As determined in part, the ball reaches its highest point at time t is 2 seconds
how many seconds does the ball strike the ground?S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.
The ball's starting speed is 64 feet per second.
(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).
(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.
(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.
v(t) = 32 - 16t = 0
or 16t = 32
out = 2 seconds.
As determined in part, the ball reaches its highest point at t = 2 seconds (c).
s(t = 2) = 32(2) - 16(2) (2)
2
or 32 feet if s(t = 2).
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Elaina bought 4.6 pounds of sliced ham at a price of $6.15 per pound. How much did she spend in total? quick
Answer:
$28.29
Step-by-step explanation:
1 pound: $6.15
4.6 pounds: 6.15 x 4.6 = $28.29
Solve systems by elimination step by step
2x + y = 180
x - y = 30
The value of x=70 and y=40
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Here, 2x+y=180
x-y= 30
Here, the coefficient of y in these two equations are equal and have opposite signs. so,
2x+y= 180
x-y= 30
Now adding equation 1 and equation 2
We get,
3x= 210
x= 210/3
x= 70
Now, to find y:
Putting the value of x in equation 2
x-y= 30
70-y= 30
y= 70-30
y= 40
so, the value of x and y are 70 and 40
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Simplify: -20z^8+ (-2z^8)
Enter the original expression if it cannot be
simplified.
Therefore , the solution of the given problem of expression comes out to be 22[tex]z^{8}[/tex].
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : -20[tex]z^{8}[/tex]+ (-2[tex]z^{8}[/tex])
=> -22[tex]z^{8}[/tex]
So ,
In order to find the solution we add them
Thus ,
simplification of given expression is:
=> - 22[tex]z^{8}[/tex]
Therefore , the solution of the given problem of expression comes out to be 22[tex]z^{8}[/tex].
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the fraction 3/5 fits into 2 1/5 less than more than 1 time
Answer:
Q = 3.667
Step-by-step explanation:
A 3-gallon container of disinfectant costs $36.24. What is the price per quart?
Answer:
10.74666666666667 per quart
Step-by-step explanation3 divided 36.24
Between 2020 and 2021, the population of a town decreased by 35%
In 2021, the population of the town was 94 900. What was the population of the town in 2020?
Answer:
Step-by-step explanation:
if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.
so, we do the rule of three:
x = (94900 * 100)/ 65
x = 146000
and that is the population in 2020.
Answer:
Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?
Which object has the largest resultant force?
10N-
10N-
30 N-
A
C
30 N
5N
-5N
10N-
5N-
5N-
5N-
B
D
10N
10 N
Answer:
To find the resultant force of an object, we need to add up all the forces acting on it. The resultant force is the overall force that the object experiences, taking into account all the individual forces.
In this case, we are given four objects, A, B, C, and D, and the forces acting on them. To find the object with the largest resultant force, we need to calculate the resultant force for each object by adding up all the forces acting on it.
For object A, the forces acting on it are: 10 N, 10 N, and 10 N, for a total of 10 N + 10 N + 10 N = 30 N.
For object B, the forces acting on it are: 5 N, 5 N, 5 N, and 5 N, for a total of 5 N + 5 N + 5 N + 5 N = 20 N.
For object C, the forces acting on it are: 30 N and -5 N, for a total of 30 N + (-5 N) = 25 N.
For object D, the forces acting on it are: 10 N and -5 N, for a total of 10 N + (-5 N) = 5 N.
Therefore, the object with the largest resultant force is object C, with a resultant force of 25 N.
Which is not a factor pair of 300
Answer:
Step-by-step explanation:
So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.
I need help with this!
Ubehebe Crater in Death Valley has a diameter of a little more than mile. If Latisha walks around its
rim at a rate of 2 miles per hour, about how long will it take her to walk all the way around the crater? Find your
answer to the nearest tenth. Use 3.14 for pi
On solving the provided question we can say that the it will 4 hrs to walk all the way around the crater, on doing the radius.
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
here,
D= 1
r = 1/2 = .5
A = 40
T = 40/10 4 hrs.
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Imagine a box with an ant at one corner. The ant wants to travel to the opposite corner by the most direct path. It must travel across the top of box at some stage. The top of the box is the light area. It cannot travel along the ground or under the box. (Hint : it does not have to travel along an edge)
The solution is Option A.
