A spring is oscillating vertically according to the equation y=3cos(2t-pi) where y is the displacement in feet and t is time in seconds. At what time will the spring be 2 ft. high? Round your answer to the nearest tenth.
Answers
we have the equation
[tex]y=3cos(2t-pi)[/tex]For y=2 ft
substitute in the given equation
[tex]\begin{gathered} 2=3cos(2t-p\imaginaryI) \\ cos(2t-p\mathrm{i})=\frac{2}{3} \end{gathered}[/tex]Solve for t
using a calculator
2t-pi=0.84
2t=0.84+pi
2t=3.98
t=1.99 -----------> round to one decimal place
t=2.0 sec
The answer is option CRelated Questions
It takes you 6 hours to row 12 miles, how long will it take you to row 32 miles.
Answers
Answer:16
Step-by-step explanation:
1 hour=2miles
A pet hotel charges $25 per night to keep a dog. When the dog arrives, there is a mandatory $15 examination fee.
Part A: Write a function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days.
Part B: How much would a 6-night stay cost?
Part C: Does a 3-night stay cost half as much as a 6-day stay since it is half the time? Explain in detail!
Answers
Part A
The function rule for total cost
f(x) = 15+25n
Part B
The cost of 6 night stay = $165
Part C
The 3 night stay cost is not half as much as a 6 day stay
The mandatory examination fee = $15
The cost per night to keep a dog = $25
Consider the number of nights as n
Part A
The function rule for total cost
f(x) = 15 + 25n
Part B
The number of nights = 6 nights
The total cost = 15 + 25n
Substitute the value of n
= 15 + 25×6
= 15 + 150
= $165
Part C
The cost of 3 nights = 15 + 25×3
= 15 + 75
= $90
The cost of 6 nights = $165
The 3 night stay cost is not half as much as a 6 day stay
Hence,
Part A
The function rule for total cost
f(x) = 15+25n
Part B
The cost of 6 night stay = $165
Part C
The 3 night stay cost is not half as much as a 6 day stay
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help mee pleasee!!
thank you <3
Answers
The equation of the line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
In this question we have been given two points.
We need to find an equation of the line passing through points (-2, 1) and (1, -4)
Using the two-point form of equation of line.
(y - y1)/(y2 - y1) = (x - x1) / (x2 - x1)
(y - 1) / (-4 - 1) = (x - (-2)) / (1 - (-2))
(y - 1) / (-5) = (x + 2) / (1 + 3)
y - 1 / (-5) = (x + 2) / 4
y - 1 = (-5/4)(x + 2)
y = -5x/4 - 10/4 + 1
y = (-5/4)x - 3/2
Let y = f(x)
so, equation of line is f(x) = (-5/4)x - 3/2
Therefore, the equation of line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
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help please
The perimeter of a rectangle is 52 feet. The length is 2 feet more than 5 times the width. Find the dimensions of the rectangle.
Answers
The dimensions of the rectangle with a perimeter of 52 ft and given parameters is; Width = 4 ft and Length = 22ft
What is the perimeter of the rectangle?The formula for the perimeter of a rectangle is;
Perimeter = 2(Length + Width)
We are given;
Perimeter = 52 ft
Length is 2ft more than 5 times the width . Thus;
Length = 2 + 5(W)
Thus, perimeter formula expression is now;
2[2 + 5W + W] = 52
2(2 + 6W) = 52
2 +6W = 26
6W = 24
W = 4 ft
L = 2 + 5(4)
L = 22ft
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Which of the following statements are true?
Choose all answers that apply:
The equation represents a proportional relationship.
The unit rate of change of y with respect to a is
7
2
The slope of the ne is
2
A change of 7 units in a results in a change of 2 units in y.
A change of 6 units in a results in a change of 21 units in y.
Answers
Based on the function given of y = 2.5x, the true statements are:
The equation represents a proportional relationship.The slope of the line is 2.5.A change of 2 units in x results in a change of 5 units in y.What is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the name of this constant.The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.
For instance, if there is a change of 2 in x, the change in y would be:
= 2.5 × x
= 2.5 x 2
= 5
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On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73folle one standard deviation above the moon. Determine the mean of the test.
Answers
On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73
folle one standard deviation above the moon. Determine the mean of the test.
we know that
3=(mean-41)standard deviation -------> first equation
1=(73-mean)/standard deviation ------> second equation
solve the system of equations
Isolate deviation standard
sd=(mean-41)/3
sd=73-mean
73-mean=(mean-41)/3
219-3mean=mean-41
3mean+mean=219+41
4 mean=178
mean=44.5Answer:
Step-by-step explanation:
let's denote the mean of the test by u. We know that a score of 41 falls three standard deviations below the mean, and a score of 73 falls one standard deviation above the mean.
From the first statement, we have:
41 = u-3o
where o is the standard deviation.
From the second statement, we have:
73 = u + o
Now we can use these two equations to solve for u. We can start by solving for o and the first equation:
41 = u -3o
41 - u = -3o
o = (u - 41) /3
We can substitute this expression for o into the second equation:
73 = u + o
73 = u + (u - 41 ) / 3
219 = 3u + u - 41
260 = 4u
u = 65
Therefore, the mean of the test is 65.
3). What is the sale price for S45 sneakers, marked down 20% and then marked down another 25% to the nearest cent?
Answers
Given:
Original Price = $ 45
1st Mark down = 20 % ( this means you 're paying only 80% of the price)
2nd mark down = 25 % ( this means you 're paying only 75% of the price)
Required : Sale price of the sneaker after the 2nd markdown
Solution:
Sale price after the 1st mark down = Orignal Price x 80% or Original Price x ( 10
A firecracker sends a small pebble vertically upward from a height of 35 feet above a
pool of water. The starting speed of the pebble is 85 feet per second. Its distance in
feet, d, above the water is given by the equation:
d=35+85t-16t2, where t is the time in seconds after the launch.
Drag statements to the table to show what each coordinate labeled on the graph
represents in this problem situation.
Answers
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included.It also goes by the name quadratic equations.The quadratic equation has the general form ax2 + bx + c = 0.where a, b, and c are numerical coefficients and x is an unknown variable.
Solve the quadratic equation?
d=35+85t-16t²
35+85-16t²-d
35+85t-16t²-d=0
35-d+85t-d=0
16t²-85t-35+d=0
t=85±√[tex]\sqrt{x}[/tex]-(85)²-4×16(-35+d)/2×16
t=85±√(-85)²-4×16(-35+d)/32
-(85)²-4×16(-35+d)
=7225-64(-35+d)
=7225-64(-35+d)
7225+2240-64d
=9465-64d
=-9401
t=85+√9465-64d/32
t=85+97
t = 182
t=85-√9465-64d/32
t=85-97
t = -12
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Suppose that y varies directly as the square root of x, and that y = 45 when x = 196. What is y when x = 83? Round your answer to two decimal places if necessary
Answers
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
y=kx
In this problem we have
[tex]y=k\sqrt{x}[/tex]we have that
For y=45 x=196
step 1
calculate the constant of proportionality k
substitute the value of y and the value of x in the expression above
[tex]\begin{gathered} 45=k\sqrt{196} \\ 45=k(14) \\ k=\frac{45}{14} \end{gathered}[/tex]step 2
we have the expression
[tex]y=\frac{45}{14}\sqrt{x}[/tex]step 3
For x=83
substitute
[tex]\begin{gathered} y=\frac{45}{14}\sqrt{83} \\ y=29.28 \end{gathered}[/tex]help me pleasee!!
thank you
Answers
The equation in slope intercept form of the line that passes through the points (-6, -2) and (-9, -1) is y = -1/3x -10/3
How to determine the equation of the line?The points are given as
(-6, -2) and (-9, -1)
Calculate the slope of the points using the following slope formula
m= (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-6, -2) and (-9, -1)
Slope = m
So, we have
m = (-1 + 2)/(-9 + 6)
Evaluate the expression
m = -1/3
The equation of the line is then calculated using the line equation formula
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (-6, -2)
So, we have
y = -1/3(x + 4) - 2
Expand
y = -1/3x - 4/3 - 2
Evaluate
y = -1/3x -10/3
Hence, the equation of the line is y = -1/3x -10/3
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The recipe serves
six people. Find
the serving size
per person.
The serving is 24
Answers
Answer:
The serving size per person is 4
Step-by-step explanation:
The recipe serves six people. Find
The serving size per person is 24 ÷ 6 = 4.
after two years $900 deposited in a savings account with simple interest had earned $18 in interest. what was the interest rate
Answers
The expression for Simple Interest is :
[tex]\text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100}[/tex]Given that Principal amount = $900
Time period = 2 years
Simple Interest = $18
Substitute the value and solve for RAte of interest
[tex]\begin{gathered} \text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100} \\ 18=\frac{900\times2\times R}{100} \\ R=\frac{18\times100}{900\times2} \\ R=1 \\ \text{ Rate of interest = 1 percent} \end{gathered}[/tex]Answer : Interest Rate = 1%
Graph the parallelogram STUV with vertices S(-3,4),T(-1 , 7), U(5, 7) and V(3, 4) on your paper then give the ordered pairs with the reflection of the line y = - x .
Answers
Graph the polygon using the coordinates of its vertices
Social security tax is 1.5%. If Jadiel earns $23,400 working part time this year, how much will he pay for social security tax this year?
Answers
If the social security tax to be paid is 1.5 percent of one's income, and Jadiel earned $23,400 this year, then he has to pay $351 as his social security tax.
As per the question statement, the social security tax to be paid is 1.5 percent of one's income, and Jadiel earned $23,400 this year working part time.
We are required to calculate the amount Jadiel has to pay from his income as his social security tax.
To solve this question, we simply need to calculate 1.5% of Jadiel's annual income to obtain our desired answer, that is,
1.5% of $23400 = $[(1.5/100) * 23400] = $(1.5 * 234) = $351.
Hence, Jadiel has to pay $351 as his social security tax for this year.
Percent: In Mathematics, a percentage is a number or a ratio, that is expressed as a fraction of 100, to indicate the amount of a part of something, and is often denoted using the percent sign, "%"To learn more about percents, click on the link below.
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Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set?2 n - 1 > 52 n - 1 ≥ 51 - 2 n ≥ 51 - 2 n > 5
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
One less than twice a number is no less than five.
Step 02:
inequalities:
We must analyze the problem to find the solution
n = number
2n - 1 ≥ 5
The answer is:
2n - 1 ≥ 5
10. Select all the expressions that have the
value of 9.
270 ÷ 3
250 ÷ 25
270 ÷ 30
207 ÷ 23
189 ÷ 21
Answers
Answer:
270 ÷ 30
207 ÷ 23
189 ÷ 21
These have a value of 9 just use a calculatorStep-by-step explanation:
Coffee Shop PricesCup CostSmall $2Regular $4Large $5David and Jon are placing coffee orders for their friends.David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill.Jon wants to know how much he spent on coffee.1. What is a good plan to find the amount Jon spent on coffee?2. Find how much Jon spent on coffee. Show the equations you used.3. Jamie says the equation 0 x $2 = $0 shows the amount Jon spent on small cups of coffee. Is he correct? Explain.4. Would David have enough money if he paid for his order with a $20 bill? Explain.3rd grade student
Answers
We are given the following details:
Small cup of Coffee = $2
Regular cup of Coffee = $4
Large cup of Coffee = $5
1.
Jon orders 4 fewer large cups than David as shown below. The amount he spent is shown below:
[tex]\begin{gathered} Jon=(10-4)\text{ }large\text{ }cups \\ Jon=6\text{ }large\text{ }cups \\ Jon=6\times5 \\ Jon=\text{\$}30 \end{gathered}[/tex]This means that Jon spent $30 on coffee
2.
The equation is shown below:
[tex]\begin{gathered} Jon=(10-6)\times\text{\$}5 \\ Jon=4\times\text{\$}5 \end{gathered}[/tex]3.
Jon bought zero small cups of coffee. This is represented as:
[tex]\begin{gathered} =0\times\text{\$}2 \\ =\text{ \$0} \end{gathered}[/tex]Hence, Jamie is correct
4.
David ordered 10 large cups of coffee as shown below:
[tex]\begin{gathered} David=10\times5 \\ David=\text{\$}50 \end{gathered}[/tex]If David paid for his order with a $20 bill, we have:
[tex]\begin{gathered} =\text{\$(}20-50) \\ =-\text{\$}30 \end{gathered}[/tex]That implies that $20 cannot cover David's order, he'd still be having a deficit of $30
What is the solution of the system of equations? 6x-2y = 4 -9x+3y = 12
Answers
We will have the following:
First, we solve both equations for y, that is:
[tex]6x-2y=4\Rightarrow-2y=-6x+4[/tex][tex]\Rightarrow y=3x-2[/tex]&
[tex]-9x+3y=12\Rightarrow3y=9x+12[/tex][tex]\Rightarrow y=3x+4[/tex]From this we can see that they are parallel lines, that do not share any common points, so there is no solution for the system.
Patricia O'Malley purchased fifty $1,000 bonds having a quoted price of 99.75. She paid a 6.5% brokerage fee of the selling price). What was the total cost of the bond sale(to the nearest whole cent)?$53,116.88$54,024.65$55,346.77$58,021.99None of these choices are correct.
Answers
It is given that 50 bonds were bought with a cost of $1000 each.
6.5% brokerage was paid.
The total price of the share without brokerage is:
[tex]C=50\times1000\times\frac{99.75}{100}=49875[/tex]The brokerage is given by:
[tex]B=49875\times\frac{6.5}{100}=3241.88[/tex]Hence the total cost of the sale is given by:
[tex]\begin{gathered} T=C+B \\ T=49875+3241.88 \\ T=53116.88 \end{gathered}[/tex]Hence the total cost of sale is $53116.88.
if 15 people with 225 total pounds of luggage plan to ride an elevator with 3000 pound weight limit write and solve an inequality to find the allowable average weight per person
Answers
The 15 people are transporting 225 pounds of luggage, this means that the total weight in the elavator is the weight of the 15 people added by the extra luggage.
[tex]\text{elevator load}=15\cdot w+225[/tex]Since the maximum load allowed in the elevator is 3000 pound, then the expression "15w+225" must be less than 3000.
[tex]15\cdot w+225<3000[/tex]To solve the inequality the first step is to subtract both sides by 225.
[tex]\begin{gathered} 15\cdot w+225-225<3000-225 \\ 15\cdot w<2775 \end{gathered}[/tex]Now we should divide both sides by 15.
[tex]\begin{gathered} \frac{15\cdot w}{15}<\frac{2775}{15} \\ w<185 \end{gathered}[/tex]The mean weight of the 15 people must be less than 185 pounds.
tern US po.. Performance Matte... Student: Login Students and Famili... ReadWorks C Clever | Portal Madison White - Su... https://usea for School: Additional Practice 1.6.AP-24 Question Help 1 Marta has 31- ft of tape to be used for taping up boxes. Complete parts a and b. 4 2 got your answer. IL 1 1 125 25 125 2. 1 31= = 12 х 4 2 4 2 4. 25 = 22 (Type whole numbers, fractions, or mixed numbers.) So, Marta can tape boxes with (Type whole numbers, fractions, or mixed numbers.) boxes with ft of tape left over. H More Enter your answer in the edit fields and then click Check Answer. 1 part Clear All Check Ans remaining
Answers
Martha has 31 1/4 ft of tape to be used for taping up boxes
Each box needs 12 1/2 ft of tape
To find how many boxes Martha can tape up, we need to divide 31 1/4 by 12 1/2
First, we need to convert these mixed numbers into fractions, as follows:
[tex]\begin{gathered} 31\frac{1}{4}=\frac{31\cdot4+1}{4}=\frac{125}{4} \\ 12\frac{1}{2}=\frac{12\cdot2+1}{2}=\frac{25}{2} \end{gathered}[/tex]Dividing by a fraction is the same as multiplying by its inverse, then:
[tex]\frac{31\frac{1}{4}}{21\frac{1}{2}}=\frac{\frac{125}{4}}{\frac{25}{2}}=\frac{125}{4}\cdot\frac{2}{25}=\frac{5}{2}=2\frac{1}{2}[/tex]Given that you can't tape up 2 1/2 boxes, Martha can only tape up 2 boxes. To tape up 2 boxes she needs the next amount of tape:
[tex]12\frac{1}{2}\cdot2=\frac{25}{2}\cdot2=25\text{ ft of tape}[/tex]The leftover is computed as follows:
[tex]31\frac{1}{4}-25=6\frac{1}{4}\text{ ft of tape}[/tex]So, Martha can tape 2 boxes with 6 1/4 ft of tape left over
The equation y = 3x + 7 is written in slope-intercept form.
True
False
Answers
Answer:
True
Step-by-step explanation:
The equation is of the form [tex]y=mx+b[/tex], which is slope-intercept form.
Need to write more bc it has to be 20 characters
Lena prepared 4.3 kilograms of dough after working 2 hours. How many hours did Lena work if she prepared 10.75 kilograms of dough? Assume the relationship is directly proportional.
Answers
Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 directly proportional 2.
What is proportional?A comparison of two numbers mathematically is called a proportion. Two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio, according to the law of proportion. The symbols "::" or "=" are used to indicate proportions.
We have given that 4.3 ∝ 2
where 4.3 kilograms is completed in 2 hours
If 4.3 ∝ 2, the constant k is
4.3 = k2
k = 4.3/2
k = 2.15
We have asked to find how many hours did Lena work if she prepared 10.75 kilograms of dough.
Let hours she took be x, Thus
10.75 ∝ x
We already have the contestant, so this gives us
10.75 = kx
10.75 = 2.15x
x = 10.75/2.15
x = 5 hours
Thus, Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 ∝ 2.
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For what value of k will the points (k, 4) and (3,6) represent a direct variation?
Answers
Let:
[tex]y=ax[/tex]The equation which represents a direct variation. where a is the constant of proportionality.
[tex]\begin{gathered} x=3,y=6 \\ 6=3a \\ a=\frac{6}{3} \\ a=2 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} x=k,y=4 \\ 4=2k \\ solve_{\text{ }}for_{\text{ }}k\colon_{} \\ k=\frac{4}{2} \\ k=2 \end{gathered}[/tex]The table shows the proportional relationship between the number of uniform shirts for a soccer team and the cost.
Number of Uniform Shirts Cost (in dollars)
8 140
15 262.50
22 385
Determine the constant of proportionality.
56
7
122.50
17.50
Answers
The constant of proportionality of the given relationship is: d. 17.50.
How to Determine the Constant of Proportionality?To determine the constant of proportionality of a proportional relationship, k, any pair of values from the given table can be used and calculated as:
k = y/x.
