 feet approximately 9.54 seconds after it was thrown. The object will reach the ground approximately 0.21 seconds after it was thrown.
To find when the height will be 307 feet, you can set the equation for the height h to 307 and solve for t:
h = -16t² + 171t + 17
307 = -16t² + 171t + 17
Now, let's rearrange the equation and set it equal to zero:
-16t² + 171t + 17 - 307 = 0
Combine like terms:
-16t² + 171t - 290 = 0
Now, you can solve this quadratic equation for t. You can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, a = -16, b = 171, and c = -290. Plug these values into the quadratic formula:
t = (-171 ± √(171² - 4 * (-16) * (-290))) / (2 * (-16))
Now, calculate the values for t:
t₁ = (-171 + √(171² - 4 * (-16) * (-290))) / (2 * (-16))
t₂ = (-171 - √(171² - 4 * (-16) * (-290))) / (2 * (-16))
Calculate t₁ and t₂ separately:
t₁ ≈ 9.54 seconds
t₂ ≈ -9.69 seconds
Since time cannot be negative in this context, we discard the negative solution. Therefore, the object will be at a height of 307 feet approximately 9.54 seconds after it was thrown.
To find when the object will reach the ground, you can set h equal to 0 and solve for t:
h = -16t² + 171t + 17
0 = -16t² + 171t + 17
Rearrange the equation:
-16t² + 171t + 17 = 0
Now, solve for t using the quadratic formula as we did before:
t = (-171 ± √(171² - 4 * (-16) * 17)) / (2 * (-16))
Calculate t₁ and t₂:
t₁ ≈ 0.21 seconds
t₂ ≈ 10.30 seconds
Again, you discard the negative solution. So, the object will reach the ground approximately 0.21 seconds after it was thrown.
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Find the x-intercepts of the parabola with vertex (-7,45) and y-intercept (0,-200). Write your answer in this form: (x1,y1), (x2,V If necessary, round to the nearest hundredth
Answer:
(-10, 0) , (-4, 0)
Step-by-step explanation:
[tex]\text{We know that the parabola is given by the quadratic equation.}\\\text{let the general equation of the parabola is}\\\\y=a(x-h)^2+k, \text{ where (h, k) is the vertex of the parabola.}\\\\\text{here we have given that vertex, }(h,k)=(-7,45), \text{ so above equation gives}\\\\y=a(x-(-7))^2+(45)\\\\y=a(x+7)^2+45\\\\\text{now this parabola has y-intercept at }(0,-200), \text{ so with this point}\\\text{above equation gives}[/tex]
[tex]-200=a(0+7)^2+45\\\\\Rightarrow -200=49a+45\\\\\Rightarrow 49a=-245\\\\\Rightarrow a=-\frac{245}{49}=-5\\\\\text{so the equation of the parabola is}\\\\y=-5(x+7)^2+45[/tex]
[tex]\\\text{Now to find the x-intercepts, we set }y=0, \text{ so we get}\\\\-5(x+7)^2+45=0\\\\\Rightarrow -5(x+7)^2=-45\\\\\Rightarrow (x+7)^2=\frac{-45}{-5}\\\\\Rightarrow (x+7)^2=9\\\\\Rightarrow (x+7)=\pm \sqrt{9}\\\\\Rightarrow x+7=\pm 3\\\\\Rightarrow x=-7\pm 3\\\\\Rightarrow x=-7-3, \text{ and } x=-7+3\\\\\Rightarrow x=-10, \text{ and } x=-4\\\\\text{so x-intercepts of parabola occur at: }(-10,0), \text{ and }(-4,0)[/tex]
LOTS OF POINTS!!!!!!!!
Please help asap!!!!! I need to solve for x
Answer:
x = 1 11/15
Step-by-step explanation:
Using ratios of similar triangles
3 5.2
-------- = ----------
4 (5.2 + x)
Using cross products
3 * (5.2 + x) = 5.2 * 4
Distribute
15.6 + 3x = 20.8
Subtract 15.6 from each side
15.6-15.6 + 3x = 20.8 -15.6
3x =5.2
Divide each side by 3
3x/3 = 5.2/3
x = 5.2/3
x=52/30
x = 26/15
x = 1 11/15
What are the coordinates of the midpoint of the line segment with endpoints A (-12,3) and B (8,-4)?