The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the shortest distance be represented as X
Let the first triangle be the first face of the rectangular box ΔABC
The length of the triangle AB = 3 cm
The height of the triangle BC = 2 cm
Now ,
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
The measure of AC = √ ( 3² + 2² )
The measure of AC = √13 cm
And , the second triangle is the second face of the rectangular box ΔDEF
The length of the triangle DE = 4 cm
The height of the triangle EF = 2 cm
The measure of DF = √ ( 4² + 2² )
The measure of DF = √18 cm
Now , the shortest distance X = The measure of AC + measure of DF
Substituting the values in the equation , we get
The shortest distance X = √13 cm + √18 cm
The shortest distance X = 3.60 + 4.24
The shortest distance X = 7.8 cm
Therefore , the value of A is 7.8 cm
Hence , the shortest distance for the ant is 7.8 cm
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Helen draws a random circle, she then measures the circumference and diameter.
She gets a circumference C of 405mm correct to 2 significant figures
She gets a diameter D of 130mm correct to 2 significant figures
Helen wants to find the value of [tex]\pi[/tex] using the formula [tex]\pi[/tex] = C÷D
Calculate the lower and upper bound for Helens value of [tex]\pi[/tex]
Give your answer correct to 3 decimal places
The value of π can be written with upper and lower limits as -
3.12 ± 0.062.
What are significant figures?Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.
We can write -
Circumference {C} = (405 ± 2) mm
Diameter {D} = (130 ± 2) mm
The value of π can be calculated as -
π = {C}/{D}
π = (405 ± 2)/(130 ± 2)
Now, divide the numbers without errors first -
405/130
3.12
Now, we will calculate the relative errors in each number -
2/405 = 0.004
2/130 = 0.016
Adding the relative errors -
0.004 + 0.016
0.02
Absolute error = 0.02 x 3.12 = 0.062
The value of π can be written with upper and lower limits as -
3.12 ± 0.062
Therefore, the value of π can be written with upper and lower limits as -
3.12 ± 0.062.
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Between 2020 and 2021, the population of a city increased by 20% In 2021, the population of the city was 420 000. What was the population of the city in 2020?
Answer:
350,000.00
Step-by-step explanation:
420,000.00 - 20% = 350,000.00
Increase percentage: 70,000.00
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 9 14
Not in Physics 24 2 26
Total 29 11 40
it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both using principle of inclusion-exclusion we can say 38 students are enrolled in either algebra or physics.
How to find the number of students enrolled in either algebra or physics?To find how many students are enrolled in either algebra or physics, you can use the principle of inclusion-exclusion, which states that the total number of elements in two sets can be found by adding the number of elements in each set and then subtracting the number of elements that are in both sets.
So, the number of students enrolled in either algebra or physics is:
29 (students enrolled in algebra) + 14 (students enrolled in physics) - 5 (students enrolled in both) = 38
So, 38 students are enrolled in either algebra or physics.
It is important to notice that in the table you provided is a two-way frequency table also known as a contingency table, it shows the relationship between two variables, in this case, Algebra and Physics and the frequencies of each combination.
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To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
52s is the maximum time that she can take on her last lap and still make the team.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).
The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
We need to find the maximum time (in seconds) that she can take on her last lap and still make the team
Let x be the maximum time (in seconds) that she can take on her last lap
60=(63+62+65+58+x)/5
300=63+62+65+58+x
300=248+x
Subtract 248 on both sides
300-248=x
x=52s
Hence, 52s is the maximum time that she can take on her last lap and still make the team.
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Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.
Answer: 5%
Step-by-step explanation:
Answer:
answer is 10
Step-by-step explanation:
evaluate the expression when m=8 and n = 37
Answer:
31Step-by-step explanation:
[tex]\sf 37-\cfrac{48}{8}[/tex]
Divide numbers ( 48/8 = 6)
[tex]\sf 37-6[/tex]Subtract numbers:-
[tex]\sf 31[/tex]31 is your answer!
___________________
Hope this helps!
Have a great day!
In Mrs. Austin's science class, 37.5% of the students have compleated their science project. Of the remaining students, 40% have compleated only half of their science project. If there are 32 students in Mrs. Austin's science class, how many of these students have compleated half of their science project?
well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.
now, of those 62.5% fellows only 40% have finished only half of it, how many are those?
well, what's 62.5% of 32? what's 40% of that much?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]
Write an equation of a line
Answer:
Step-by-step explanation:
Steps to find the equation of a line from two points:
1) Find the slope using the slope formula. ...
