The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.
A function is defined as a expression containing one or more variables.
Technically speaking, a function is a means of linking a set of inputs to a set of outputs.
The height of the ball at any time t is given by the function:
[tex]h(t)=-16t^2+38t+2[/tex]
Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.
Let us substitute the values:
[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]
This is in the form of a quadratic equation in t.
Solving by using the quadratic formula:
We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Therefore for the above quadratic equation:
[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]
Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.
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find the total amount and total interest after eight months if the interest is compounded every four months
The total amount is $ 6050, and the total interest after 8 months is $1050.
What is interest?
Interest is the financial charge for the honor of adopting a plutocrat, generally expressed as a periodic chance rate( APR).Interest is the quantum of plutocrat a lender or fiscal institution receives for advancing out money. However, you do it in order to achieve that result or maintain that situation, If you do commodity in the interests of a particular result or situation. There are basically three(3) main types of interest rates the nominal interest rate, the effective rate, and the real interest rate. The nominal interest of a (one) investment or loan is simply the stated rate on which interest payments are calculated.Here,
Period per year = 124 = 3
Total amount = amount (1 + periodic rate)period
= $6,050
Total interest = Total amount - amount
= 6050 - 5000
= $1,050
Thus,
The total amount is $ 6050, and the total interest after 8 months is $1050.
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For a party, Ashley wants to make 12 hamburgers. If she has 2.964
pounds of meat, how much would each patty weigh? _________ pounds
Answer:
247
Step-by-step explanation:
divides 2964 entre 12 y obtienes 247
The mean diameter of holes produced by a drilling machine bit is 4.05 mm and the stan dard deviation of the diameters is 0.0028 mm For twenty holes drilled using this machine, determine, correct to the nearest whole num ber, how many are likely to have diame ters of between (a) 4.048 and 4.0553 mm and (b) 4.052 and 4.056 mm, assuming the diameters are normally distributed.
The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
The sum of all values divided by the total number of values constitutes a dataset's mean.
The mean of the holes are given as 4.05 mm([tex]\mu=4.08[/tex])
The standard deviation is given as 0.0028 mm([tex]\rho=0.0028[/tex])
Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.
Here [tex]Pr(4.048\leq X\leq 4.0053)[/tex] ,so we need to compute the z-values
[tex]Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143[/tex]
Similarly:
[tex]Z_2=1.8929[/tex]
Therefore from the above statements we can say that
[tex]Pr(-0.7143\leq X\leq 1.8929)[/tex]
Solving for probability distribution we get
[tex]Pr(4.048\leq X\leq 4.0053)=0.7333[/tex]
Total number of holes=0.7333 × 20= 14.666..
Therefore the number of holes is 15
Similarly
The z-value corresponding to 4.052 mm is given by 0.71
The z-value corresponding to 4.056 mm is given by:2.14
The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227
The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20
= 4.454
= 4, correct to nearest whole number
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How many platelets are in 3 milliliters of blood write your answer in standard form
En que líquido se hunda más rápido un huevo
Answer:
Se hunde mas rapido en agua salada.
Step-by-step explanation:
Find the solution to the system of equations. Round to the nearest tenth if necessary.
f(x) = 3x+6
g(x) = x² + 4x + 1
Answer:
The solutions are
(-2.8, -2.4) and
(1.8, 11.4)
- to the nearest tenth.
Step-by-step explanation:
x² + 4x + 1 = 3x+6
x² + 4x - 3x + 1 - 6 = 0
x² + x - 5 = 0
Using the quadratic formula:
x = [-1 +/- √((1)² - 4*1*(-5)] / 2
= (-1 - 4.583) / 2 , (-1 + 4.583) / 2
= -2.791, 1.792.
Substituting for x in the equation:
y = -2.374, 11.374.
A house is purchased for $145,000 and each year increases in value by 6% of its value the previous year. (6 marks) Let be the value of the house in year . Write a difference equation which gives the value of the house after years. Solve the difference equation. Find the projected value of the house in 15 years.
The projected value of the house after 15 years is $347500.
A house is purchased for $145,000.
The value of the house increases each year by 6% of its value the previous year.
Let y(n) denote the value of the house after n years.
Initial value is $145,000.
⇒ y(0) = 145,000
The value of the house increases each year by 6% of its value the previous year.
Therefore the growth is exponential, and we have
y(n) = y(0)(1+0.06)ⁿ
When n = 1
⇒y(1) = 145000 × (1.06)
⇒y(1) = 153700
When n = 2,
⇒y(2) = 145000 × (1.06)²
⇒y(2) = 162922
Therefore, when n = 15,
⇒y(15) = 145000 × (1.06)¹⁵
⇒y(15) = 3,47,500
Therefore, the projected value of the house after 15 years is $347500.
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5. Explain how to determine which operation to complete first when simplifying the expression (15 ÷ 5+4²) − [4³ − |(13² + 2) ÷ (4 − 1)]. Be specific.
Answer: Parentheses
Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.
Find the square root of: 2 + sqrt5
Answer:
3.65
Step-by-step explanation:
The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6
What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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Solve the formula for the specified variable.
I = Prt
t
You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a club
Event C has ____ outcome(s)
The total outcomes for the event C: selecting a club card from a standard deck of 52 playing cards = 13
In this question, we have been given an event of a random experiment.
You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a club.
We need to find the total number of outcomes for event C.
Number of cards in a deck = 52
We know that, the number of club cards in the standard deck of cards = 13
Therefore, the total outcomes for the event C: selecting a club card from a standard deck of 52 playing cards = 13
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Quadrilateral A' B'C'D' is the image of quadrilateral ABC D under a translation.
what is the complement of 14 17'
The complement of the angle 14° 17' would be; 75° 43'
What is the Complement of the Angle?We want to find the complement of the angle 14° 17'
The complement of 14° is the angle that when added to 14° forms a right angle (90° ).
Now, when an apostrophe is found in the word angles, it means 'angular minutes, while " denotes angular seconds. For instance, "75degree 20′ 39" means "75 degrees, 20 minutes, and 39 seconds."
Thus, 14° 17' means 14 degrees, 17 minutes.
Now, 17 minutes when converted to degree is;
17/60 degrees = 0.283. Thus; 14° 17' = 14.283
Now, the complement of 14° 17' would be;
90 - 14° 17' = 75° 43'
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9 less than nine times a number.
Answer:
9-9x
Step-by-step explanation:
Converted from word to standard form.
The value of the equation 9 less than nine times a number is A = 9n - 9 , where n is the number
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 9 less than nine times a number
Let the number be represented as n
On simplifying the equation , we get
A = 9n - 9
Therefore , the value of A is 9n - 9
Hence , the equation is A = 9n - 9 , where n is the number
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This is the question
Answer:
x<0: 0<x<1; x>1
Step-by-step explanation:
The denominator cannot be 0 (since division by 0 is undefined), meaning x cannot be 0 or 1.
So, the domain is x<0: 0<x<1; x>1.
The distance between two places of interest is 2/3km. I go 1/4 of this distance on foot. How far is still to go?
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
Step-by-step explanation:
If I have traveled 1/4th of the distance between two places, I still have 1 - 1/4 = 3/4th of the distance yet to cover
If the distance between the two places is d, distance left =(3/4) . d
In this case, d = 2/3 km
So distance left to cover = [tex]\dfrac{2}{3}\cdot \dfrac{3}{4}[/tex]
We can cross-cancel the 3 which appears as the denominator in the first fraction and the numerator in the second fraction
[tex]\dfrac{2}{\cancel{3}}\cdot\dfrac{{\cancel{3}}}{4}=\dfrac{2}{4}[/tex]
Dividing both numerator and denominator by 2 gives us
[tex]\dfrac{2\div2}{4\div2}=\dfrac{1}{2}[/tex]
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
(2,−3) and (0,−8) answer
Answer:
y2-y1/x2-x1
-8--3/0-2
Step-by-step explanation:
-8+3/-2=-5/-2=5/2
The U.S. Census Bureau defines a household as all of the people who occupy a housing unit as their usual
place of residence. The number of households is not equal to the population because multiple people may
live in the same housing unit.
82.1% of Cincinnati households have a computer. If 111.804 households in Cincinnati have a computer, how
many households are there altogether in Cincinnati? Show your work. Round to the nearest whole number.
Answer: total household present are 136
Step-by-step explanation:
Given:
82.1% of Cincinnati households have a computer.
111.804 households in Cincinnati have a computer.
According to ratio and proportions we have:
let total number of houses be x;
then
(111.804/x)*100=percentage of Cincinnati households having a computer. [[tex]gain/total*100 =gain %[/tex]]
then
(111.804/x)*100=82.1
cross multiplying we have
x=(111.804*100)/82.1
x=136 households (Round to the nearest whole number.)
so total household present are 136
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How many times larger is 8 x 10^5 than 4 x 10^3?
The value 8 x 10^5 is 200 times greater than 4 x 10^3
Scientific notationsThe standard scientific notation is expressed as A * 10^n
where
A is the values between 1 and 10
n is any integer
In order to determine how many times larger is 8 x 10^5 than 4 x 10^3, we will take the ratio;
Ratio = 8 x 10^5/4 * 10^3
Ratio = 8/4 * 10^5/10^3
Ratio = 2 * 10^2
Ratio = 200
Hence the value 8 x 10^5 is 200 times greater than 4 x 10^3
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QUESTION 8
Simplify 6a+ (-12b) - 9b+8a
O 2a + 3b
O 14a-21b
O2a-21b
O 14a + 3b
After simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.
What are expressions?An expression is a collection of numbers or variables that have been combined using the operations +, -, × or ÷. Arithmetic expressions consist only of numbers and mathematical operators, whereas algebraic expressions consist of variables, numbers, and mathematical operators.So, 6a + (-12b) - 9b + 8a:
6a + (-12b) - 9b + 8a6a + -12b -9b + 8a6a - 21b + 8a14a - 21bTherefore, after simplification of the given expression, 6a + (-12b) - 9b + 8a the value is (B) 14a - 21b.
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The correct question is given below:
Simplify 6a+ (-12b) - 9b+8a
A. 2a + 3b
B. 14a-21b
C. 2a-21b
D. 14a + 3b
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
How to determine the possible rectangle's length and width?The given parameters are
Area = 15 square cm
The area is given as
Area = 15 square cm
The formula of area is
Area = Length x Width
Using the above formula, we have:
A) 1 cm and 15 cm ⇒ 15 square cm
B) 2 cm and 7 cm ⇒ 14 square cm
C) 3 cm and 5 cm ⇒ 15 square cm
D) 4 cm and 4 cm ⇒ 16 square cm
Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
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Possible question
The area of a rectangle is 15 square cm
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
I just need that one answer please
Answer:50.5
Step-by-step explanation:
because if you put the numbers from the smallest to largest in a line and take the middle numbers and divide by 2 you get 50.5.
Find the average rate of change of the function from x₁ to X₂.
x-Values
X1 = 1, X₂ = 6
Function
f(x) = x² - 2x + 6
What is the factored form of x2−9
Answer:
(x+3)(x-3)
Step-by-step explanation:
When factoring x^2-9 you'd look for square multiples of -9.
Because 3×3 is 9, 3 is your square. You can't just use (x+3) because your outcome is a -9. Which is why your answer would be (x+3)(x-3)
Negative 16/72 in simplest form
Answer:
Negative 2/9 I believe
Step-by-step explanation:
sorry if i am wrong
Answer:
-2/9
Step-by-step explanation:
-16/72
Simplify
We can divide the top and bottom by 8
16 divided by 8 = 2
72 divided by 8 = 9
-2/9
Jim began a 145mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour, find the amount of time he spent on the bicycle.
The amount of time he spent on bicycle is 4.5 hours.
Given Jim began a 145 mile bicycle trip.
The whole trip took 7 hours.
Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour.
speed = distance / time
time = distance / speed
ride:
d = distance ridden
t = d/30 (given from the problem)
walk:
t = (145 - d)/4 (given from problem)
total trip time:
7 = d/30 + (145 - d)/4.
7 = 4d/120 + 30(145 - d)/120
7×120 = 4d + 30(145 - d)
840= 4d +4350-30d
840 ₋ 4350 = ₋30d ₊ 4d
₋3510 = ₋26d
d = 3510/26
d = 135
d=135 then from here using the formula t = d / s we can solve
t=135/30 = 4.5 hours
hence the amount of time Jim spent on the bicycle is 4.5 hours.
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Suppose you make monthly mortgage payments of $1,345 and have 10 years left on the mortgage (next payment due next month). Assuming a 3.6% stated annual interest rate for the mortgage, how much would you need today to pay off the mortgage?
I will need $1,61,884.2 to pay off the mortgage.
This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.
The monthly mortgage payment is $1,345.
Rate of interest is 3.6% per annum.
Time is given to be 10 years.
Simple interest for 10 years = 1345×3.6×10/100
= $ 484.2
So, the total money required to clear the mortgage
= $(1345×12×10) + $ 484.2
= $161400 + $484.2
= $ 1,61,884.2
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evaluate the function f(x) = square root of x at given value
Answer:
2/11
Step-by-step explanation:
since the square root of 4 is 2 and that of 121 is 11
Question 5(Multiple Choice Worth 1 points) (01.05 LC) Which of the following is an equivalent form of the compound inequality -22 -5x - 72-33? -5x - 7-22 and -5x - 72-33 O-5x - 7-22 and -5x - 72 −33 O-5x = -22 and -7 2 -33 -5x 7-22 and -5x - 7 ≤ -33
The equivalent form of the compound inequality where the compound inequality is given as -22 > -5x - 7 ≥ -3 is -15 > -5x ≥ 4
How to determine the equivalent form of the compound inequality?The compound inequality is given as
-22 > -5x - 7 ≥ -3
Add 7 to all sides of the compound inequality
So, we have
7 -22 > -5x - 7 + 7 ≥ -3 + 7
Evaluate the sum in the above compound inequality
So, we have
-15 > -5x ≥ 4
Hence, the equivalent form of the compound inequality where the compound inequality is given as -22 > -5x - 7 ≥ -3 is -15 > -5x ≥ 4
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