Answer:
Step-by-step explanation:
You already have this set up to answer your question. This quadratic is in work form, aka vertex form, where the vertex is (3.5, 15). The first coordinate of the vertex is the time it takes to reach its max height, which is the second coordinate of the vertex. So it takes 3.5 seconds to reach a max height of 15 meters.
the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960
Answer:
The correct answer is = 15.
Step-by-step explanation:
Formula:
The sum of the first n terms of an arithmetic progression with first term a and constant difference d is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]
using this formula in this problem
Solution:
The sum of the first ten terms is
[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]
[tex]S_{10}=5(2a+9d)[/tex]
The sum of the 20th, 21st, and 22nd terms is three times the 21st term:
[tex]3a_{21}=3(a+(21-1)d)[/tex]
[tex]3a_{21}=3(a+20d)[/tex]
[tex]3a_{21}=3a+60d[/tex]
The problem then tells us
[tex]S_{10}=3a_{21}[/tex]
[tex]10a+45d=3a+60d[/tex]
[tex]7a=15d[/tex]
there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is
then, 15, 22, 29, 36, ...
The problem says to find the number of terms n for which the sum is 960:
putting value in the formula
[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]
solving quadratic will give n = 15
thus, the correct answer is 15.
answer plz pix inside plz find both answers
Answer:
pixxer
Step-by-step explanation:
please pick inside please
Answer:
I dont now
Step-by-step explanation:
plz conprendation
An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled twice in succession and that the face values of the two goals are added together. This song is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event a: the sun is greater than six
Answer:
ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6
Two dice
Assuming that the dice are unbiased or not " loaded".
Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.
How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?
These are the possibilities
Case 1.
D1 =1 & D2=5
Or
D1= 5 & D2=1
Case 2.
D1 =2 & D2=4
Or
D1= 4 & D2= 2
Case 3. D1=3, D2=3
P3 =0.027778
Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.
The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.
P1= 0.02778+ 0.02778 =0.055558
P2= 0.02778+0.02778 =0.055558
Same way,
P3=0.027778, when there is only one way to get the sum 6.
So, P = 0.138894
Based on truncating at the sixth decimal place.
A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.
Hope This Helps!!!
Answer my question you heathens
Each month your cell phone company charges you $ 40 for your plan plus 2 cents for each text you send. You have $ 120 budgeted for cell phone expenses for the month. Construct an inequality to make a determination about the number of texts you can send each month. Note that you cannot send a fraction of a text. You must send __________ _______________ texts this month in order to stay within your budget.
Answer:
50 text messages would have to be sent or received in order for the plans to cost the same each month.
Step-by-step explanation:
x = number of text messages sent
0.2x+40=50
0.2x = 10
5(0.2x) = 5(10)
x = 50
Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.
Cuanto es 91972×898972819
Answer:
82,680,328,109,068
Step-by-step explanation:
Use the on-line Big Number calculator
Can anyone help me with the question?
Answer:
-9
Step-by-step explanation:
(f-g) (x) = 2x²-7x+24-5x²-5x+3
= -3x²-12x+27
(f-g) (2) = -3(2)²-12(2)+27
= -12-24+27
= -9
In an examination every student took history or geography or both of 500 candidates 60% took history whiles 72% took geography. How many students took both subjects
Answer:
80 students
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
60% of 500 = 300
72% of 500 = 360
40% of 500 = 200
28% of 500 = 140
300+360 = 660
660 - 2x = 500
660 - 500 = 2x
160 = 2x
2x = 160
x = 80
What are the solutions to the system of equations graphed below
Please help with this
Answer:
i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds
3.6 subtract by 1.487 is egual to ______.Pls write in step by step.
Answer:
2.113
Step-by-step explanation:
[tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]
a + b·c = a + c·b is an example of the associative property.
Answer:
yes , This is an example of the associative property.
Step-by-step explanation:
Evaluate 12 sin 85° correct to two decimal places.
Answer:
12 x sin(85)
12x 0.99619
155.40
Solution:
12 x sin (85) = 11.95 (Since sin85 is 0.996194)
So, the answer is 11.95.
please give full solutions
√8281
Answer:
the answer is 91
Step-by-step explanation:
solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.
Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]
Step-by-step explanation:
Given
In equality is [tex]x^3+4x>5x^2[/tex]
Taking terms one side
[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]
Using wavy curve method
[tex]x\in (0,1)\cup (4,\infty)[/tex]
What is the smallest three-digit number that is divisible by 3? Explain how you know without multiplying or dividing.
express the ratio as a fraction in it's lowest term.2mm:100cm
Answer:
2/1000 broken down to 1/500
Step-by-step explanation:
convert 100cm to mm
10mm-1cm
x-100
x=1000mm
since the question says as a fraction
2mm/1000mm
1mm/500mm
The ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].
To express the ratio 2mm:100cm as a fraction in its lowest term, we need to convert both measurements to the same unit.
Since 1cm is equal to 10mm, we can convert the ratio as follows:
[tex]2mm:100cm[/tex]
[tex]= 2mm : (100cm \times 10mm/cm)[/tex]
[tex]= 2mm : 1000mm[/tex]
Now, we can write the ratio as a fraction: [tex]\frac{2mm}{1000mm}[/tex]
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
[tex]\frac{2mm}{1000mm}[/tex]
= [tex]\frac{1 mm}{500mm}[/tex]
Therefore, the ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].
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By visual inspection, determine the best-fitting regression model for the
scatterplot.
X
10
.
-10
A. No pattern
B. Exponential
C. Quadratic
D. Linear
Answer:
The answer is B since the chance is expontential since it gets bigger over time and each one is farther apart
The best-fitting regression model for the scatterplot is Exponential, the correct option is B.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve(exponential) on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
We are given;
The graph representation
Now,
By visual inspection of the scatterplot, we can see that the points do not follow a clear pattern that suggests an exponential or quadratic relationship. However, there appears to be a linear relationship between the variables.
Therefore, the answer will be exponential.
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2. If 5 mg in 2 ml of liquid medication, how many mg is in 4 ml of medication?
Answer:
10mg
Step-by-step explanation:
We have a proportional relationship.
We know that there are 5mg in 2ml of liquid medication.
Now we want to know how many mg there are in 4 ml of medication.
First, we can rewrite it as:
4ml = 2ml + 2ml
And we know that, in every 2 ml of medicine, there are 5mg.
Then if we have two times 2ml of medicine, we have two times 5mg.
This is:
2*5mg = 10mg
Complete the angle addition postulate for the following angle
Answer:
measurement m<GEM+m<MEO=m<GEO
Question 5 of 10
Select the correct answer.
The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
Average Temp.
90
80
70
60
50
404
30
20
10
1 1 2 3 4 5 6
X
Inches of Rain
The equation for the line of best fit is y = -3.32x + 97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?
Answer:
53.06°F
Step-by-step explanation:
Given the equation of best fit :
y=-3.32x +97.05.
The average temperature for a month with 13.25 inches of Rainfall
Amount of Rainfall = x
Average temperature = y
To make our prediction ; put x = 13.25 in the equation and solve for y ;
y = -3.32x +97.05
Put x = 13.25
y = -3.32(13.25) +97.05
y = - 43.99 + 97.05
y = 53.06°F
answer please don't skip plz answer
What is the value of x^2
-2xy+y^2
if x-y = 4 ?
please answer
Answer:
16
Step-by-step explanation:
[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]
[tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]
The value of x^2-2xy+y^2
will be 16 .
Explanation is in the attachment .
hope it is helpful to you ☺️
Hello can anyone pls help with this multiple choice question
Answer:
The correct answer is the last one
Step-by-step explanation:
How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually
Answer:
11 half years
Step-by-step explanation:
The formula for compound interest is
A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.
If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus
1000 = 500 (1+0.07)^(t)
divide both sides by 500
2 = (1+0.07)^(t)
2 = (1.07)^(t)
Using logarithms, we can say that
[tex]log_{1.07} 2 = t[/tex]
and using a calculator, we get
10.24 = t
Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11
Chris is riding her bike for 10 miles. She averages 12 mi/h. how many more minutes must she ride before she travels 60 miles?
Answer:
5 Minutes
take 10 and add 12 for each minute until you pass 60
SCALCET8 3.9.004.MI. The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 15 cm and the width is 7 cm, how fast is the area of the rectangle increasing
Answer:
The area of the rectangle is increasing at a rate of 169 cm²/s
Step-by-step explanation:
Given;
increase in the length of the rectangle, [tex]\frac{dL}{dt} = 7 \ cm/s[/tex]
increase in the width of the rectangle, [tex]\frac{dW}{dt} = 8 \ cm/s[/tex]
length, L = 15 cm
width, W = 7 cm
The increase in Area is calculated as;
[tex]Area = Length \times Width\\\\A = LW\\\\\frac{dA}{dt} = L(\frac{dW}{dt} )\ + \ W(\frac{dL}{dt} )\\\\\frac{dA}{dt} = 15 \ cm(8\ \frac{ cm}{s} ) \ + \ 7 \ cm(7\ \frac{ cm}{s} ) \\\\\frac{dA}{dt} = 120 \ cm^2/s \ + \ 49 \ cm^2/s\\\\\frac{dA}{dt} = 169 \ cm^2/s[/tex]
Therefore, the area of the rectangle is increasing at a rate of 169 cm²/s
A senior class of 420 students will rent buses and vans for a class trip. Each bus can transport 50 students and 3 chaperones and costs $1200 to rent. Each van can transport 10 students and 1 chaperone and costs $100 to rent. There are 36 chaperones available (so they can't all go in vans). How many vehicles of each type should be rented in order to minimize the cost
Answer:
37 buses and 1 van.
Step-by-step explanation:
The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .
The cost of renting buses for 50 students is $500
What we do is rent 37 buses and 1 van
37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.
Then rent 1 van to take in 50 students and 1 chaperone.
The total cost here will be
$3700 + $1200 = $ 4900
This will help to safe cost.
What is the probability that in a sample of 400 registered voters to at least 290 voted in their most recent local
Answer:
The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:
= 72.5%
Step-by-step explanation:
Sample of registered voters = 400
Sample of voters that actually voted = 290
Probability = 290/400 * 100
= 72.5%
b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted. Probability measures the chance of an event occurring given other events. Therefore, one can conclude that the voting was at least 72.5%. Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.
Evaluate the expression below for x = 2, y = -3, and z = -1.
x?2? - y? (x +z)
A. -23
B. -5
C 13
D
27
Please select the best answer from the choices provided
Ο Α
ОВ
ОС
OD
The value of the expression for the given values of x, y and z is B. -5.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
x²z² - y²(x + z)
We have certain values for x, y and z.
x = 2, y = -3 and z = -1.
Substituting the values,
(2²)(-1²) - (-3²) (2 + -1) = (4 × 1) - (9 × 1)
= 4 - 9
= -5
Hence the value of the expression is -5.
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Which statement best compares the two functions? The minimum of function A occurs 1 unit higher than the minimum of function B. The minimum of function A occurs 3 units higher than the minimum of function B. The minimum of function A occurs 5 units lower than the minimum of function B. The minimum of function A occurs 7 units lower than the minimum of function B.
Answer: D: The minimum value of A occurs 7 units lower than minimum of function B.
Step-by-step explanation: The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.
The minimum value of A occurs 7 units lower than the minimum of function B.
We have given that,
Statement best compares the two functions
What is the minimum and maximum function?
The maxima and minima of a function, known collectively as extrema, are the largest and smallest value of the function, either within a given range, or on the entire domain.
The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.
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Find the values of X and Y that makes these triangles congruent by the HL theorem
Answer:
C. x = 3, y = 2
Step-by-step explanation:
If both triangles are congruent by the HL Theorem, then their hypotenuse and a corresponding leg would be equal to each other.
Thus:
x + 3 = 3y (eqn. 1) => equal hypotenuse
Also,
x = y + 1 (eqn. 2) => equal legs
✔️Substitute x = y + 1 into eqn. 1 to find y.
x + 3 = 3y (eqn. 1)
(y + 1) + 3 = 3y
y + 1 + 3 = 3y
y + 4 = 3y
y + 4 - y = 3y - y
4 = 2y
Divide both sides by 2
4/2 = 2y/2
2 = y
y = 2
✔️ Substitute y = 2 into eqn. 2 to find x.
x = y + 1 (eqn. 2)
x = 2 + 1
x = 3