10, -0.5)
(10, 4.5)
(-2,4.5)
(-2, -0.5)
Answer:
D.
Step-by-step explanation:
Add the x values and divide by the amount of x's and same with the y's
Cyrus is inviting 11 friends over for pizza.He would like to have enough pizza so each friend can have 1/4 of a pizza. About how many pizzas should be order?
11(.25)= 2.75
Cryus should order 3 pizzas.
The marker cost 1/3 as a pen.The pen cost 1/3 as much as the book.The book cost 1/3 as much as the game. The price of the marker is what fraction of the price of the game?
Billie buys materials for a project at a fabric store. She has $16.95 to spend. She buys fabric for $8.69, craft glue for $1.95, and craft paper for $4.29. How much money does she left after she pays for the items?
Final answer:
Billie has $2.02 left after buying fabric, craft glue, and craft paper, which in total cost her $14.93 from her initial $16.95.
Explanation:
To find out how much money Billie has left after purchasing her items, we need to calculate the total cost of the items and subtract it from the amount she had initially.
Fabric cost: $8.69
Craft glue cost: $1.95
Craft paper cost: $4.29
We add these amounts together to find the total cost of the items:
$8.69 (fabric) + $1.95 (glue) + $4.29 (paper) = $14.93.
Now, we subtract the total cost of items from the amount she had to start with:
$16.95 - $14.93 = $2.02.
Therefore, Billie has $2.02 left after her purchases.
Bryan started to evaluate a decimal expression. 2.5(42 ÷ 3.2 – 10(0.2) + 3)– 5.2 2.5(16 ÷ 3.2 – 10(0.2) + 3) – 5.2 What should Bryan's next step look like?
Answer:
The answer is C
Step-by-step explanation:
I just answered it on edg
The second step is
2.5 (42 ÷ 3.2 – 2 + 3) - 5.2
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Step 1:
2.5 (42 ÷ 3.2 – 10(0.2) + 3) - 5.2
Step 2:
2.5 (42 ÷ 3.2 – 2 + 3) - 5.2
Step 3:
2.5 (13.125 + 1) - 5.2
Step 4:
2.5 (14.125) - 5.2
Step 5:
35.3125 - 5.2
Step 6:
30.1125
Thus,
The value of the expression is 30.1125.
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Which equation represents the sentence? Four more than a number is half the number.
A.n+4=n/2
B.n-4=n/2
C.4+n/2=n
D.n/2-4=n
According to the table listing average daily expenses for a tourist by country based on high and medium categories, Brazil has a range from $12.25 to $18.33, and Greece has a range from $9.48 to $16.55. Which of the two countries has the larger difference between categories?
a.Greece
b.Brazil
Answer:
Option a. Greece.
Step-by-step explanation:
According to the table listing average daily expenses for a tourist by country based on high and medium categories,
Brazil has a range from = $12.25 to $18.33
Greece has a range from = $9.48 to $16.55
To find out the difference in range, first we get range of both the countries.
by subtracting lowest from highest
Brazil = $18.33 - $12.25 = 6.08
Greece = $16.55 - $9.48 = 7.07
= 7.07 > 6.08
Therefore, Greece has the larger difference between categories.
Option a. Greece is the correct answer.
The length of a rectangle it twice it's within. If the perimeter of the rectangle is 30 cm, find its area.
w - width
2w - length (l)
30 cm - perimeter
w + w + 2w + 2w = 6w - perimeter
The equation:
6w = 30 divide both sides by 6
w = 5 cm
2w = 2(5) = 10
l = 10 cm
The area of a rectangle: A = lw.
Substitute:
A = (5)(10) = 50
Answer: The area is 50cm²Jose is going to order wrenches for his hardware store. He can order four different types and the table shows the profit margin for each type in tens of dollars and the probability. Which wrench should he order?
Answer:
B
Step-by-step explanation:
The expected value of profit margin is the sum of the product of profit margin and probability.
