Susan launches a rocket straight up into the air. The table below gives the height (t) of the rocket (in meters) at a few times t (in seconds) during its flightTimet(seconds)02.26.68.813.2Height HD(meters)0110198440(a) Find the average rate of change for the height from oseconds to 2.2 seconds.Il meters per second(6) Find the average rate of change for the height from6.6 seconds to 13.2 secondsI meters per second
Answers
The average rate of change from t1 to t2 where t2>t1 for a function the function H(t) is given as:
\(\frac{H(t_2)-H(t_1)}{t_2-t_1}\)Next substitute H(t2)=110, t2=2.2, H(t1)=0, t_1=0 into the formula:
\(\begin{gathered} \frac{110-0}{2.2-0} \\ =\frac{110}{2.2} \\ =50\text{ m/s} \end{gathered}\)For the "b" part, substitute H(t2)=0, t2=13.2, H(t1)=198, t_1=6.6 into the formula:
\(\begin{gathered} \frac{0-198}{13.2-6.6} \\ =-\frac{198}{6.6} \\ =-30\text{ m/s} \end{gathered}\)The negative in the rate of change here represent a decrease in height as time increases.
Related Questions
Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
Answers
Answer:
39 3/8 ft ^2
Step-by-step explanation:
To find the area of a rectangle, multiply the length times the width.
A = l*w
= 7 1/2 * 5 1/4
Change the mixed numbers to improper fractions.
A = 15/2 * 21/4
=315/8
Change back to a mixed number.
8 goes into 315 39 times with 3 left over.
= 39 3/8
Answer:
Area = 39.375 ft²
(you can round to 39.4)
Step-by-step explanation:
Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
7 1/2 = 7.5 ft
5 1/4 = 5.25 ft
Area = L x W
Area = 7.5 x 5.25
Area = 39.375
I need help this is due Tuesday!
Answers
Whats the total package cost of the pond and he said he would have to be full of Candy :')
I wasnt paying attention and class help please.-.
Answers
Answer:
The picture is just black... Can you try typing it and I can try to help?
Step-by-step explanation:
Two parallel lines are cut by a transversal as shown below. Suppose m<6=102 degrees. Find m< 1 and m< 4.
Answers
Answer:
m∠1=78°
m∠4=102°
Explanation:
Given: m∠6=102°
In the figure, angles 6 and 4 form an extended Z-shape. Thus, angles 6 and 4 are alternate angles.
Since alternate angles are equal in measure:
\(\begin{gathered} m\angle4=m\angle6 \\ \implies m\angle4=102\degree \end{gathered}\)Next, angles 4 and 1 are on a straight line, therefore:
\(\begin{gathered} m\angle4+m\angle1=180\degree \\ \implies102\degree+m\angle1=180\degree \\ m\angle1=180\degree-102\degree \\ m\angle1=78\degree \end{gathered}\)The measures of angles 1 and 4 are 78 degrees and 102 degrees respectively.
Given two equations, MN = 20 and S=2-M+N Find the positive values of M and N . when S is minimum.
Answers
The positive values of M and N are; 3.6 and 5.6 respectively.
Simultaneous equationsWhen S is minimum, s can be equated to 0.
On this note, it follows that the resulting equations are;
MN = 200=2-M+NFrom Substitution of M = 2 +N in the second equation; it follows that;
(2+N)N = 20N² + 2N -20 = 0.Hence, upon solving the quadratic equation;
N = 5.6 or N = -3.6Therefore, the positive value of N is; 5.6 and hence,
M = 20/N = 20/5.6 = 3.6Read more on simultaneous equations;
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The positive values of M and N are; 3.6 and 5.6 respectively.
Simultaneous equationsWhen S is minimum, s can be equated to 0.
On this note, it follows that the resulting equations are;
MN = 200=2-M+NFrom Substitution of M = 2 +N in the second equation; it follows that;
(2+N)N = 20N² + 2N -20 = 0.Hence, upon solving the quadratic equation;
N = 5.6 or N = -3.6Therefore, the positive value of N is; 5.6 and hence,
M = 20/N = 20/5.6 = 3.6Read more on simultaneous equations;
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Write these as normal numbers.
a) 6 x 10° b) 3 x 10° c) 9 x 105 d) 2 x 10"
Answers
Answer:
D
Step-by-step explanation:
A pet store has 11 puppies, including 4 poodles, 5 terriers, and 2 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random with replacement (they may both select the same one), find the probability that Rebecka selects a terrier and Aaron selects a retriever.
Answers
The probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121
How to determine the probability?The distribution of the puppies is given as:
4 poodles, 5 terriers, and 2 retrievers
The probability of selecting a terrier is;
P(terrier) = 5/11
The probability of selecting a retriever is;
P(retriever) = 2/11
The required probability is
P = 5/11 * 2/11
Evaluate
P = 10/121
Hence, the probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121
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Help me pleaseeeeee!
Answers
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
In algebra, what is a rectangle?A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
check the attachment given belοw tο understand.
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Write 4.48 as a mixed number in simplest form.
Answers
Answer:
4 12/25
Step-by-step explanation:
4.48 can be written as 4 48/100
Simplify
4 24/50
Simplify some more.
4 12/25
Hope this helped :)
Greg washes cars on Saturdays at his dad’s car dealership. His dad pays him $50 plus $5 for each car that he washes. Greg washed 11 cars last Saturday. Use function notation to write an equation that gives the total amount Greg earns as a function of the number of cars he washes. Use the equation to find how much he earned last Saturday.
(SHOW WORK)
Answers
Answer:
605
Step-by-step explanation:
11x55=605
You work as a residential painter. A customer wants two tables and eight chairs painted using one coat of the same color paint. Each table requires 158
5
8
quarts of paint, and each chair requires 23
2
3
quarts of paint. How many total quarts of paint should you bring to paint this furniture?
Answers
Each table requires = 158 quarts paint
Each chair = 23 quarts of paint
Total no. Of coats = 1
Total chairs = 8
Total table = 2
Total paint required = (158×2)+(23×8)
= 500 quarts of paint
Must click thanks and mark brainliest
Work out the following without using a calculator
11101010 base 2 + 2122 base 8 + ABC base 16 - 123 base 8, Give your answer in decimal
Answers
Answer:
Step-by-step explanation:
To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:
11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:
1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.
2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:
2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.
ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:
10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.
123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:
1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.
Now, let's perform the arithmetic operations:
234 + 1090 + 2748 - 83 = 3989.
Therefore, the result of the given expression in decimal form is 3989.
An obtuse triangle has side lengths of (5.5x + 6.2y) centimeters, (4.3x + 8.3z )and (1.6z + 5.1y) centimeters. Which expression represents the perimeter, in centimeters of the obtuse triangle? PLZ HELP ASAP :)
Answers
Answer:
The expression \(9.8x+11.3y+9.9z\) represents the perimeter, in centimeters of the obtuse triangle.
Step-by-step explanation:
An obtuse triangle is a triangle where one of the internal angles is obtuse (greater than 90 degrees).
The perimeter of a triangle is the total distance around the outside of a triangle, which can be found by adding together the length of each side. Or as a formula:
\(P=a+b+c\)
where:
a, b and c are the lengths of each side of the triangle.
We know that the triangle has side lengths of \(a = 5.5x + 6.2y\), \(b= 4.3x + 8.3z\) and \(c=1.6z + 5.1y\) centimeters. Therefore, the perimeter is
\(P=a+b+c\\P=(5.5x + 6.2y)+(4.3x + 8.3z)+(1.6z + 5.1y)\\\\\mathrm{Group\:like\:terms}\\P=5.5x+4.3x+6.2y+5.1y+8.3z+1.6z\\\\\mathrm{Add\:similar\:elements:}\\P=9.8x+11.3y+9.9z\)
On a map, the scale shown is 1 inch : 5 miles. If
a wildlife refuge is 50 square miles, what is the
area of the refuge on the map?
Use the proportion to solve for x.
1 in. 2
25 mi2
x in. ²
50 mi²
Cross
multiplication
can help!
=
The area of the wildlife refuge is [?] square
inches on the map.
Enter
Answers
Answer:
Step-by-step explanation:
6
A charity is considering the possibility of having a benefit night at two different restaurants. The owner of the local Italian restaurant has offered to make a donation of $462 and $1 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $235 plus $2 per diner. Based on the number of diners who have promised to participate in the event, it appears that each restaurant would donate the same total amount. How many diners promised to participate? How much would each restaurant donate?
Answers
Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:
Italian restaurant:
Donation = $462 + $1 per diner
Donation = $462 + $1x
Mexican restaurant:
Donation = $235 + $2 per diner
Donation = $235 + $2y
Since both restaurants will donate the same total amount, we can set their donations equal to each other:
$462 + $1x = $235 + $2y
Simplifying this equation, we get:
$2y - $1x = $227
We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.
For example, if we try x = 200, then we can solve for y:
$2y - $1(200) = $227
$2y = $427
y = 213.5
Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:
$2y - $1(250) = $227
$2y = $477
y = 238.5
Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:
$2y - $1(300) = $227
$2y = $527
y = 263.5
Still not a whole number, so we try x = 350:
$2y - $1(350) = $227
$2y = $577
y = 288.5
Finally, we get a whole number for y, so we have our solution:
Italian restaurant: x = 350 diners, donation = $812
Mexican restaurant: y = 289 diners, donation = $812
Therefore, 350 diners promised to participate and each restaurant would donate $812.
In any year, the weather can inflict storm damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 95% of the years Y = $0, but in 5% of the years Y = $20,000.
A. The mean of the damage in any year is $__. nothing. The standard deviation of the damage in any year is $____.
B. Consider an "insurance pool" of 100 people whose homes are sufficiently dispersed so that, in any year, the damage to different homes can be viewed as independently distributed random variables. Let barY denote the average damage to these 100 homes in a year. The expected value of the average damage barY, is $____. The probability that exceeds $is____.
Answers
Answer:
a. mean = 1000
standard deviation = 4358.9
b. expected value of average damage bar Y = 1000
probability bar y exceeds 2000 = 0.011
Step-by-step explanation:
we have p1 = 95%, y1 = 0, p2 = 5%, y2 = 20000
Mean = (0.95 * 0) + (0.05 * 20000)
= 1000
var(y) = E(y²) - E(Y)²
= we solve for E(y)²
= 0²*0.95 + 20000²*0.05
= 0 + 20000000
then the variance of y = 20000000 - 1000²
=20000000-1000000
= $19000000
standard deviation is the square root of variance
= √19000000
= 4358.9
2.
a. Expected value of average is also the mean = 1000
b. we are to find probability that barY exceeds 2000
\(z=\frac{2000-1000}{\sqrt{19000000/100} }\)
= 1000/435.889
= 2.29
1-p(z≤2.29)
= 1 - 0.989
= 0.011
so the probability that barY exceeds 2000 is 0.011
What point on the graph represents the unit cost at Florentino’s? What is the unit cost?
Answers
Answer: I think it 2,24
Step-by-step explanation:
what is 5 ft to 18 in.
Answers
Answer:
68 inches
Step-by-step explanation:
its sixty eight inches
2. Students who wish to represent the school at a school board meeting are asked to stop
by the office after lunch. After lunch, 5 students wish to represent the school.
Answers
Answer: Biased sample
Step-by-step explanation:
This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.
A ________ function specifies the relationship between the demand for a product LaTeX: x and the price of the product LaTeX: p.
Answers
Answer:
Price demand function
Step-by-step explanation:
The price demand function is the function in which there is a relationship between the demand and the price of the product
The Price demand function is
\(= Price \times demand\)
\(= p \times x\)
hence, the price demand function represents that there is a relationship that lies between the demand and the price
a student spends 18 out of 35 of his pocket money on transport and fruit what is the fraction left?
Answers
To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.
The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.
Therefore, the fraction of pocket money left can be written as 17/35.
A study of bone density on 5 random women at a hospital produced the following results.
Age 41, 53, 57, 61, 65.
Bone density: 360, 355, 340, 325, 310
Calculate the correlation coefficient, r. Round your answer to three decimal places.
Answers
The correlation coefficient when there is a study of bone density on 5 random women is -0.909.
What is the correlation coefficient?It is the statistical measure of the strength of the linear relationship that's between two variables. The correlation coefficient is calculated by calculating the covariance of the variables and dividing that number by the product of the standard deviations of those variables.
The steps for calculating the correlation coefficient are as follows:
Choose your data sets.Determine the standardized value for your x variables.Determine the standardized value for your y variables.Find the sum by multiplying.Determine the correlation coefficient by dividing the total.The statistical software was used and the values include
Dependent variable = y
Independent variable = x
It should be noted that linear regression has an equation that is in the form of Y = a + bx. The equation is y = 451.674 - 2.051. This was gotten through the statistical software used.
Sample size = 5
Correlation coefficient = -9.09
In conclusion, the coefficient is -9.09.
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Choose the correct simplification of (5xy^7)^2(y^4)^3.
25x^2y^22
10x^2y^14
25x^2y^14
10x^2y^20
Answers
The simplified form of the given expression is 25 x² y ²⁶.
