The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.
What is function f(x)?An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).
A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."
Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).
In the given question,
The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).
S'(t) = 112
Therefore, when S'(t) = 112, t = 3.5.
This means that the rocket reaches its maximum height at t = 3.5 seconds.
Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.
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I really need help! Can you help??
Answer:
To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.
Step-by-step explanation:
Enter the denominator of the fraction is simplest form that is equal to 0.7
The simplest form of the fraction equivalent to 0.7 is 7/10
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, to show the denominator of the fraction in the simplest form that is equal to 0.7
To convert 0.7 into a fraction, we have to write it in p/q form, where p and q are positive integers.
we can write .7 as 0.7/1
now to remove the decimal point we will multiply and divide by 10
therefore,
0.7/1 × 10/10 = 7/10
Hence, the simplest form of the fraction equivalent to 0.7 is 7/10
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you shuffle a standard deck of cards, then draw four cards.(a) what is the probability all four are the same suit? (b) what is the probability all four are red? (c) what is the probability each has a different suit?
a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105
Total number of cards =52
No. of cards for each suit =13
Total types of four suit =4 (heart, spades, diamonds, clubs)
Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways
a) number of ways choosing four cards of the same suit
= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]
= [tex]4 \times ^{13}C_4\\[/tex]
= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]
=2860 ways
Probability that all four are the same suit is 2860/270,725 = 0.0106
b) Number of ways all four cards are red
=[tex]^{26}C_4[/tex]
= 4,950 ways
Probability that all four are red = 4950/270,725 =0.055
c) Number of ways each card has a different suit
=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]
= 28,561 ways
Probability each has a different suit is 28561/270725 = 0.105
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Show that x(x -3m) = 5m² is non-real
The equation x(x - 3m) = -5m² is non-real as the discriminant of the quadratic equation will be negative.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions = zero real solutions.The equation for this problem is defined as follows:
x(x - 3m) = -5m²
x² - 3mx + 5m² = 0.
The parameters are given as follows:
a = 1, b = -3m, c = 5m².
Hence the discriminant is given as follows:
Δ = (-3m)² - 4(1)(5m²)
Δ = 9m² - 20m²
Δ = -11m².
-11m² is always negative, hence the discriminant is negative and the equation is non-real.
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i don’t understand what i’m supposed to do
The function with a greater stretch factor is the function graphed and the value is 3 times greater
How to find the function with the greater stretch factorThe function with a greater stretch factor is the function which has a greater number multiplying the function
The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2
The stretch factor is determined by the coefficients which are
a(x): 1/3 and b(x): 1
comparing this numbers
= b(x) / a(x)
= 1 / 1/3
= 3
this shows that b(x) which is 1 is greater by 3 times.
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car rental company a charges an $80 service fee plus $22 per day. car rental company b does not have a service fee and charges $32 per day. which equation will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b? responses 32d
Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]
For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.
Let the number of days be d.
For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.
= [tex]\frac{80+22d}{d}[/tex]
For company b, we will multiply the per day charges with the number of days.
= [tex]32d[/tex]
Now, we will equate both the formed equation
[tex]\frac{80+22d}{d} = 32d[/tex]
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Deshaun rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 80 cents for each mile driven. Deshaun had to pay $250.55 when he returned the truck. For how many miles did he drive the truck?
Answer:
287 miles
Step-by-step explanation:
20.95+ .80x =250.55
250.55-20.95=229.6
.80x=229.6
229.6/.80=x
x=287 miles
Which of the following sequences is an arithmetic sequence?
O {1, 2, 4, 7,...}
O {1, -2, 4, -8,...}
O {1, 4, 7, 10, ...}
O {1, 3, 9, 27,...}
Answer:
The third option
Step-by-step explanation:
The third option, {1, 4, 7, 10, ...} is an arithmetic sequence because you add 3 to get from 1 to 4, and then you add 3 to get to 7, and then you add another 3 to get to 10.
