A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Answers
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]Related Questions
If the revenue function for a certain item is R(x)=20x−0.25x2, what is the marginal revenue for the 8th item? Do not include the dollar sign in your answer.
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The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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Riley has $955 in a savings account that earns 15% interest, compounded annually.To the nearest cent, how much interest will she earn in 2 years?
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In order to calculate the interest generated in 2 years, we can use the formula below:
[tex]I=P((1+r)^t-1)[/tex]Where I is the interest generated after t years, P is the principal (initial amount) and r is the interest rate.
So, for P = 955, r = 0.15 and t = 2, we have:
[tex]\begin{gathered} I=955((1+0.15)^2-1) \\ I=955(1.15^2-1) \\ I=955(1.3225-1) \\ I=955\cdot0.3225 \\ I=307.99 \end{gathered}[/tex]Therefore the interest generated is $307.99.
In a recent survey of dog owners, it was found that 901, or 34%, of the owners take their dogs on vacation with them. Find the number of dog owners in the survey that do NOT take their dog on vacation with them rounded to the nearest whole number
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we have that
34% represents 901 owners that take their dogs on vacation with them
so
the percentage of dog owners in the survey that do NOT take their dog on vacation is equal to
100%-34%=66%
Applying proportion
901/34=x/66
solve for x
x=(901/34)*66
x=1,749 ownersJackson bought a Ford Mustang for $40,000 and it depreciates in value 9% per year. Write an equation that
models the value of Jackson's car.
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Answer:
[tex]v = 40000( {.91}^{x} )[/tex]
Perform the indicated operation of multiplication or division on the rational expression and simplify
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The division of two fractions is the same as multiplying the first by the inverted second fraction:
Then, in this case:
[tex]\frac{24y^2}{5x^2}\div\frac{6y^3}{25x^2}=\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}[/tex]Step 2: multiplication of two fractionsWe multiply two fractions by multiplying the numerators and the denominators:
[tex]\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}=\frac{24y^2\times25x^2}{5x^2\times6y^3}[/tex]Step 3: simplifying the numbers of the fractionWe know that
[tex]\frac{25}{5}=5\text{ and }\frac{24}{6}=4[/tex]Then, we can use this in our fraction:
[tex]\begin{gathered} \frac{24y^2\times25x^2}{5x^2\times6y^3}=5\cdot4\frac{y^2x^2}{x^2y^3} \\ \downarrow\text{ since 5}\cdot4=20 \\ 5\cdot4\frac{y^2x^2}{x^2y^3}=20\frac{y^2x^2}{x^2y^3} \end{gathered}[/tex]Step 4: exponents of the resultWe know that if we have a division of same base expressions (same letters), the exponent is just a substraction:
[tex]\begin{gathered} \frac{y^2}{y^3}=y^{2-3}=y^{-1} \\ \frac{x^2}{x^2}=x^{2-2}=x^0=1 \end{gathered}[/tex]Then,
[tex]20\frac{y^2x^2}{x^2y^3}=20y^{-1}\cdot1=20y^{-1}[/tex]Since negative exponents correspond to a division, then we can express the answer in two different ways:
[tex]20y^{-1}=\frac{20}{y}[/tex]Answer:[tex]20y^{-1}=\frac{20}{y}[/tex]How many different arrangements of 5 be formed if the first must Work (of allowed?
Answers
ANSWER
There are 913,952 different 5-letter combinations that can be formed.
EXPLANATION
Recall that there are 26 letters in the English Alphabet.
From the question, we are to find the arrangement of 5 letters with the first letter being either W or K, and repetition of letters is allowed.
The possibilities for the 1st letter is 2 since the 1st letter can be either W or K;
More so, the possibilities for the 2nd letter is 26;
The possibilities for the 3rd letter is 26;
The possibilities for the 4th letter is 26, and
The possibilities for the 5th letter is 26;
The possibilities of arranging 5 letters = 2 x 26 x 26 x 26 x 26 = 913,952.
Hence, a total of 913,952 different 5-letter combinations can be formed.
Hi can you help me find the correct match to each question?
Answers
GIVEN:
We are given a set of 4 statements as indicated in the attached image.
Required;
Determine whether each statement is TRUE or FALSE.
Solution;
(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.
This statement is TRUE
(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.
