After answering the presented question, we can conclude that Softball graphs players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a relationship between two or more things. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential growth. A triangle-shaped logarithmic graph.
70% of track athletes drink 4 to 8 glasses of water every day.
We can observe that the blue segment, which represents the number of track athletes who drink 4 to 8 glasses of water each day, accounts for almost 70% of the whole bar. The graph does not support any of the other statements. According to the graph, approximately 25% of track athletes take less than 4 glasses of water, while approximately 5% consume more than 8 glasses. Baseball players drink less than 4 glasses of water, 35% drink 4 to 8 glasses, and 25% drink more than 8 glasses. Softball players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
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The line of elements from the lower left corner to the upper right corner of the second order determinant is called?
The line of elements from the lower left corner to the upper right corner of a second order determinant is called the main diagonal or simply the diagonal. In general, the diagonal of an n x n determinant consists of the elements a11, a22, ..., ann, where ai,i denotes the element in the i-th row and i-th column of the determinant.
HELP PLSSSSSSssssssSSSSS
Answer:
B
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] fathom = 1 yard = 3 feet
then 1 fathom = 2 × 3 feet = 6 feet
1 furlong = 660 feet , then
660 feet ÷ 6 feet = 110
there are 110 fathoms in 1 furlong
what is the common meaning of m and b, 2 + 3x + 5 - 2x = y
Answer:
m=the slope
b=the y intercept
If a Jared is paid time and a half for overtime and he makes $13.00 per hour, how much will he make if he works 52 hours this week? Remember. Jared will only be paid time and a half for the hours that he worked over 40 hours.
Answer:
754
Step-by-step explanation:
First, find the amount of overtime Jared worked by subtracting 40 from 52 hours: 52 - 40 = 12 hours
Then multiply the overtime hours by 1.5 to find the overtime pay rate: 12 * 1.5 = 18
Then multiply the overtime pay rate by the hourly wage to see the overtime pay: 18 * 13 = 234
Then multiply the regular hours by the hourly wage to see the regular pay: 40 * 13 = 520
Then add the regular pay and the overtime pay to see the total pay: 520 + 234 = 754
So the answer is 754
A 19 lb monkey is prescribed a drug to be given for 5 days. The dosage is 28mg/lb body weight. The drug is supplied as an 85mg/mL solution. What is the total number of mL given over five days?
The monkey should be given 6.25 mL of the drug each day for five days, for a total of 31.25 mL
Define mg/lbmg/lb is a unit of measurement that represents milligrams per pound. It is often used in the field of medicine to indicate the dosage of medication per unit of body weight.
The monkey weighs 19 lbs, and the dosage is 28mg/lb. So, the monkey needs:
19 lbs x 28 mg/lb = 532 mg
This is the total amount of the drug that the monkey needs to be given over five days.
Next, we need to find the amount of the drug in milliliters that should be given to the monkey each day.
The drug is supplied as an 85mg/mL solution, so we can calculate the amount of solution needed as:
532 mg / 85 mg/mL = 6.25 mL
Therefore, the monkey should be given 6.25 mL of the drug each day for five days, for a total of:
5 days x 6.25 mL/day = 31.25 mL
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Kareem borrowed money from a credit union for 6 years and was charged simple interest at an annual rate of 6%. The total interest that he paid was $2520 . How much money did he borrow?
Kareem borrowed $7000 from the credit union based on the given interest rate.
We may use the simple interest formula to figure out how much Kareem borrowed:
I = Prt
Where r: yearly interest rate represented as a decimal, P: borrowed principal, I: interest paid, and t: amount of time in years.
We are aware that Kareem borrowed money for 6 years at an interest rate of 6% each year. We also know that he spent $2520 on interest in total. We may determine P using the following formula:
2520 = P0.066
2520 = 0.36P
P = 7000
Kareem thus took out a $7000 loan from the credit union.
In conclusion, we utilized the simple interest formula and the provided data on the interest rate, time, and total interest paid to calculate how much money Kareem borrowed from the credit union. We discovered that he took out a loan for $7000, the principal of which accrued $2520 in interest over the course of six years at an annual rate of 6%.
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What is the value of tan (−284°24′) to the nearest ten-thousandth?
