If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.
Maximum heightGiven equation:
y = 88t - 16t²
Maximum height dy/dt = 0
88-32t = 0
32t = 88
t = 88/32sec
t = 2.75sec
Hence,
Maximum height attained by the ball :
Maximum height attained by the ball = 88(2.75)-16(2.75)²
Maximum height attained by the ball = 242 - 121
Maximum height attained by the ball = 121 feet
Therefore the maximum height is 121 feet.
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Use the information provided to find the vertex form equation of each parabola:-2x^2 + 36x -171
The vertex form of a parabola is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the horizontal and vertical coordinates of the vertex.
Recall, the general expression for a quadratic equation is
y = ax^2 + bx + c
By comparing with the given equation,
a = - 2, b = 36, c = - 171
The formula for the x coordinate of the vertex is
x = - b/2a
x = - 36/(2 * - 2) = - 36/- 4 = 9
Substituting x = 9 into the equation, we have
y = - 2(9)^2 + 36(9) - 171
y =
you borrow $200,000.00 that charges you 6.3% interest, compounded monthly. You will make payments monthly in the amount of $1,300.00. How many payments will it take for you to pay off the loan?
The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.
How is the number of payments computed?Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.
In this situation, we used the online finance calculator to determine the number of payments.
Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.
At the end of the period, the balance is made up of the principal and compounded interest.
I/Y (Interest per year) = 6.3%
PV (Present Value) = $200,000
PMT (Periodic Payment) = $-1300
FV (Future Value) = $0
Results:
N (# of periods) = 314.854
Sum of all periodic payments = $-409,309.97
Total Interest $209,309.97
Thus, you are likely to make 315 monthly payments to settle the loan.
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The shape shown below is made from a triangle and a rectangle.
a) Work out the area of the triangle.
b) Work out the area of the whole shape.
OLA
O
4 cm
3 cm
10 cm
Watch video
7 cm
Not drawn accurately
Answer
Raining now â
(a) The area of the triangle = 6 cm squares
(b) The area of the whole shape = 76 cm squares
The shape given is formed by a triangle and a rectangle.
First we need to find the area of the triangle.
Height of the triangle = 3 cm
Base of the triangle = 4 cm
Area of the triangle = 1/2 x base x height
= 1/2 x 4 x 3
= 6 cm squares
Area of the whole shape = Area of the triangle + Area of the rectangle
Length of the rectangle = 10 cm
Width of the rectangle = 7 cm
Area of the rectangle = length x width
= 10 x 7
= 70 cm squares
Therefore, area of the whole shape = 6 + 70
= 76 cm squares
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Si la suma de un número y 5 se multiplica por 3, el resultado es igual a 7 veces el número
disminuido en 13. Halla el número.
We construct an equation and calculate that number as 7 .
The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. The word equation and its cognates can have slightly different meanings in different languages. For instance, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign, whereas in French, an equation is defined as containing one or more variables.
The equation's solutions are the values of the unknown variables that satisfy the equality, which are often referred to as the variables for which the equation must be solved.
let the number be x .
9 times the number is = 9x
5 times the number added to 3 is
(x + 3) × 5
Now let us set up an equation and find that number :
(x + 3) × 5 = 9x - 13
Simplifying the given equation we get :
5 (x + 3) = 9x - 13
5x + 15 = 9x - 13
5x - 9x = - 13 - 15
- 4x = - 28
x = - 28/-4
x = 7
Hence the required number calculated from the equation is 7 .
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If the sum of a number and 3 is multiplied by 5 , the result is equal to 9 times the number decreased by 13. Find the number
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Please help :)..................................
Answer:
(d) Domain: {x|x∈ℝ} and range: {y|y∈ℝ}
Step-by-step explanation:
You want the domain and range of the relation shown in the graph.
GraphThe graph shows a line. The arrows on the end of it mean that it extends to infinity in both directions (up and left; down and right).
DomainThe domain is the horizontal extent. It includes all real numbers (from -∞ to +∞).
RangeThe range is the vertical extent. It includes all real numbers (from -∞ to +∞).
Domain: {x|x∈ℝ} and range: {y|y∈ℝ}
How much 36% acid solution should be added to 8% acid solution to make 196mL of a 10% acid solution?
Answer:
[tex]x = \frac{196}{13} [/tex]
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive, given that he or she did not have the disease.
The individual actually had the disease
No positive 9 negative 133
Yes
Positive 140
Negative 18
The probability is approximately.
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
What is probability ?Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.
Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .
Yes No
Positive : 140 9
negative : 18 133
P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]
= [tex]\frac{140}{142}[/tex]
=0.985
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
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What is the equation of a line that passes through the points (3, 6) and (8, 4)?
y=5/2x - 3/2
y=5/2x - 27/2
y=-2/5x - 24/5
y=-2/5x + 36/5
Answer: y= -2/5 + 36/5
Step-by-step explanation: when graphed, the slope is negative so it has to be -2/5x, and the y-intercept is positive so it has to be +36/5 (+7.2)
-1.4 repeating as a fraction in simplest form
1.4 repeating as a simple fraction is 13/9
Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.
Decimal number is a number that consist of one whole number and a fractional part and those are separated by a decimal point
The repeating decimal = 1.4444
Consider the value x = 1.4444
Then multiply 10 on both side of the equation
We get
10x = 14.444
Subtract x from the 10x
10x-x = 14.444-1.4444
Subtract the like terms in the equation
9x = 13
Move 9 to the right hand side
x = 13/9
Hence, 1.4 repeating as a simple fraction is 13/9
The complete question is
1.4 repeating as a fraction in simplest form
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А с 5 Find the missing side C 4 9 3 6.4 41
Use the pythagorean theorem to find side C
[tex]\begin{gathered} C=\sqrt[]{5^2+4^2} \\ C=\sqrt[]{25+16} \\ C=\sqrt[]{41} \\ C=6.4 \end{gathered}[/tex]The right answer is 6.4
cept 3) Which equation represents a pt for line that is parallel to the line y=-4x + 5? 1) y=-4x + 3 cept_ = + 5 5 cept for 3) y = 4x+3 ) 4) y = 4x + 5 2) y=-x+ ) "
y=-4x + 3
EXPLANATION
Given:
y = -4x + 5
To find the equation which represent a line that is parallel to the above, all we need to do is to oserve their slope.
Using a unique properties that states : slope of parallel lines are equal.
Observe that comparing the equation y =-4x + 5 with y=mx + b
slope = m= -4
From the option given, the only equation when compared with y=mx + b that has a slope of -4 is y=-4x + 3.
Therefore, the equation which represent a line that is parallel to y=-4x + 5 is y=-4x + 3
What is the solution of the linear-quadratic system of equations?
y = r2 +52 _ 3
y = x=2
The value of x is 1 , -5 and y is 3 , -3
What is quadratic equation ?A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.
Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .
y = [tex]x^{2}[/tex] +5x - 3 .....(i)
y = 2+ x.....(ii)
put the value of y in equation i
2 + x = [tex]x^{2}[/tex] +5x - 3
[tex]x^{2}[/tex] +4x - 5 = 0
[tex]x^{2}[/tex] +(5-1)x - 5 = 0
x(x + 5) -1(x + 5) = 0
(x -1)(x + 5)=0
x=1
x=-5
now put value of x in equation ii
y = 2+ x.....(ii)
y = 3 (when x = 1)
y = -3(when x = -5)
The value of x is 1 , -5 and y is 3 , -3
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the width of a rectangular field is 3 meters less than its length. Find the length and width is the perimeter is 58meters
Let the Length of the rectangle be l and the width of the rectangle be w
The width of a rectangular field is 3 meters less than its length, this can be represented as
w = l - 3
Given the perimeter = 58meters
Perimeter of the rectangle = 2(l + w)
58 = 2(l + l-3)
58 = 2(2l - 3)
58 = 4l - 6
58 + 6 = 4l
64 = 4l
4l = 64
l = 64/4
l = 16
w = l - 3
w = 16 - 3
w = 13
Hence, the length of the rectangle is 16 meters while the width is 13 meters.
In an election, 112 votes were cast and the
winning candidate beat her opponent by a
4:3 ratio. How many more votes did the
winning candidate receive?
8
16
23
28
35
Answer:
16
Step-by-step explanation:
112/7=16, 16x4=64, 16x3=48, 64-48=16
Help me solve the first problem please
Question 14
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
Question 15
[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]
Suppose that $2000 is invested at a rate of 3.4% compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years. Do not round any intermediate computations and round your answer to the nearest cent.
Given data:
The amount invested ( principal) is
[tex]P=\text{ \$2,000}[/tex]The interest rate given is
[tex]r=3.4\%[/tex]The number of years is
[tex]t=4\text{ years}[/tex]The number of times compounded is quarterly
A quarterly event happens four times a year, at intervals of three months.