The population of rabbits on an island is growing exponentially. In the year 2000, the population of rabbits was 950, and by 2003 the population had grown to 1000. Predict the population of rabbits in the year 2013, to the nearest whole number.
The population of rabbits in the year 2013 is 1186.
How to predict the population of rabbits in the year 2013?
To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:
P = P₀ * e^(rt)
where:
P = final population
P₀ = initial population (950)
r = the growth rate (we need to find this)
t = time elapsed (13 years)
We can use the data from 2003 to find the growth rate:
1000 = 950 * e^(r * 3)
1000 = 950 * e^(3r)
1000/950 = e^(3r)
ln (1000/950) = 3r
r = (ln(1000 / 950)) / 3
r = 0.0171
Now that we have the growth rate, we can use it to find the population in 2013:
P = 950 * e^(0.0171 * 13)
P = 1186
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For what values of x and y must ABCD be a parallelogram?
The correct answer is,
x = 39
y =21
What is Parallelogram ?A different type of quadrilateral known as parallelogram has both pairs of its opposite sides parallel and equal.
The figure shows a parallelogram ABCD with the parameters AB II CD and AD II BC. Furthermore, AB = CD and AD = BC.
In a parallelogram, the opponent angles are equal.. So it means that side /A is equal to side /C, let's equate the two angles and solve for x;
5y - 3 = x + 3y
2y - x = 3 ........(1)
Also, consecutive angles of a parallelogram are supplementary,
therefore,
/C + /D = 180
x + 3y + 2x = 180
3x + 3y = 180
x + y = 60 .......(2)
Now, add equations (1) and (2)
(2y-x) + (y+x) = 3 + 60
3y = 63
y = 21
now put this value of y in (2) we get,
x + y = 60
x + 21 = 60
x = 39
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Last week, Vanessa bought 14 shirts and 6 hats for a total of $198.
Today, Vanessa bought 10 shirts and 6 hats for a total of $150.
Assuming neither item has changed in price, what is the cost of a
shirt in dollars?
khora
Answer: Shirt-$12 Hat-$5
Step-by-step explanation:
14T + 6H = 198
10T + 6H = 150
4T=48
T=12$
10(12)+6H = 150
120 + 6H =150
H = 5$
HELP ASAP, GUITAR CLASS, WILL MARK FIRST ANSWER BRAINLIEST,
What is the name of the note shown above?
A
B
C
G
Answer:
C
Step-by-step explanation:
The spaces go F A C E. The note shown is C.
Find the missing measurements of the triangle.
35
A
21
B
Round all answers to the nearest whole number.
Bc=?
The measure of BC from the triangle ABC is 40.82 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, in triangle ABC, AB=21 units and AC=35 units.
By using Pythagoras theorem,
BC²=AB²+AC²
BC²=21²+35²
BC²=441+1225
BC²=1666
BC=√1666
BC=40.82
Therefore, the measure of BC is 40.82 units.
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If it takes 2 cups of rice to make 5 servings, how many cups of rice are needed to make 12 servings?
12 servings of rice require six cups of rice. In order to make 12 servings, 6 cups of rice would be needed, or 2/5 of a cup.
1. It takes 2 cups of rice to make 5 servings.
2. Divide 12 by 5 to determine how many cups of rice are required to prepare 12 servings.
3. The final product is 2.4 cups.
4. Round up to the nearest whole number, which is 6 cups, to get 12 servings.
You will require 6 cups of rice to produce 12 servings of rice. The number of servings that can be made from 2 cups of rice can be used to determine this. 5 servings can be produced from 2 cups of rice. This indicates that 2/5 of a cup of rice is needed for each serving. Divide 12 by 5 to see how many cups of rice are required for 12 servings. This results in 2.4 cups of liquid. Round the amount up to the nearest whole number, which is 6 cups, to make 12 servings. 6 cups of rice are therefore required to make 12 servings.