The answer of the given question based on the trigonometry is the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.
What is Equivalent angle?An equivalent angle is an angle that has the same degree measure as another angle. In geometry, two angles are said to be equivalent if they have the same measure, regardless of their orientation or position in space.
Equivalent angles can be found by adding or subtracting multiples of 360° degrees from an angle. This is because an angle that has been rotated a multiple of 360° degrees has the same orientation and position as the original angle.
We can use the fact that the tangent function has period 180 degrees and that tan(x + 180°) = tan(x) for any angle x. Therefore, we can add or subtract multiples of 180° from −284°24′ to find an equivalent angle in the range of −90° to 90°.
Adding 360° to −284°24′ gives us an equivalent angle of 75°36′. Since the tangent function is positive in the first and third quadrants, we can find the value of tangent of 75°36′ or its reference angle of 14°24′.
Using a calculator, we get:
tan(14°24′) ≈ 0.2493
Therefore, to the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.
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To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583.
Define tangent function?We need to keep in mind that the tangent function is periodic in order to determine the value of tan(-284°24'). This means that the tangent of an angle is the same as the tangent of that angle plus or minus any multiple of 180 degrees.
So, we can add 360 degrees to -284 degrees to get an equivalent angle in the range of -180 to 180 degrees:
-284 + 360 = 76
So, we can find the tangent of -284°24' by finding the tangent of 76°24'. Using a calculator, we get:
tan(76°24') ≈ 3.7583
Therefore, To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583. Note that the negative sign indicates that the angle is in the third quadrant of the unit circle.
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HELPPPPPPP MEEEEE PLEASEEEE
24. The price of the motorcycle before tax was $11,500. 25. the instructor earns $28.75 per class after the raise. 26. the sum that Kay and Shay paid, including tax, was $28.62.
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. Equations are used to represent relationships and constraints between variables, and are commonly used in many fields of science, engineering, and mathematics.
An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). Each side of the equation can contain numbers, variables, mathematical operations (such as addition, subtraction, multiplication, and division), and parentheses.
The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true. This is typically done by applying mathematical operations to both sides of the equation in order to isolate the variable on one side and simplify the expression on the other side.
24. Let the price of the motorcycle before tax be represented by x. Then, we can write an equation based on the given information:
0.125x = 1437.50
Solving for x, we get:
x = 1437.50 / 0.125 = $11,500
Therefore, the price of the motorcycle before tax was $11,500.
25. The instructor now earns 115% of $50, or:
$50 x 1.15 = $57.50
Since this is the amount earned for teaching 2 classes, the amount earned per class after the raise is:
$57.50 / 2 = $28.75
Therefore, the instructor earns $28.75 per class after the raise.
26. To find how much Kay paid, we first need to calculate the tax:
0.08 x $14.50 = $1.16
So the total amount Kay paid was:
$14.50 + $1.16 = $15.66
Similarly, the tax Shay paid was:
0.08 x $12 = $0.96
So the total amount Shay paid was:
$12 + $0.96 = $12.96
Therefore, the sum that Kay and Shay paid, including tax, was:
$15.66 + $12.96 = $28.62
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This system of equations has been placed in a matrix:
y = 650x + 175
y = 25,080 − 120x
Column 1 Column 2 Column 3
Row 1 _ -1 _
Row 2 75 _ _
Answer:
The system of equations can be represented by the matrix equation A*x = b, where A is the coefficient matrix, x is the array of unknowns, and b is the array of right-hand sides of the equations. In this case, the coefficient matrix is:
A = [[650, -1, 0],
[75, 0, 1],
[0, -120, 1]]
And the vector of right-hand sides is:
b = [650, 25080, -120]
To solve this system of equations, we need to find the value of x that satisfies the equation A*x = b. This can either be done by manual methods or by using software such as MATLAB.
Manual methods include solving for x using row-reduction techniques, such as Gaussian elimination, or using an algebraic formula for solving linear systems.
Using MATLAB, we can enter the coefficient matrix A and the vector b, create the system of equations, and solve for x using a built-in function:
A = [[650, -1, 0];
[75, 0, 1];
[0, -120, 1]];
b = [650;
25080;
-120];
x = linsolve(A,b);
format long;
disp(x);
This will output x = [0, 25.2142857143, 1.5714285714].
Alternatively, we can use an online calculator such as Wolfram|Alpha to solve the system of equations:
less
A = {{650, -1, 0}, {75, 0, 1}, {0, -120, 1}}
b = {650, 25080, -120}
Solve[A . {x, y, z} == b, {x, y, z}]
ans = {x -> 0, y -> 25.2143, z -> 1.57143}
This will output x = 0,
Which histogram depicts a higher standard deviation?
Jouenbeij
10-
8-
6
4-
2-
40 44 48 52 56 60
(a)
Choose the correct answer below.
OA. Histogram a depicts the higher standard deviation, because the bars are higher
than the average bar in b
H
OC. Histogram a depicts the higher s
more dispersion
deviation, because the distribution has
r.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandlesLocale=true#
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10-
Aouanbes
5% 6+20
30
40 50 60 70
(b)
Q
Q
Submit quiz
OB. Histogram b depicts the higher standard deviation, because the distribution has
more dispersion
O D. Histogram b depicts the higher standard deviation, since it is more bell shaped
Time Remaining: 00:50:04
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The histogram that depicts a higher standard deviation is B. Histogram B depicts the higher standard deviation, because the distribution has more dispersion.
How does dispersion relate to standard deviation ?Dispersion is a measure of how spread out the values in a data set are. Standard deviation is a specific measure of dispersion that quantifies the average amount of variation or dispersion of data points from the mean in a data set.
A histogram with a higher standard deviation will generally show a wider distribution of data, with data points spread further from the mean. We see more dispersion with Histogram B with the figures having a wide range of values so it has more standard deviation.
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can i have helpp tyy
1. An aluminum recycling center pays $0.25 per pound for aluminum cans. Draw a
diagram or picture to illustrate this situation.
2. How much money will someone earn if they bring 8 pounds of cans? Draw a
picture and solve.
3. Ms. Cheese’s 7th grade class needs to earn $50 in their fundraiser. How many
pounds of cans will they need to sell? Be sure to show your work.
From expression 8 pounds x $0.25 per pound and $50 / $0.25 per pound , Earnings = $2.00 and Total pounds of cans = 200 pounds and check attachment for illustration.
What exactly are expressions?An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be basic or complicated, containing a variety of numbers, variables, and mathematical processes.
Now,
1.
Let the total money earned by selling aluminium cans be y and the no. of cans recycled be x then this situation can be represented by the function y = 0.25x, see attachment for illustration.
2.
If someone brings 8 pounds of cans, they will earn:
Earnings = 8 pounds x $0.25 per pound
Earnings = $2.00
3.
To earn $50, the class needs to sell:
Total pounds of cans = Total earnings / Price per pound
Total pounds of cans = $50 / $0.25 per pound
Total pounds of cans = 200 pounds
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Roger wrote a novel 120 pages long. The introduction is 15 pages long, and the chapters average 7 pages in length. How many chapters are in Roger's novel if the book only consists of the introduction and the chapters? A. 12 14 16 18 20 22 B. 12 14 16 18 20 22 C. 12 14 16 18 20 22 D.
Answer:
120 - 15 = 105 pages for the chapters 105 ÷ 7 = 15 chapters Therefore, there are 15 chapters in Roger's novel. The answer is not given in the options provided, so I cannot select one.
The graph represents the distance in miles, y, that Car A travels in x minutes. The function y = 56 x represents the distance, y, that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars? Responses A The rate of Car A is 12 of a mile per minute less than the rate of Car B.The rate of Car A is 1 2 of a mile per minute less than the rate of Car B. B The rate of Car B is 16 of a mile per minute less than the rate of Car A.The rate of Car B is 1 6 of a mile per minute less than the rate of Car A. C The rate of Car B is 16 of a mile per minute greater than the rate of Car A.The rate of Car B is 1 6 of a mile per minute greater than the rate of Car A. D Car A and Car B are traveling at the same rate per minute.
Option D : Since the slopes of the lines representing the distance traveled by Car A and Car B over time are equal, the rates of the two cars are equal.
The graph represents the distance traveled by Car A as a function of time, and the function y = 56x represents the distance traveled by Car B as a function of time.
Since both cars are moving at a constant speed, we can compare their rates by comparing the slopes of the lines representing their distances traveled over time. The slope of a line represents the rate of change of the distance traveled over time (i.e., the speed) of the car.
The slope of the line representing Car A's distance traveled over time is equal to the rise over run, or (14 - 0)/(15 - 0) = 14/15.
The slope of the line representing Car B's distance traveled over time is equal to the rise over run, or (56 - 0)/(60 - 0) = 56/60 = 14/15.
Since both slopes are equal, the rates of the two cars are equal as well. Therefore, the correct answer is:
D) Car A and Car B are traveling at the same rate per minute.
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The graph represents the distance in miles, y, that Car A travels in x minutes. The function y = 56 x represents the distance, y, that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars? Responses
A. The rate of Car A is 12 of a mile per minute less than the rate of Car B.
B. The rate of Car B is 16 of a mile per minute less than the rate of Car A.
C. The rate of Car B is 16 of a mile per minute greater than the rate of Car A.
D. Car A and Car B are traveling at the same rate per minute.
Can anyone help me pls?? You don’t have to do all of them just help me with some pls!!! :(
Answer:
I'll give you a basic idea on how to do them
Pythagoras theorem
If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:
a² + b² = c²
If a is the missing side, then transform the equation to the form where a is on one side and take a square root:
a = √(c² - b²)
If b is unknown, then:
b = √(c² - a²)
If c is unknown, then:
c = √(a² + b²)
5.
a=5, b=7 and c=?
c=√(5^2 + 7^2)
c= √(25 + 49)
c= √74
Hope it helps:)
HELPPPPP IM CONFUSED AND IM TURNING THIS IN LATE
Following are the correct pairs given for verbal mapping statements to symbolic statements.
What is mapping?In mathematics, mapping, or function, is a relation between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).
According to given information,
The verbal mapping statements can be matched to their equivalent symbolic statements as follows:
The figure is translated 4 units right and 3 units down.
Symbolic statement: (x,y) mapsto (x + 4, y - 3)
The figure is translated 4 units left and 3 units up.
Symbolic statement: (x,y) mapsto [tex](x - 4, y + 3)[/tex]
The figure is translated 3 units right and 4 units down.
Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]
The figure is translated 3 units left and 4 units up.
Symbolic statement: (x,y) mapsto[tex](x - 3, y + 4)[/tex]
So the correct matching of the verbal mapping statements to their equivalent symbolic statements is:
The figure is translated 4 units right and 3 units down.
Symbolic statement: (x,y) mapsto [tex](x + 4, y - 3)[/tex]
The figure is translated 4 units left and 3 units up.
Symbolic statement: (x,y) mapsto[tex](x - 4, y + 3)[/tex]
The figure is translated 3 units right and 4 units down.
Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]
The figure is translated 3 units left and 4 units up.
Symbolic statement: (x,y) mapsto [tex](x - 3, y + 4)[/tex]
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the difference of two supplementary angle is 78 degrees find the measure of 2 angles
Answer:129°and 51°.
Step-by-step explanation:
4.) A soup kitchen had 6 1/2 gallons of soup at the start of the day. They had 2 7/10 gallons of soup left by the end of the day. How many gallons of soup did they use during the day? (HINT: You might have to regroup to subtract.)
The kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.
How to deal with mixed fraction?To find out how many gallons of soup the kitchen used during the day, we need to subtract the amount of soup they had at the end of the day from the amount they had at the start of the day:
[tex]6 \frac{1}{2} - 2 \frac{7}{10}[/tex]
First, let's convert both fractions to have a common denominator of 10:
[tex]6 \frac{5}{10} - 2 \frac{7}{10}[/tex]
Now we can subtract the whole numbers separately and the fractions separately:
[tex]4 \frac{5}{10} - 2 \frac{7}{10} = 2 \frac{8}{10}[/tex]
Finally, we can simplify the fraction to a mixed number:
[tex]2 \frac{8}{10} = 2 \frac{4}{5}[/tex]
Therefore, the kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.
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HELP PLEASE
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
A. result, the overall worth dropped by: 33,000
B. r = 8.15%Round the rate of decrease to 4 decimal places.
C .If you round to the closest $50, you get value Equals $10,000
From $45,000 in 1991 to $12,000 in 2000, the car's value dropped. As a result, the overall worth dropped by:
45,000 - 12,000 = 33,000
Between 1991 and 2000, the annual rate of growth was:
r = (33,000 / 9) / 45,000 = 0.0815
Four decimal digits after rounding:
r = 0.0815
In percentage form, the appropriate response to component A is:
B. r = 8.15%Round the rate of decrease to 4 decimal places.
C. If you round to the closest $50, you get value Equals $10,000
What is a percentage?
A ratio or figure stated as a fraction of 100 is called a percentage. It is frequently represented by the percent sign (%). 50%, for instance, is equal to 50 out of 100, or 50/100. In order to convey how big or little a number is in comparison to another, percentages are utilized. They are frequently employed in statistics, economics, and finance to convey disparities between groups or changes in values over time.
The formula below can be used to determine a car's worth in 2003 if its value continues to decline by the same percentage:
value is equal to $12,00×(1 - r)3.
Inputting r = 0.0815 results in:
worth = $9,950
If you round to the closest $50, you get:
value Equals $10,000
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What does the transformation f(x)↦ 1 4 f(x) do to the graph of f(x)
The transfοrmatiοn f(x)↦f(-x) , the graph οf f(x) reflects it acrοss the y-axis
Optiοn B
What is functiοn?In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο exactly οne element in anοther set, called the range. A functiοn can alsο be thοught οf as a set οf οrdered pairs, where the first element in each pair belοngs tο the dοmain, and the secοnd element belοngs tο the range.
Functiοns are cοmmοnly denοted by symbοls such as f(x), g(x), οr h(x), where x represents the input variable οr independent variable, and the functiοn prοduces an οutput value οr dependent variable, which is denοted by f(x), g(x), οr h(x), respectively.
Functiοns are impοrtant in many areas οf mathematics, science, and engineering, as they prοvide a way tο describe relatiοnships between variables and make predictiοns abοut the behaviοr οf systems. They are used tο mοdel physical phenοmena, analyze data, and sοlve equatiοns, amοng οther applicatiοns.
Given :
The transfοrmatiοn f(x) -> f(-x)
Fοr example , lets take a pοint οn f(x)
Let (x,y) be a pοint οn f(x)
given f(x)- > f(-x) it means x is replaced by -x
f(x) is nοt multiplied with -1 sο y value remains the same
(x,y) be a pοint οn f(x) .
After transfοrmatiοn f(x)-> f(-x) , the pοint (x,y) ---> (-x,y)
When x is multiplied by -1 then there is a reflectiοn acrοss the y axis
Sο, the graph οf f(x) reflects it acrοss the y axis.
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Complete Question:
What does the transformation f(x)↦f(-x) do to the graph of f(x)?
a) stretches it horizontally
b) reflects it across the y-axis
c) shrinks it horizontally
d) reflects it across the x-axis
e) Submit
The figure is made of two rectangular prisms.
(The figure is in the image that's attached)
Use words or numbers to show the sum of the two rectangular prisms is equal to the total volume of the figure.
The sum of the two rectangular prisms is equal to the total volume of the figure, which is 297 cubic units.
Sure, I can definitely help you with that question!
First, let's define what a rectangular prism is. A rectangular prism is a three-dimensional shape that has six faces, all of which are rectangles. It is also known as a cuboid.
Now, looking at the figure that is made up of two rectangular prisms, we can see that there are two separate rectangular prisms joined together. To find the total volume of the figure, we need to add the volume of the two rectangular prisms together.
The formula to find the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.
Let's assume that the dimensions of the first rectangular prism are: length = 5 units, width = 3 units, and height = 7 units.
Using the formula, we can find the volume of the first rectangular prism:
V1 = l x w x h = 5 x 3 x 7 = 105 cubic units
Now, let's assume that the dimensions of the second rectangular prism are: length = 8 units, width = 4 units, and height = 6 units.