[tex]n=4[/tex]Concept:
The formula to calculate the amount compounded is given below as
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where,} \\ A=\text{amount} \\ P=\text{principal} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{ number of years} \end{gathered}[/tex]By substituting the values above in the formula, we will have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2,000(1+\frac{3.4}{400})^{4\times4} \end{gathered}[/tex]By solving the equation above, we will have
[tex]\begin{gathered} A=2,000(1+\frac{3.4}{400})^{4\times4} \\ A=2,000(1+0.0085)^{16} \\ A=2000(1.0085)^{16} \\ A=2,290.05 \end{gathered}[/tex]Hence,
The final answer = $2,290.05
Create a table that represents the transformation of f given by g.
g(x) = 3f(x)
The table which represents the transformation of function f given by g(x) = 3f(x) is:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
g(x) = 3f(x) - 15 - 3 9 21
When a function is transformed, the graph's curve of the parent function either "moves to the left/right/up/down," "expands or compresses," or "reflects."
A table for every value of x and its corresponding value of f(x) is given as:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
Now the transformed function g is given as:
g(x) = 3f(x)
Therefore, the table that represents the transformation of f given by g will be:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
g(x) = 3f(x) - 15 - 3 9 21
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Isaiah is measuring 3 1/2 inches using a ruler marked in 1/8 inch increments. Which of the following below is the total number of eighths that Isaiah will need to count out to make his measurement? Hint: turn 3 1/2 into an improper fraction with a denominator of 8.
A.24
B.28
C.30
D.36
If Isaiah is measuring 3 1/2 inches using a ruler marked in 1/8 inch increments. The total number of eighths that Isaiah will need to count out to make his measurement is B.28.
Total numberWe would be making use of the given hint to determine the total number of eight.
The hint is to use 3 1/2 into an improper fraction with a denominator of 8.
Hence,
Converting 3 1/2 to improper fraction
3 1/2 = 7/ 2 inches
Now let determine the total number with a denominator of 8.
= 7 × 4 / 2 ×4
= 28 /8
Therefore the correct option is B.
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I can’t find the answer for this question
Answer:
[tex]x = \frac{20}{91}[/tex]
Step-by-step explanation:
Since this is a proportion, first you need to cross multiply.
[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]
[tex]\frac{26}{25} x = \frac{40}{175}[/tex]
Now multiply both sides by the reciprocal of 26/25 which is 25/26.
[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]
Cancel on the right side, 25 and 175, by 25. Then cancel 40 and 26 by 2.
[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]
[tex]x = \frac{20}{91}[/tex]
A Short answer Question
Using multiplication of matrices, it is found that the values of a and b are given as follows:
a = 4.b = 6.How does multiplication of matrices work?To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.
Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:
3(-1) -2(2) + a(3) = 5
-3 - 4 + 3a = 5
3a = 12
a = 4.
The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:
4(3) - 1(b) + 2(-2) = 2
12 - b - 4 = 2
8 - b = 2
b = 8 - 2
b = 6.
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Ms. Lantz recently participated in the Rocket Run 5k. The distribution of finishing time for females is approximately normal with a mean of 57 minutes with a standard deviation of 8 minutes. According to the Houston Chronicle, a healthy female person should be able to run a 5K in less than 50 minutes.
Part B: Ms. Lantz wanted to use her 5K time to qualify for the Houston Marathon. In order to qualify you need to be in the fastest 20% of times. What finishing time would she need in order to qualify for the Houston Marathon?
Answer =___ minutes
**Round to the 4th decimal**
The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.
What exactly is the z-score?A Z-Score is just a measurable statistic that represents a score's relationship to the mean across a set of scores.A Z-score can inform a trader why a value is typical for a particular set of data or out of the ordinary.A Z-score of the less than 1.8 indicates that a business is nearing bankruptcy, whereas a score closer to 3 indicates that what a company is in good financial status.The formula for calculating the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the sample
σ = standard deviation of the sample
The given values are-
μ = 57 minutes
σ = 8 minutes
Probability = 20% = 0.20
Find the z-score from the negative z table for 0.20
z score = -0.84
Put the values in z formula and find x.
z = (x - μ)/σ
-0.84 = (x - 57)/8
Simplifying;
x = -6.72 + 57
x = 50.28 minutes
Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.
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How does finding the prime factorization of a group of numbers help
you to find their GCF
Take the prime factorization of both numbers to find the GCF. Then list the characteristics that they share. If they have more than one of the same factor (for example, two 2's), write them both down. Then multiply the factors they share.
What is prime factorization?A positive integer's prime factors are the prime numbers that divide it exactly. Finding these numbers is known as integer factorization or prime factorization. According to the fundamental theorem of arithmetic, every positive integer has a unique prime factorization.
What is GCF?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among the given numbers' common factors. The greatest common factor (GCF) of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder. GCF can be calculated in three ways: division, multiplication, and prime factorization.