From the given table able that represents a proportional relationship, we can use a pair of values, (8, 140):
Constant of Proportionality, k = 140/8
Constant of Proportionality, k = 17.50
Or, we can also decide to use (22, 385):
Constant of Proportionality, k = 385/22
Constant of Proportionality, k = 17.50
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Question of 10 stepeCorrectThe denominator of a fraction is two more than the numerater both womerator and wominator are increased by on the wheeltraction (DO NOT SimplyFind the wil
Answers
Let the numerator be n; the fraction is:
[tex]\frac{n}{n+2}[/tex]The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by one; then:
[tex]\frac{n+1}{n+3}[/tex]The simplified result is 6/7; then:
[tex]\frac{n+1}{n+3}=\frac{6}{7}[/tex]Solving for n:
(n + 1) x 7 = (n + 3) x 6
7n + 7 = 6n + 18
7n - 6n = 18 - 7
n = 11
The original fraction is:
[tex]\frac{11}{13}[/tex]8. In the accompanying diagram of isosceles triangle ABC, AB = BC, m
Answers
In the given Isosceles triangle,
AB = BC
Since, from the property of issoceles triangle
Angle opposite to equal sides of a triangle are always equal,
So, in the given figure
Angle Opposite to side AB is angle C
Angle Opposite to side BC is angle A
so, Angle A = Angle C
[tex]\begin{gathered} \angle A=\angle C \\ \text{ Since, it is given that }\angle A=x^{\circ} \\ So,\text{ }\angle C=\angle A=x^{\circ} \end{gathered}[/tex]The sum of all angles in a triangle is equal to 180 degrees
[tex]\begin{gathered} In\text{ triangle ABC} \\ \angle A+\angle B+\angle C=180^{\circ} \\ x^{\circ}+(x+30)^{\circ}+x^{\circ}=180^{\circ} \\ x^{\circ}+x^{\circ}+30^{\circ}+x^{\circ}=180^{\circ} \\ 3x^{\circ}+30^{\circ}=180^{\circ} \\ 3x^{\circ}=180^{\circ}-30^{\circ} \\ 3x^{\circ}=150^{\circ} \\ x^{\circ}=\frac{150^{\circ}}{3} \\ x^{\circ}=50^{\circ} \end{gathered}[/tex]Answer : b) x = 50
g(x) = 4x²-2 on [x, x + h] average rate of change
Answers
The average rate of change of function g(x) = 4x²-2 on [x, x + h] is 4h+8x.
What is average rate of change?The average rate at which one quantity changes in relation to another's changing is referred to as the average rate of change function. A process that computes the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
The average rate of change of y = g(x)over an interval between 2 points (a, f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
To calculate the average rate of change between the 2 points.
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
f(x + h) = 4(x+h)²-2
= 4x² + 8hx + 4h² − 2
f(x) = 4x²-2
The average rate of change between (1 ,4x²-2) and (5 ,4x² + 8hx + 4h² − 2) is
[tex]\frac{(4x^2 + 8hx + 4h^2-2) -(4x^2-2) }{(x+h)-x}[/tex]
= 4h+8x
This means that the average of the slopes of lines tangent to the graph of f(x) between (1 ,4x²-2) and (5 ,4x² + 8hx + 4h² − 2) is 4h+8x.
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what is the value to the four decimal places for sin 88°
Answers
sin 88° = 0. 999390827
Appproximating it to four decimal place will give
0.9994
*Using this model, what would be the weight of someone who is 5.8 ft tall? Round your answer to the nearest tenth. You must find the quadratic regression equation first.
Answers
The weight of someone who is 5.8 feet tall is 149.6 lbs.
We are given the height and weight of several adults in the form of a table. We first need to convert this discrete data into the form of an equation. We will use Newton's forward interpolation formula. We find that a quadratic equation fits the data most accurately. The quadratic equation is of the form y = ax² + bx + c. The quadratic equation suitable for the given data is given below :
y = (5.607)x² + (-12.009)x + 30.648
The variable "x" represents the height in feet, and "y" represents the weight in lbs. We need to find the weight of someone whose height is equal to 5.8 feet.
y = (5.607)(5.8)² + (-12.009)(5.8) + 30.648
y = 188.62 - 69.65 + 30.65
y = 149.62
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