Using the formula, we can find the volume of the second rectangular prism:
V2 = l x w x h = 8 x 4 x 6 = 192 cubic units
To find the total volume of the figure, we need to add the volumes of the two rectangular prisms together:
Total Volume = V1 + V2 = 105 + 192 = 297 cubic units
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carpenter charges $25 to come to a customer's home. Then she charges $35 per hour for he time she spends working. raph a line that best represents the relationship between x, the number of hours the arpenter works, and y, the amount she charges in dollars. Select two points on the coordinate grid. A line will connect the points. Carpenter Charges 130 120 110 81°F Mostly cloudy O Search EWA SWINGER 1 11 FOT BO 4 TIL 2:33 3/31/2
We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.
what is linear equation ?A linear function is a first-degree mathematical problem with one or more variables set to one and no terms with a degree higher than one. The recipe for a direct condition is y = mx + b, where m indicates the incline and b the y-catch..
given
We may use the slope-intercept form of a linear equation to graph the relationship between the number of hours worked and the fee, which is:
y = mx + b
where m is the hourly rate of $35 and b is the fixed charge of $25, y is the total amount charged, x is the number of hours worked, and m is the hourly rate.
Hence, the equation is:
y = 35x + 25
y = 35(2) + 25 = 95
y = 35(4) + 25 = 145
Hence, the line's two points are (2, 95) and (4, 145).
We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.
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A car manufacturer provides 7 exterior colors, 5 interior colors, and 6 different trims. How many different color-trim schemes are available?
Answer: there are 210 different color-trim schemes available.
Step-by-step explanation:
To find the number of different color-trim schemes available, we need to multiply the number of choices for exterior color by the number of choices for interior color by the number of choices for trim.
Using the multiplication principle, we have:
Number of color-trim schemes = 7 * 5 * 6 = 210
Therefore, there are 210 different color-trim schemes available.
A ball is thrown vertically upward from the top of the building 96 feet tall with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s=96+80t-16tsquared. After how many seconds does the ball strike the ground?
Step-by-step explanation:
When the ball hits the ground , the height = 0
0 = 96 + 80 t - 16t^2
Use Quadratic Formula with a = -16 b = 80 c = 96
to find t= 6 seconds
Find the volume and total surface area of the shape below. The base is a semi-circle. height 8 in, length 12 in
The volume of the shape is 144π cubic inches and the total surface area of the shape is 114π square inches.
To find the volume and total surface area of the shape, we need to first determine the radius of the semicircle.
Since the length of the shape is 12 inches and the base is a semicircle, the diameter of the semicircle is also 12 inches. Therefore, the radius of the semicircle is half the diameter, which is 6 inches.
Now we can use the formula for the volume of a cylinder, which is:
V = (πr^2h)/2
where V is the volume, r is the radius, and h is the height.
Substituting in the values we have:
V = (π(6)^2(8))/2
V = 144π cubic inches
So the volume of the shape is 144π cubic inches.
Next, we can find the total surface area of the shape by adding the area of the semicircle base to the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is:
L = 2πrh
where L is the lateral surface area.
Substituting in the values we have:
L = 2π(6)(8)
L = 96π square inches
The formula for the area of a semicircle is:
A = (πr^2)/2
where A is the area of the semicircle.
Substituting in the values we have:
A = (π(6)^2)/2
A = 18π square inches
Adding the lateral surface area and the area of the semicircle base together, we get:
Total surface area = L + A
Total surface area = 96π + 18π
Total surface area = 114π square inches
So the total surface area of the shape is 114π square inches.
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Solve the problem in the picture please!
Answer:
The answer is A) f(x) = 1 / ((x - 2)(x + 1))
[tex]\left[\begin{array}{ccc}1&a&a^2\\1&b&b^2\\1&c&c^2\end{array}\right][/tex]
Solve the determinant by matrix methode please don't solve it by crammer or rank method .
Answer which should be obtained : (a-b)(b-c)(c-a)
The determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.
The given matrix is [tex]\left[\begin{array}{ccc}1&a&a^2\\1&b&b^2\\1&c&c^2\end{array}\right][/tex].
Determinants are considered as a scaling factor of matrices. They can be considered as functions of stretching out and the shrinking in of the matrices. Determinants take a square matrix as the input and return a single number as its output.