Wrench A:
... 10×.05 +20×.6 +30×.2 +40×.15 = 0.5 +12 +6 +6 = 24.5
Wrench B:
... (20+40)×.3 +(30+50)×.2 = 18 +16 = 34
Wrench C:
... 15×.4 +30×.5 +(45+60)×.05 = 6 +15 +5.25 = 26.25
Wrench D:
... 5×.2 +10×.4 +15×.15 +20×.25 = 1 +4 +2.25 +5 = 12.25
___
Clearly, Wrench B has the greatest expected profit margin. That would be the one Jose should order if he's trying to maximize his profit.
Please help me!!!!!!!!!!!!!!!!!!
Answer:
I'm not sure if it is correct but i hope it helps you
Step-by-step explanation:
So you subtract 25 and 15 and you will get 10
then you add 65 and 5 and you will get 70
you add 45 and 20 and you will get 65
40 copies of a popular paper book fit perfectly on a 5ft shelf. How many copies would fit perfectly on an 8ft shelf
helppppppppppppppppppppppppp
Answer:
It should be A, $12.75
Step-by-step explanation: Add 10.5+10.5+10.5+4.5+4.5+6.75= $47.25, subtract 60-47.25= $12.75
Can someone please help me with this question? Thank you!
Answer:
The arcs are not congruent which makes the statement false.
Step-by-step explanation: Congruent means equal to my understanding.
A regulation soccer field has an area of 59,400 square feet. If the length is 330 feet, what is the width in feet
To find the width of a rectangle when given the area and length, divide the area by the length:
Width = 59,400 / 330 = 180 feet
On a factory floor 20 out of every 170 toy robots is defective what percent of toy robots are disaffected round the number to the nearest hundred
Answer:
We are given that there are total 170 toy robots
Number of defective robots out of total 170 toy robots [tex]=20[/tex]
We have to find the percentage of toy robots that are disaffected.
The percentage of toy robots that are disaffected is given below:
[tex]\frac{20}{170} \times 100[/tex]
[tex]0.1176 \times 100[/tex]
[tex]11.76[/tex]
Therefore, the percent of toy robots that are disaffected is [tex]\bold{11.76\%}[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
An on-line electronics store must sell at least $5000 worth of computers and printers per day. Each printer costs $350 and each computer costs $750. The store can ship a maximum of 20 items per day. Which system of inequalities models correctly the number of computers, c, and number printers, p, the store could sell per day?
Answer: D
Step-by-step explanation:
An on-line electronics store must sell at least $5000 worth of computers and printers per day.
"at least" means ≥Each printer costs $350 and each computer costs $750.
350p750cThis equation is: 350p + 750c ≥ 5000
The store can ship a maximum of 20 items per day
"maximum" means "no more than" which is ≤This equation is: c + p ≤ 20
see attachment! please im really stuck!!
Answer:
Max for g(x) is 3
Max for f(x) is 2
Step-by-step explanation:
The maximum value of a function is the highest value on the graph of the function. It is the greatest value of the function and is always a y value. We can see on the graph that the blue function peaks at 3. The max is 3.
A normal sine or cosine without any transformations has the max of 1. We can see in the equation for f(x) that there is a vertical stretch of 2. So the max here is 2(1)=2.
which of the following is equal to the expression listed below?
11 x 5 +9
A . 9 x 11 + 5
B . 5 x 9 + 11
C . 5 x 11 + 9
D . 11 x 9 + 5
Lisa went on a 52 \text { km}52 km hike. She divided the distance traveled evenly over 44 days. How many meters did Lisa walk each day?
Answer:
13,000 meters.
Step-by-step explanation:
We have been given that Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.
Let us convert our given distance in meters.
1 km = 1,000 meters.
52 km= 52*1,000 meters = 52,000 meters.
Let us divide total distance traveled by total number of days to find the distance traveled per day.
[tex]\text{Lisa walked each day}=\frac{52000\text{ meters}}{\text{ 4 days}}[/tex]
[tex]\text{Lisa walked each day}=13,000\frac{\text{ meters}}{\text{ day}}[/tex]
Therefore, Lisa walked 13,000 meters each day.
Lisa hiked 52 km in 4 days, equaling to 13 km per day. However, this must be converted to meters, so Lisa hiked 13,000 meters each day.
Explanation:This problem is an exercise in unit conversion and division. Since Lisa divided the total distance of 52 kilometers evenly over 4 days, she hiked 13 kilometers each day (52 km / 4 = 13 km/day). However, the question asks for the answer in meters, not kilometers. Therefore, we must convert kilometers to meters. We know that 1 kilometer is equivalent to 1000 meters, so Lisa hiked 13,000 meters each day (13 km * 1000 = 13,000 m/day).
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An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?
Answer:
2.4 hours Electrician works.
Step-by-step explanation:
Let us assume that the number of hours Electrician works be x.
As given
An Electrician charges $30 for a service call plus $75 per hour of service.
If Electrician charged $210.
Than the equation becomes
30 + 75x = 210
75x = 210 - 30
75x = 180
[tex]x =\frac{180}{75}[/tex]
x =2.4 hours
Therefore 2.4 hours Electrician works.
Convert 453° to radians.
A)
151π
30
B)
151π
60
C)
151π
90
D)
151π
120
The formula:
[tex]\theta=\dfrac{\theta\pi}{180}[/tex]
We have
[tex]\theta=453[/tex]
Substitute:
[tex]453^o=\dfrac{453\pi}{180}=\dfrac{453\pi:3}{180:3}=\dfrac{151\pi}{60}\to\boxed{B)}[/tex]
The conversion of 453° into radians is 151π/60.
What is radian?The angle made by taking the radius and wrapping it round the circle.
Given that, 453°
To convert any degree into radians, we multiply by π/180
453*π/180 = 151π/60
Hence, The conversion of 453° into radians is 151π/60.
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Compute the missing data in the table for the following exponential function
Answer:
missing data for the following exponential function is 27
Step-by-step explanation:
To find out missing data , we use the given f(x) equation
Given f(x) = 3^x
WE need to find the missing number f(x) when x=3
To find f(x) we plug in 3 for x in f(x) = 3^x
[tex]f(x) = 3^3= 3*3*3= 27[/tex]
So missing number is 27
Answer:
B. 27
Step-by-step explanation:
Given that a 12 foot long piece of steel pipe weighs 5 pounds per foot, how much does it weigh in kilograms per meter? 1 pound = 0.454 kilograms 1 foot = 0.305 meters A) 6.34 kg/m B) 6.84 kg/m C) 7.44 kg/m D) 7.94 kg/m ( plz answer correct and quick)
Answer:
1 foot = 0.305 meters.
Convert 1 meter to feet:
1 meter = 1/0.305 = 3.28 feet
Find the weight in pounds per meter:
5 pounds x 3.28 feet = 16.4 pounds per meter.
Convert pounds per meter to kilograms per meter:
16.4 pounds x 0.454 kilograms per pound = 7.44 kg/m
please help me with these questions
3. Answer: y = 4
Step-by-step explanation:
Need to find the slope (m):
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\dfrac{4 - 4}{-3-1}[/tex]
= [tex]\dfrac{0}{-4}[/tex]
= 0
Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - 4 = 0(x - 1)
y - 4 = 0
y = 4
********************************************************************
4. Answer: [tex]\bold{y = \dfrac{2}{3}x + 3}[/tex]
Step-by-step explanation:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 1 = \dfrac{2}{3}(x - (-3))[/tex]
[tex]y - 1 = \dfrac{2}{3}(x + 3)[/tex]
[tex]y - 1 = \dfrac{2}{3}x + 2[/tex]
[tex]y = \dfrac{2}{3}x + 3[/tex]
What is the third quartile of this data set 21,24,25,28,29,35,37,43,44
Answer:
40
Step-by-step explanation:
The data is
21,24,25,28,29,35,37,43,44
To find the third quartile we have to arrange the data in increasing order
so the data in increasing order is
21,24,25,28,29,35,37,43,44
total number of values = 9
Median value = (n + 1 )/ 2
=(9+1)/2
=5th value
so the median is 29
Lower half of the data is the values before the median and upper half of the data is values after the median
so lower half = {21,24,25,28}
Upper half = {35,37,43,44}
so to find the third quartile we will use the upper half of the values
Third quartile means that the median of the values of upper half of the data
As the total No of value in upper half is 4 which is an even no
we will take the middle values of the upper half and take their mean
so
Third Quartile = [tex]\frac{37+43}{2}[/tex]
=[tex]\frac{80}{2}[/tex]
=40
so the value of third quartile is 40
Final answer:
The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.
Explanation:
To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.