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Find the missing value in the proportion 3/7 = 15/p.
A.21
B.35
C.45
D.75
thomas think that 3 7/8 +2 11/12 is pretty close to 56 but lorinda thinks it’s is closer to 6. Todd disagree with both of them , and thinks it is closer to 7! what do you think? be clear and complete in you’re response
Todd has done correct calculation its values is equal to 6.79, which is closer to 7.
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number on the top side, it indicates the number of equal parts taken or whole quantity and denominator is on the bottom side, it indicates the equal parts of the whole quantity.
Given that,
Two fraction numbers in the form of addition,
⇒ 3 7/8 + 2 11/12
It can be further solved as
⇒ (24 + 7)/8 + (24 +11)/12
⇒ 31/8 + 35/12
Now taking LCM of (8, 12)
LCM(8, 12) = 24
making denominator same in the both terms
⇒ 93/24 + 70/24
⇒ 163/24
⇒ 6.79
Thus, the values is closer to 7
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choose the best data type for each of the following so that any reasonable value is accommodated but no memory storage is wasted. give an example of a typical value that would be held by the variable, and explain why you chose the type you did.
a. The best data type for the number of siblings would be an integer.
An example of a typical value for this variable would be 3, as someone might have 3 siblings. An integer is the best data type because the number of siblings is a whole number and can never be a fraction or a negative number.
b. The best data type for the final grade in this class would be a floating-point number. An example of a typical value for this variable would be 85.5, as a final grade may include decimal points. A floating-point number is the best data type because a final grade can have a decimal point and may include fractions.
c. The best data type for the population of Earth would be a long integer. An example of a typical value for this variable would be 7,794,798,739, as of the year 2020. A long integer is the best data type because the population of Earth is a large number and cannot be expressed using a regular integer.
d. The best data type for the population of a U.S. county would be an integer. An example of a typical value for this variable would be 100,000, as the population of a county can vary greatly. An integer is the best data type because the population of a county is a whole number and can never be a fraction or a negative number.
e. The best data type for the number of passengers on a bus would be an integer. An example of a typical value for this variable would be 20, as a bus can carry a varying number of passengers. An integer is the best data type because the number of passengers on a bus is a whole number and can never be a fraction or a negative number.
f. The best data type for one player's score in a Scrabble game would be an integer. An example of a typical value for this variable would be 45, as a score in Scrabble is calculated in whole numbers. An integer is the best data type because a score in Scrabble is a whole number and can never be a fraction or a negative number.
g. The best data type for one team's score in a Major League Baseball game would be an integer. An example of a typical value for this variable would be 7, as a team's score is calculated in whole numbers. An integer is the best data type because a team's score is a whole number and can never be a fraction or a negative number.
h. The best data type for the year a historical event occurred would be an integer. An example of a typical value for this variable would be 1776, as the year the United States declared independence. An integer is the best data type because a year is a whole number and can never be a fraction or a negative number.
i. The best data type for the number of legs on an animal would be an integer. An example of a typical value for this variable would be 4, as many animals have four legs. An integer is the best data type because the number of legs an animal has is a whole number and can never be a fraction or a negative number.
j. The best data type for the price of an automobile would be a floating-point number. An example of a typical value for this variable would be $25,000.50, as a price for a car can include decimal points. A floating-point number is the best data type because the price of a car can have a decimal point and may include fractions.
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Help me with this math homework pls!
Rewrite every expression underneath, while replacing every sign "x" implied.
23 + 8b = .......
㎡ - 5g = .......
⅛ q + 7a/3 = .....
12k (g+h) =......
(2x + 3)(2 - 5x) = ......
The following expressions rewritten below;
23 + 8bm² - 5g(3q + 56a) / 2412kg + 12kh -10x² -11x + 6How to write algebraic expressions?23 + 8b
No common terms or factors
= 23 + 8b
㎡ - 5g
No common terms or factors
= m² - 5g
1/8 q + 7a/3
= (3q + 56a) / 24
12k (g+h)
= 12kg + 12kh
(2x + 3)(2 - 5x)
= 4x - 10x² + 6 - 15x
combine like terms
= -10x² -11x + 6
Therefore, algebraic expressions are solved by multiplying and combining like terms.
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write the equation for the given graph.
The absolute value function on the graph is:
f(x) = -|x + 4| - 5
What is the equation of the absolute value function?Remember that an absolute value function that has a vertex at (a, b) will be written as:
f(x) = |x - a| + b
Here the vertex is at (-4, -5), replacing that in the general formula we will get:
f(x) = |x + 4| - 5
And we also can see that the absolute value function opens downwards with slopes of 1, then there must be a leading coefficient of -1, the actual function is:
f(x) = -|x + 4| - 5
That is the graphed function.
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Jordan recorded the number of sit-ups he completed during the first 4 track practices. Which of Jordan's friends completed double the amount of sit-ups that Jordan completed during each practice?
The required proportionality relationship between Jordan and his friend for the sit-up is y = 2x.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Jordan recorded the number of sit-ups he completed during the first 4 track practices, we can establish the proportionality relationship between Jordan and his friend by comparing the number of sit-ups each completed during each practice.
Let's call the number of sit-ups that Jordan and his friend completed during each practice "x" and "y". Then, the number of sit-ups that his friend completed during each practice would be "2x".
The proportionality relationship between Jordan and his friend can be expressed as,
y = 2x
This means that for every 1 sit-up that Jordan completed, his friend completed 2 sit-ups, or that Jordan's friend completed twice the number of sit-ups that Jordan completed during each practice.
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Classify each pair of angles as Complementary, Supplementary, or Neither. Drag and drop the choices into the boxes to correctly complete the table. Each category may have any number of pair of angles. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complementary Supplementary Neither
Answer:
Complementary is 2 angles that add up to 90 degrees and supplementary is 2 angles that add up to 180 degrees
48+32=80 so that would be neither
101+77=178 so that would be neither
107+73=180 so that would be supplementary
Step-by-step explanation:
have a nice day.
Answer:
only here for points
Step-by-step explanation:
shaniece has a bag that contains strawberry chews, cherry chews, and lime chews. she performs an experiment. shaniece randomly removes a chew from the bag, records the result, and returns the chew to the bag. shaniece performs the experiment 57 times. the results are shown below: a strawberry chew was selected 31 times. a cherry chew was selected 2 times. a lime chew was selected 24 times. if the experiment is repeated 1200 more times, about how many times would you expect shaniece to remove a lime chew from the bag? round your answer to the nearest whole number.
Shaniece is expected to select a lime chew about 505 times in the next 1200 selections.
Based on the given results, Shaniece selected a lime chew 24 times out of 57 selections. To estimate the expected number of times she would select a lime chew in the next 1200 selections, we can use the proportion of lime chews selected in the first 57 selections:
The proportion of lime chews selected = 24/57
To estimate the expected number of lime chews in the next 1200 selections, we can multiply the proportion by the total number of selections:
expected number of lime chews in the next 1200 selections = (24/57) x 1200
The expected number of lime chews in the next 1200 selections = 505.263
Rounding to the nearest whole number, we would expect Shaniece to select a lime chew about 505 times in the next 1200 selections.
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a square $10$ cm on each side has four quarter circles drawn with centers at the four corners. how many square centimeters are in the area of the shaded region? express your answer in terms of $\pi$.
A square of 10 cm on each side has four quarter circles drawn with centers at the four corners, then the area of the shaded region is 21.46 centimeter square
The side of the square a = 10 cm
The area of the square = a^2
Substitute the values in the equation
The area of the square = 10^2
= 100 centimeter square
There are 4 quarter circle in the figure. We know 4 quarter circle is one circle
The area of the circle = πr^2
Where r is the radius of the circle
The radius of the circle = 5 cm
The area of the circle = π × 5^2
= 78.54 centimeter square
The area of the shaded region = The area of the square - The area of the circle
= 100 - 78.54
= 21.46 centimeter square
Therefore, the area of shaded region is 21.46 centimeter square
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A 3 inch radius circle is drawn inside a 7 inch radius circle. If you throw a dart at these circles, what is the probability AS A PERCENT that you land inside the smaller circle? Round to the nearest whole percent. Use 3.14 for pi.
Answer:
Step-by-step explanation:
NEED HELP
Solve for x.
X=
The measure of the angle x would be 25.2°.
What is a circle theorem?
The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.
By using the circle theorem, we can write
5x-7 = 119
5x = 119 + 7
5x = 126
x = 126/5
x = 25.2°
Hence, the measure of the angle x would be 25.2°.
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Solve 2 ―8―33 = 0 by factoring.
Answer:
the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer
Step-by-step explanation:
To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:
2 - 8 + 33 = 0
becomes
33 - 8 + 2 = 0
Next, we can rewrite this as:
33 - 6 = 0
Finally, we factor the left-hand side of the equation to get:
33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0
So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.
Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:
27 = 0, which is true.
Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.
Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {1, 3, 7}
A ∪ B?
The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}
The event A has data - A = {6, 8, 10}
The event B has data - B = {5, 6, 9, 12}
The event C has data - C = {1, 3, 7}
The probability formula is -
Probability = No. of outcomes that is favorable / Total number of outcomes
The value for A∪B is -
A∪B = 3/4
The value of A∪B in data set is the values that are present in U data set and in A and B data set.
So, the value is - {5, 6, 8}
Therefore, the value is 3/4 or {5, 6, 8}.
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Please help (will mark as brainlest)
Answer:
TRIANGLE PROBLEM:
area : 6a^4
perimeter : 12a^2
SIMPLIFY problem:
-40c^2+26a^2+30ac
EVALUATE & FACTOR:
(q^2 - p) ( p^2 - q)
and the solved form is 240
hope it helps :)
Step-by-step explanation:
lol im an rsm kid too. but i hope these are right,
first i'm gonna start with 263 c.
AREA = 4a^2 * 3a^2 divided by 2.
12a^4 divided by 2 = 6a^4.
AREA = 6a^4
Perimeter you can find with the pythag. th.
(4a^2) ^2 + (3a^2 ) ^2 = c^2
16a^4 + 9a^4 = c^2
, the missing side is 5a^2
therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2
ok next, im gonna do 266
the answer is -40c^2+26a^2+30ac
make sure to check this w/ symbo or mthway
ok last one!!
factored form is (q^2 - p) ( p^2 - q)
and the solved form is 240
Find the value of h such that the line 27hx -9y = -18 would be parallel to the line y = 1 - 6x
For given linear equations, 27hx -9y = -18 and y = 1 - 6x
h will be 2.
What is a linear equation, exactly?
When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.
Now,
As general equation of a line is y=mx + c where m=slope and c=constant
and here given lines are 27hx -9y = -18 and y = 1 - 6x
transforming these into general equations
y=-3hx+2 where m=-3h
and y=-6x+1 where m=-6
Now As slope of parallel lines is equal
therefore, -3h=-6
h=6/3
h=2
Hence,
h will be 2.
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there 10 cars in a race. in how many ways can three cars finish the race as the 1st, 2nd, and the 3rd places?
There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.
There are 10 cars in the race,
Three cars finish the race in the 1st ,2nd and 3rd order
1st finish the race have 10 chances
P(A) = 10
2nd finish the race have 9 chances
P(B) = 9
3rd finish the race have 8 chances
P(C) = 8
The number in which this can be put,
= P(A) x P(B) x P(C)
= 10*9*8
=720 ways
Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
Learn more about Permutation:
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