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4) On average, Aliah drinks of a 6 ounce glass of water in hour. How much water does she
drink in an hour?
Answer: 60
Step-by-step explanation:6x10=60
ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
5. Betty wants to mail a package. The flat rate for mailing a package is $20, plus $3 per
pound. Write an expression that can be used to determine the total cost of mailing a package
that weighs p pounds.
If Betty spent $56 to mail her package, how many pounds did it weigh?
1. The mathematical expression that can be used to determine the total cost of mailing a package weighing p pounds is f(Tc) = 20 + 3p.
2. Since Betty spent $56 to mail her package, the weight in pounds of the mail must be 12 pounds.
What is a mathematical expression?A mathematical expression is a statement containing numbers, variables, and an arithmetic operation.
Flat (fixed) rate for mailing a package = $20
Variable mailing rate per pound = $3
Expression to model the total cost:
Let Tc = total cost
p = number of pounds
Tc = 20 + 3p
If Betty spent $56 to mail her package, the number of pounds, using the mathematical expression above:
Tc = 20 + 3p
56 = 20 + 3p
56 - 20 = 3p
36 = 3p
p = 12
Check:
Tc = 20 + 3p
56 = 20 + 3 (12)
56 = 20 + 36
56 = 56
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A passenger train traveled 35 miles in 50 minutes. At this rate, how many miles can the train travel in one hour?
Given:
A passenger train traveled 35 miles in 50 minutes.
[tex]\begin{gathered} \text{Number of miles the train travelled in one hour=}\frac{35}{50}\times60 \\ \text{Number of miles the train travelled in one hour=}42\text{ miles} \end{gathered}[/tex]umber of miles that train can travel in one hour is 42 miles.
5y – 3 = 6y + 3
solve y
Answer: y = −6
Step-by-step explanation:
Answer:
5y−3=6y+3
Step 1: Subtract 6y from both sides.
5y−3−6y=6y+3−6y
−y−3=3
Step 2: Add 3 to both sides.
−y−3+3=3+3
−y=6
Step 3: Divide both sides by -1.
−y
−1
=
6
−1
y=−6
Step-by-step explanation:
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The line y=kx+4 goes through the point (2, -2)
K = -3
Sketch the graph of the line (need answer ASAP!!)
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch the graph of the line?
To draw a line, we just need to find two points that belong to the line, graph them, and then connect them with a line.
Here we know that we have the line:
y = k*x + 4
Where k = -3, then:
y = -3*x + 4
By evaluating this in a value of x, for example, x = 0, we will get:
y = -3*0 + 4 = 4
Then we also have the point (0, 4) (and the given one, (2, -2))
So we can draw these two points and then connect them with a line (just use a ruler and draw a line that passes through both points).
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please can someone help… A cuboid with a volume of 924 cm' has dimensions
4 cm, (x + 1) cm and (x + 11) cm.
Show clearly that x2 + 12x – 220 = 0
By substitute values in formula for volume of cuboid we get;
x² + 12x – 220 = 0
What is mean by Volume?
Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.
Given that;
A cuboid with a volume of 924 cm' has dimensions,
4 cm, (x + 1) cm and (x + 11) cm.
Since, Volume of cuboid = Length x width x height
After substitute we get;
Volume of cuboid = 4 × (x + 1) × (x + 11)
924 = 4 (x² + 11x + x + 11)
924 = 4 (x² + 12x + 11)
Divide 4 both side;
231 = x² + 12x + 11
x² + 12x + 11 - 231 = 0
x² + 12x - 220 = 0
Thus, By the formula of volume of cuboid we get;
x² + 12x - 220 = 0
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2 tablets 3 times per day 14 day supply 15 tablets needed per bottle. How many bottles are needed
6 bottles are needed.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
given:
2 tablets 3 times per day
so, total tablets = 6 tablets
Total days = 14
so, total tablets in 14 days = 14 x 6 = 96
and, tablets per bottle= 15
Then, the number of bottles required = 96 /15 =6.4
Hence, 6 bottles are needed.
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Which of the following is equivalent to 2.76? 2.76%, 27.6%, two and nineteen twenty fifths, or twenty five over nineteen?
The equivalent value to 2.76 is C. two and nineteen twenty-fifths.
What is an equivalent value?An equivalent value is an amount or numerical expression possessing the same value as the other.
Equivalent values are expressed as equations, using the equation symbol (=).
Equations are a class of the properties of mathematical expressions, including numbers and variables.
Two and nineteen twenty-fifths = 2¹⁹/₂₅.
When expressed as a decimal, 2¹⁹/₂₅ = 2.76.
Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.
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