What is the simplified form of the expression?
Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.
What are the exponent rules?
The different Laws of exponents used to solve the above mentioned question are:
\(x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }\)
According to the given question.
We have an expression (5xy⁷)²(y⁴)³
To simplify the above expression we use the exponent rules.
Therefore,
(5xy⁷)²(y⁴)³
(5² x² y²×⁷) (y ⁴׳)
(25 x² y¹⁴ ) (y¹²)
25 x² y¹⁴⁺¹²
25 x² y ²⁶
Therefore, the simplified form of the given expression is 25 x² y ²⁶
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an office manager purchased 39 boxes of pens for the staff. each box contains 6 black pens and 4 blacks pens. Use the distribute property to write an equivalent expression for the total number of pens. them, simplify the expression
Answers
Answer:
390 pens in total
Step-by-step explanation:
Each box has 6 black and 4 black
so the total amount of pens per box should be 10 because 6+4=10
Since we have to use distributive property you can write the equation (6+4)*39 because you need to figure out the total amount of pens in all the boxes.
6+4 is 10
and 10 * 39 is 390
therefore the answer is 390 pens in total
You have one type of chocolate that sells for $3.40/lb and another type of chocolate that sells for $9.00/lb. You would like to have 44.8 lbs of a chocolate mixture that sells for $5.00/lb. How much of each chocolate will you need to obtain the desired mixture?
Answers
Using a system of equations, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed to obtain the desired mixture.
How to Apply System of Equations?Let x be the amount of the $3.40/lb chocolate needed, and y be the amount of the $9.00/lb chocolate needed to make 44.8 lbs of a $5.00/lb mixture.
We can set up the following system of equations:
x + y = 44.8 (total amount of mixture)
3.4x + 9y = 5(44.8) (total cost of mixture)
Solving this system of equations, we get:
x = 32 lbs of the $3.40/lb chocolate
y = 12.8 lbs of the $9.00/lb chocolate
Therefore, to obtain the desired mixture, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed.
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Solve the inequality. 9 + 9(x + 7) >= 36 The solution is
Answers
Answer:
x≥ -4
Step-by-step explanation:
9 + 9(x + 7)≥ 36
Subtract 9 from each side
9 -9+ 9(x + 7) ≥ 36-9
9(x + 7) ≥ 27
Divide each side by 9
9/9(x + 7) ≥ 27/9
x+7≥ 3
Subtract 7 from each side
x+7-7 ≥ 3-7
x≥ -4
Answer:
x >= -4.
Step-by-step explanation:
9 + 9(x + 7) >= 36
9 + 9x + 63 >= 36
9x >= 36 - 63 - 9
9x >= -36
x >= -4.
Please help me solve this question will give you braisnlt !
Answers
Answer:
C
Step-by-step explanation:
In slope intercept form y=mx+b
m is your rate of change/ slope
since the slope is +5
This means that your rate of change, in this case elevation, is 5 feet per minute.
As for b which is your y intercept, the -30 can be represented by the point (0,-30) on a graph it would be -30ft below the x axis. Meaning that if the diver lets say is the point he is 30 feet below sea level and acsending at a rate of 5 feet per minute.
Each of four test scores in Connie’s class is to be weighted equally. On the first three tests, Connie scored 80%, 90% and 95%. What percent must she score on her fourth test to have an overall average of exactly 90%?
Answers
Answer:
95%is the answer
Step-by-step explanation:
Answer:
95%
Step-by-step explanation:
We can use the balancing method to do this.. first what is the total below 90?
The total is 10% because 90-80 which was the only percentage below 90 is 10%. Then, what is the total above 90?
The total is 5% because the only percentage above 90 is 95 and 95-90 is 5%
Now we use the balancing method to get from 5-10.
Using the balancing method we get 95%
The area of a room is 56 square feet. The width of the room is 7 feet. Of Alicia is going to put an animal wall border on all four walls of the room, how many feet of border does she need
Answers
Length of room = area / width
Length of room = 56/7 = 8 feet.
She will need 7 + 7 + 8 + 8 = 30 feet of border.
the base of the triangle prism shown below is a right triangle. What is the lateral surface area of the prism
Answers
Given data:
The given triangular prism.
The expression for lateral surface area is,
\(\begin{gathered} LS=(8\operatorname{mm}+\text{ 6mm +}10\text{ mm)}\times12\text{ mm} \\ =288\text{ sq-mm} \end{gathered}\)Thus, the lateral surface area is 288 sq-mm.