2) Use the slope and one of the points to solve for the y-intercept (b). ...
3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.
Given U(-6, 7), V (1, -7), W (6, 4), and X (10, y). Find y such that
UV LWX.
standard equation for hyperbola with vertices (-2, 1), (2, 1) and foci (-3, 1) (3,1)
Will give brainliest
Answer:y=(x+3)2−17
Step-by-step explanation: 3,11 5,15
PLEASEEEE HELP MEE WITH THIS EQUATION
Answer:
Basically, LON would be 8z + 112 + 6z - 17
So, our equation will look like this
8z + 112 + 6z - 17 = -1z + 65
Subtract the 6z from the 8z
2z + 112 - 17 = -1z + 65
112 - 17 = 95
2z + 95 = -1z + 65
add the 1z
3z + 95 = 65
subtract the 95
-30
3z = -30
The answer is -10 :)
Step-by-step explanation:
Answer:
LON=75
Step-by-step explanation:
LON= LOM=NOM
-1z+65=8z+112-6z-17
-1z+65=2z+95
3z=-30
z=-10
LON= -1z+65
= -1(-10)+65
= 10+65
LON= 75
What is the area of the circle if BC = 6cm?
Answer:
[tex]A=9\pi cm^{2}[/tex][tex]=28.27cm^{2}[/tex]
Step-by-step explanation:
If BC= 6
then r = BC/2 = 6/2 = 3cm
[tex]A=\pi r^{2} =\pi (3)^{2} =9\pi[/tex]
[tex]A=28.27cm^{2}[/tex]
Hope this helps
AP TEST QUESTION 1
PLEASE HELP
ILL GIVE BRAINLIST ANSWER
IMAGE ABOVE
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x).
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
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A condominium owner pays property taxes of $2,000 per year. If taxes are figured
at a rate of $1.25 for every $100 in value, what is the value of his condominium?
Step-by-step explanation:
the tax rate gives us a ratio of tax amount to value.
this ratio (in our case 1.25/100) is constant for any value.
therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.
in other words, we multiply
1.25/100 × f/f
so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.
f = 2000 / 1.25 = 1600
so, we get
1.25/100 × 1600/1600 = 2000 / 160000
so, the value of the condominium is
value = $160,000
The average number of customers at the cafe fell by 10% in the month of May. If 140 fewer customers visited the cafe in May, how many customers visited in April?
Answer:
1400
Step-by-step explanation:
You want to know the number of customers in April if the number in May was 10% lower. That number was 140 fewer.
PercentThe problem statement is telling us ...
April - (10% × April) = April - 140
10% × April = 140 . . . . . . . . subtract April, multiply by -1
April = 140/10% = 1400 . . . . divide by 10%
The number of customer visits in April was 1400.
__
Additional comment
The 1400 customers in April fell by 140 to 1260 in may. That's 10% fewer than in April.
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10. What is a composition of rigid motions and a dilation that maps APZY onto ARST
I’m confused on this subject please explain to me how you got an answer thank you
Answer:
dilation by a factor of 1/2reflection over the line y = -xStep-by-step explanation:
You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.
DilationFirst of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.
The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...
k = RS/PZ
Counting grid squares in the figure, we see this ratio is ...
k = 2/4 = 1/2
Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.
Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.
ReflectionWhen we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.
The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.
We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.
Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.
This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.
__
RotationIf we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.
So, another sequence of transformation that will make the required mapping is ...
dilation by a factor of 1/2reflection across the y-axisrotation 90° CCWThe order of reflection and rotation is important. The dilation can occur anywhere in the sequence.
Alternate solutionPerhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...
dilation by a factor of 1/2reflection across the x-axisrotation 90° CWIf you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.
__
Additional comment
Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.
Tracing paper and/or transparencies can be helpful for these exercises.
2 points How Did I Do? The cost of renting a car is $42 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=42+0.25x , where x is the number of miles traveled.
The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.
How to formulate the equation ?The total cost of renting the car at any given point, would be:
= Cost to rent per week + ( Cost per mile x Number of miles driven)
If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x
If we further take y to be the total cost, the equation then becomes :
y = 42 + 0. 25 x
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823× 3.6 weekly math review homework for fifth grade
Which graphs show continuous data?
Select each correct answer.
HELP ME PLEASE!!!
Answer: the bottom two graphs show continuous data
Step-by-step explanation: