Answers
Step-by-step explanation:
the flight path of a rocket or a thrown object is a parabola as described by the function.
h(t) = -16t² + 40t + 7
the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.
we get the extreme point of a curve by finding the zero solution of the first derivative of the function.
and the extreme value itself by using that value in the original equation and calculate the result.
h'(t) = -32t + 40
0 = -32t + 40
32t = 40
t = 40/32 = 5/4 = 1.25 seconds
h(5/4) = -16×(5/4)² + 40×5/4 + 7 =
= -16×25/16 + 10×5 + 7 =
= -25 + 50 + 7 = 32 ft
the rocket will reach its maximum height of 32 ft after 1.25 seconds.
Related Questions
pasagot po nito
(A) 4, 9, 14, 19, 24, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(B) 8, 10, 12, 14, 16, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(C) 1, 8, 15, 22, 29, …
Give the next two terms:
Give an expression for the nth term:
Find the 20th term:
Answers
For each of the arithmetic sequences, we have that:
a)
The next two terms are 29 and 34.The expression for the nth term is of: [tex]a_n = 4 + 5(n - 1)[/tex].The 30th term is: 149.b)
The next two terms are 18 and 20.The expression for the nth term is of: [tex]a_n = 8 + 2(n - 1)[/tex].The 30th term is: 66.c)
The next two terms are 36 and 43.The expression for the nth term is of: [tex]a_n = 1 + 7(n - 1)[/tex].The 20th term is: 134.What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
For the sequences in this problem, we have that:
The first terms are, respectively, 4, 8 and 1.The common ratios are, respectively, 5, 2 and 7.Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.
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help wanted .............................................................
Answers
Answer:
I'm pretty sure the answer would be >
Answer: |-8|>-2
Step-by-step explanation:
Because of the lines on both sides of the "-8" you don't pay attention to the "-" sign. That is because this is an absolute value sign. So instead you would read that as 8 ? -2 and which of course 8 is clearly greater
Hope this helps ;)
A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
Answers
The minimum cost will be 1091 units.
Define Vertex Formula.
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
Given expression is,
C = 70,000 - 120x + 0.055x²
For this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, plug in the values and find 'x'
minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )
= 120 / 0.11
= 120 / 0.11
= 1090.90 or 1091 units
Therefore, the minimum cost will be 1091 units.
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Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.
Answers
Answer:
Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. a. using variables, write out the formula for the point-slope form of the equation. b. identify the values for m, x1, and y1. c. fill these values into the point-slope form of the equation from part (a), and simplify as needed. use the box provided to submit all of your calculations and final answers.
Answers
The point slope form of the equation is = P2 = (11, 2)
What is point slope?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:Form of point slopeForm of a slope-interceptTwo-point form for interceptingacc to our question-
Since m = and P1 = (2, -1) then x1 = 2 and y1 = -1. 1y – y1 = m (x – x1)y – (-1) = (x – 2)y + 1 = (x – 2)3 (y + 1) = 1(x – 2)3y + 3 = x – 25 = x – 3y or x – 3y = 5(This the standard formula of the line)Step 2: Calculate P2.Select any valueyou with for x or y and substitute it into the equation found instep 1. For this example y will equal 2.x – 3y = 5x – 3(2) = 5x – 6 = 6x = 11learn more about slope click here:
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Of the students at Milton Middle School, 112 are girls. If 40% of the students are girls, how many total students are there at Milton Middle school
Answers
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
A: $69
B: $90
C: $420
D: $1,080
Answers
Oliver has to pay an amount of B: $90 with simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business.
The bank offered him an interest rate of 12% for 6 months.
P = $1500, r= 12% and t = 6 months or 1/2 or 0.5 years.
∴ SI = (1500×12×0.5)/100.
SI = 15×6.
SI = $90.
The amount of simple interest Oliver has to pay is $90.
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→
Enter a formula using k to connect the two
variables.
y is proportional to x³
Answers
Directly proportional to x.
What is propotionality?In algebra, proportionality is the equality of two ratios. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem. By multiplying one numerator by the opposing denominator and equating the result to that of the other numerator and denominator, the equation can be solved. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.Acc to our question-
If two variables' ratios (yx)(x and y) have the same value as a constant (k=yx)therefore the ratio's variable (y) in the numerator is the sum of the other variable and the constant (y=k:x).With a proportionality constant of k, it is claimed that y is directly proportional to x in this instance.Hence,Directly proportional to x.
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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? Round your answer to four decimal places.
Answers
The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1
How to determine the probability value?From the question, the given parameters about the distribution are
Mean diameter = 127Variance = 36 The actual data value, x = Less than 0.5The standard deviation is the square root of variance
So, we have
Standard deviation = 6
The z-score is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (0.5 - 127)/6
Evaluate
z = -21.08
The probability is then calculated as:
P(x > 0.5) = P(z > -21.08)
From the z table of probabilities, we have;
P(x < 0.5) = 1
Hence, the probability is 1.0
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Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answers
The relationship between the number of weeks and cars are proportional since they are dependent on each other.
ProportionRatio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.
This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.
Let;
x = number of weeksy = number of carsy = 3x
At week 10, Alfred will have
y = 3(10) = 30 cars
After 10 weeks, Alfred will have 30 cars
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I need this answer as soon as possible.It will be nice if you do it in a paper.
Answers
Answer:
as shown in underline ^^
Step-by-step explanation:
Fill in the missing words:
When a solid mixes with a liquid and becomes part of the liquid it dissolves.
A solid that dissolves in a liquid is soluble.
A solid that does not dissolve in a liquid is insoluble.
manufacture of a certain component requires three different machining operations. machining time for each operation has a normal distribution, and the three times are independent of one another. the mean values are 15, 20, and 30 min, respectively, and the standard deviations are 2, 1, and 1.8 min, respectively. what is the probability that it takes at most 1 hour of machining time to produce a randomly selected component? (round your answer to four decimal places.)
Answers
The probability that it takes at most 1 hour of machining time to produce a randomly selected component is 0.04074
we are provided with the independent time which are 15, 20, and 30 min and the respective standard deviations which are 2, 1, and 1.8 min.So the total mean X= 15+20+30 =65, as we know that
Variance = ( standard deviation )²
=> Variance = 2² + 1² + 1.8² = 8.24
since standard deviation = √variance
=>Standard deviation = 2.87
so the z score = X -mean /standard deviation
since here X = 1 hour = 60 mintues
z = 60-65/2.87 = -1.74216
So the probability, P( z≤ -1.74216) = 0.04074
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PLEASE HELP will mark brainliest
Answers
The slope of the given line in the graph is 0.
What is slope?
The steepness and direction of a line are measured by its slope. Any two points along the line can be used to calculate it. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The Slope, also known as the Gradient, of a straight line displays how steep the line is. The change in y coordinate relative to the change in x coordinate is known as the slope of an object.
Here the given graph points are,
[tex](x_1-y_1)=(1,1)\\(x_2,y_2)=(4,1)[/tex]
Using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{1-1}{4-1}[/tex]
=> slope m = 0/3
=> slope m=0.
Therefore slope of the line is 0.
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Graph the image of △IJK after the following sequence of transformations:
Translation 17 units left and 5 units up
Reflection across the line y=1
Answers
Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5
What is a transformation in geometry?A transformation is an operation that changes the location, size and shape of geometric figures.
The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)
The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎
The location of the vertices of the image of ΔIJK following the translation transformation are;
[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]
[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]
[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]
The coordinates of a point following a reflection across the line y = 1 are as follows;
The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;
I'(-3, 13), Relative point I'(-3, 12)
J'(-9, 10) has a relative point at (-9, 9)
K'(-3, 7) has a relative point (-3, 6)
The coordinates of the vertices of the reflected image are therefore;
(x, y) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] (x, -(y - 1))
Which gives;
I'(-3, 12) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)
J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)
k'(-3, 6) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)
Please find attached the image of the ΔIJK following the translation and reflection transformation
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In the first round of math contest, each students had to answer 2 questions. Miriam averaged 76 seconds per question. Jake and Rafael averaged 84 seconds per question, and Sam averaged 80 seconds per question. At the end of the first round, what was the total time for all 4 students?
a) 324 seconds
b) 400 seconds
c) 480 seconds
d) 568 seconds
e) 648 seconds
Answers
At the end of the first round, the total time is 648 seconds ( option E )
What is average ?An average is the result that you get when you add two or more numbers together and divide the total by the number of numbers you added together.
For example, if there are 10 students in a class with ages 10, 11, 12, 10, 10,12,12,10,11,12 their average age will be( 10+ 11+12+10+10+12+12+10+11+12)/10
for Mariam her average time is 76 which means her total time is 76× 2= 152
for Jake and Rafael their average time is 84 which means their total time is 84×4= 336
for Sam,his average time is 80 which means is total time is 80×2= 160
therefore the total time spent by the 4 students is 152+336+160=648seconds
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Use the formula A = nr² to find the area of a circle.
PLEASE HELP
Answers
The area of a circle is 12πx-60π unit².
How to use the formula to find the area of a circle?By examining the given figure, there are two circles i.e the small circular hole and the bigger circle. Since the small is a hole then we have to subtract its area from the area of the bigger circle.
Given:
radius of small circle(r₂) = x+2
radius of bigger circle(r₁) = x+8
The formula of Area(A) = πr²
Area of the figure = A₁ - A₂
= πr₁² - πr₂²
= π(x+8)²- π(x+2)²
= π(x²+16x+64) - π(x²+4x+4)
= x²π+16πx+64π - x²π-4πx-4π
= 12πx-60π unit squared
Therefore, the area of the circle is 12πx-60π unit squared. So the 2nd option is the answer.
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On the first day of an experiment, a scientist counts 31 bacteria. On the eighth day of the experiment, the count is 310,000 bacteria.
How many times greater is 310,000 than 31?
A. 310,000
B. 10,000
C. 1,000
D. 31
Answers
A store is instructed by corporate headquarters to put a markup of %67 on all items. An item costing $12 is displayed by the store manager at a selling price of $8
. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
Answers
The correct selling price of the item has being solved as $20.04 The error that the manager has made is $12.04
How to solve for the markupGiven that there is a markup, the item that is being sold for 12 dollars would be affected by the percentage of the mark up.
This mark up is a 67% markup
This would be solved as
12$ + 67% of 12$
= $12 + 8.04
= $20.04
Hence the correct selling price is $20.04
Next we would have to find the likely error that the manager has made
= $20.04- $8
= $12.04
The likely error of the manager is $12.04
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The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028. In the year 2028, the total average credit card debt for a U.S. household will be $
Answers
Step-by-step explanation:
The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.
2028 - 1995 = 33 years, so t = 33
D = 401t + 5940
D = 401(33) + 5940
D = 13,233 + 5940
D = 19,173
Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173
I NEED SOME HELP URGENT
solve for the missin lengths in the sets of sumilar figures below.
Answers
The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units
Similar triangles:Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
When two triangles ΔABC and ΔXYZ are similar then
AB/XY = BC/YZ = AC/XZ
Here we have
ΔABC and ΔOPQ which are similar and right-angled triangles
As we know in a right-angled triangle
=> Hyp² = side² + side²
From ΔABC,
AB² = AC² + BC²
=> AB² = 6² + 4²
=> AB² = 100 = 10²
=> AB = 10 units
Since ΔABC and ΔOPQ are similar
=> AB/OP = BC/OQ = AC/PQ
=> 10/OP = 4/ f = 6/ 6
Take 10/OP = 6/ 6
=> 6(10) = 6(OP)
=> OP = 10 units
4/ f = 6/ 6
=> f = 4 units
Therefore,
The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units
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What is the equation of the line that passes through the point (−2,−7) and has a slope of 6?
Answers
The equation of the line in slope intercept form is y = 6x + 5
How to determine the equation of the line?The given parameters are
Slope, m = 6
Points, (x₁, y₁) = (-2, -7)
A linear equation can be represented as
y = slope * x + y-intercept
i.e.
y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = 6(x + 2) - 7
Expand
y = 6x + 12 - 7
Evaluate the like terms
y = 6x + 5
Hence. the linear equation is y = 6x + 5
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Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
Answers
I think so ya is does you just need to tell your teacher if you don't understand
"15 fish per fish tank" translated expression
Answers
Answer:
15/x
Step-by-step explanation:
x = fish tank
x= fish tank!!!!!!!!!!
12 mushrooms $3 How much for one
Answers
Answer:
4
Step-by-step explanation:
12÷3=4
show your work using standard athgorithm
Answers
The answers are in the (square)
which of the following is a quantitative research method that aims to observe the relationship between an independent variable and a dependent variable? a.) a questionnaire b.) secondary data analysis c.) a focus group d.) an experiment
Answers
The correct option is a.) a questionnaire, used as observing the relationship between independent variable as well as a dependent variable is the goal of a quantitative research technique known as employed as.
Define the term quantitative research method?Quantitative methods place an emphasis on accurate measurements or the statistical, quantitative, or numerical evaluation of information gathered through surveys, polls, and other types of research, as well as the manipulation of statistical data that has already been obtained using computing methods.
Quantitative research involves gathering numerical information and using it to understand a specific event or generalise it across groups of individuals.
Its primary attributes are:
Typically, organised research tools are used to acquire the data.Given its high reliability, the research study can typically be replicated or redone.The researcher has a specific study question to which unbiased solutions are sought.Before data is collected, the study's various components are all carefully designed.Numbers and statistics make up data, which are frequently displayed in tables, charts, and other non-textual formats.To know more about the quantitative research method, here
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50 POINTS!! NEED HELP
Drag each label to the correct location on the image.
Identify which equations have one solution, infinitely many solutions, or no solution.
Answers
Answer:
the label are marked by numbers
A) A box of mass 9 kg contains x articles each of mass 1.2 kg. Write down an expression for the total mass of the box and its contents.
B) How many articles are there in the box if the total mass of the box and articles is 21 kg?
Answers
Step-by-step explanation:
A. total mass = 9 + (x × 1.2)
B. 21 - 9 = 12kg
12 ÷ 1.2 = 10 articles.
hope it helps. :)
Which of the coordinate pairs below are separated by a vertical
distance of greater than 6 units? Select all that apply.
A) (5.1, -3.3) and (5.1, 3.4)
B) (-1, 2.6) and (-1, -4.2)
C) (3.7, 2.2) and (3.7, -3.4)
D) (6, 1.5) and (6, -2)
Answers
Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.
(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7
Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5
Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
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Solve the inequality statement:
2v+1> 7
v > 3
v > 4
v < 3
v < 4
Answers
Answer:
v>3
Step-by-step explanation:
2v>7-1
2v>6
v>6/2
v>3