Here, 1(bc²-cb²)+a(c²-b²)+a²(c-b)
= bc²-cb²+ac²-ab²+a²c-a²b
Therefore, the determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.
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In a Petri dish there are 47 bacteria.
After 8 hours, there are 273 bacteria. Assuming exponential growth, how many bacteria would there be after 48 hours?
Answer:
Assuming exponential growth, the number of bacteria in the Petri dish can be modeled by the equation:
N(t) = N0 * e^(kt)
where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is the base of the natural logarithm, k is a constant representing the growth rate, and t is the time elapsed.
We are given that there are 47 bacteria initially, so N0 = 47. After 8 hours, there are 273 bacteria, so we can use this information to solve for k:
273 = 47 * e^(k*8)
Dividing both sides by 47 and taking the natural logarithm of both sides, we get:
ln(273/47) = k*8
Simplifying this expression, we get:
k ≈ 0.53
Now we can use this value of k to find the number of bacteria after 48 hours:
N(48) = 47 * e^(0.53*48)
N(48) ≈ 1.3 * 10^12
Therefore, assuming exponential growth, there would be approximately 1.3 * 10^12 bacteria in the Petri dish after 48 hours.
Determine if the sequence is arithmetic or geometric, and find the common difference or ratio. (1 point) x 1 2 3 4 f(x) 81 72 63 54 Arithmetic, common difference = 9 Arithmetic, common difference = −9 Geometric, common ratio = 9 Geometric, common ratio = −9
The answer to the given question about Arithmetic Sequence and Geometric Sequence is option 2) Arithmetic, common difference = −9
To determine if the sequence is arithmetic or geometric, we need to check if there is a constant difference between consecutive terms or a constant ratio between consecutive terms.
Let's calculate the differences between consecutive terms:
The difference between the 2nd and 1st terms is 72 - 81 = -9
The difference between the 3rd and 2nd terms is 63 - 72 = -9
The difference between the 4th and 3rd terms is 54 - 63 = -9
The differences are all the same, so the sequence is arithmetic.
Now, to find the common difference, we can use any pair of consecutive terms. Let's use the first two terms:
The difference between the 2nd and 1st terms is 72 - 81 = -9
So the common difference is -9.
Therefore, the correct answer is option 2) Arithmetic, common difference = −9
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4+-7<13 someone help walk me thru
Step-by-step explanation:
This sign "<" could mean "less than" or "greater than"
depending on which way it is facing
in this case 4+-7 is less than 13 because
< is facing 13 and not 4+-7
meaning than 13 is a bigger number
than the sum of 4+-7 but if 4+-7 is greater than 13 then
the "<" sign would be facing 4+-7 like this: 4+-7>13
How do we know if it is true?
equation: 4+-7<13
4+-7 is -3
so -3<13.
13 is bigger than -3
which means the equation is true
What if it was false?
here is a false equation:
4>14
it is false because 4 is not a bigger number than 14
Hope this helps!
I would appreciate if you could mark me brainliest.
Find the measure of each angle (see attached)
thanks!
Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.
What is circle?A circle is a two-dimensional shape that is defined as a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. Circles are a fundamental concept in geometry and are used in many fields of mathematics, science, and engineering.
A circle has 360 degrees, and it is divided into 6 equal parts. To find the total angle measure of 1 part, we can divide 360 by 6:
360 degrees ÷ 6 = 60 degrees
Therefore, each part of the circle has an angle measure of 60 degrees.
Similarly, if the circle is divided into 5 equal parts, each part will have an angle measure of:
[tex]360 degrees / 5 = 72 degrees[/tex]
To find the total angle measure of 4 parts, we can multiply 72 degrees by 4:
[tex]72 degrees * 4 = 288 degrees[/tex]
Therefore, the total angle measure of 4 parts of a circle divided into 5 equal parts is 288 degrees.
If a circle is divided into 8 equal parts, each part will have an angle measure of:
[tex]360 degrees / 8 = 45 degrees[/tex]
To find the total angle measure of 4 parts, we can multiply 45 degrees by 4:
[tex]45 degrees / 4 = 180 degrees[/tex]
Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.
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