This statement is TRUE.
(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.
This statement is FALSE.
(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.
This statement is FALSE.
Finding the intercepts, asymptotes, domain, and range from the graph of a rational function
Answers
From the given graph
The asymptotes are the dotted lines in the graph, then
The vertical asymptote is x = 3
The horizontal asymptote is y = 1
The domain is all values of x that make the function defined
Since x can not equal 3, then
The domain is
[tex]D=(-\infty,3)\cup(3,\infty)[/tex]The range is all values of y corresponding to the values of the domain (x)
Since y can not equal 1, then
The range is
[tex]R=(-\infty,1)\cup(1,\infty)[/tex]The x-intercept is the value of x at the graph intersecting the x-axis
Since the graph intersects the x-axis at the point (6, 0), then
The x-intercept is 6
The answer is the first choice 6
The y-intercept is the value of y at the graph intersection the y-axis
Since the graph intersects the y-axis at point (0, 2_, then
The y-intercept is 2
The answer is the second answer 2
Given that angle A lies in Quadrant I and sin(A)= 30/31, evaluate cos(A)
Answers
You have a huge review project for English where you have to answer 300 questions. You start on it after school at 5:00. At 6:30, you have answered 55 questions.What time will you finish your assignment if you don't take any breaks?
Answers
Given :
The total questions = 300
Time of starting = 5:00
At 6:30 the number of answered questions = 55
The time spent to answer 55 questions = 6:30 - 5:00 = 1:30 hours
Which is equal to : 1 hour and 30 minutes = 90 minutes
So, the rate of answering the questions =90/55 = 18/11 minute per question
So, for solving the 300 questions, the time will be :
[tex]300\cdot\frac{18}{11}=490\frac{10}{11}\min [/tex]So, 490 10/11 minutes = 8 hours and
In the picture below, angle 2 = 130 degrees, what is the measurement of angle 1?
Answers
Answer:
50°
Step-by-step explanation:
[tex]\angle 1[/tex] and [tex]\angle 2[/tex] form a linear pair, and are thus supplementary (meaning they add to 180°).
Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
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The breakeven point of Angel Corporation equals to 11,500 units.
How do we get the breakeven point?Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x
Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x
Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/$7.04
x = 11,500 units
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A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the rate of 8 mL/min, how fast is the outer surface area of ice changing when the outer diameter of the ball with ice on it is 24 cm?
Answers
When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
As given in the question,
Spherical ball is coated with uniform thickness.
Ice melts at the rate of 8ml/min
= (8/60)cm³/sec
Consider r as the radius of given spherical ball
Diameter = 24cm
⇒Radius 'r' =12cm
Volume 'V' = (4/3)πr³
⇒ dV /dt = (4/3)π(3r²r')
⇒-(8/60) = (4/3)π(3 ×12²×r')
⇒r' =-(8/60)×(1/576π)
⇒r' = - 1/ 4320π
Rate at which change in surface area
A =4πr²
⇒A' = 4πrr'
⇒A' = 4π (12) ( - 1/ 4320π)
= -1/90 cm²/sec.
Decrease in surface area = 1/90 cm²/sec.
Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
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Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
Answers
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbEsmeralda rents a car from a company that rents by the hour. she has to pay an initial fee of $50, and they charge her $8 per hour. she has $150 available to spend on car rental. what is the greatest number of hours for which she can rent the car?A. 18 hoursB. 12.5 hoursC. 12 hoursD. 13 hours
Answers
Let the number of hours be x,
Initial fee is $50,
Amount charged per hour is $8
The charge for a number of x hours is'
[tex]x\times8=8x[/tex]The total amount Esmeralda has is $150,
Therefore,
[tex]8x+5\leq150[/tex]Solving for x to find the greates number of hours,
[tex]\begin{gathered} 8x+50\leq150 \\ \text{Collect like terms,} \\ 8x\leq150-50 \\ 8x\leq100 \\ \text{Divide both sides by 8} \\ \frac{8x}{8}\leq\frac{100}{8} \\ x=12.5\text{ hours} \end{gathered}[/tex]Hence, the greates number of hours is 12.5 hours.
Option B is the right answe
1. Sally uses 312 cups of flour for each batch of cookies.
How many cups does she need to make 4 batches of cookies?
Answers
Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
pls show how did u solve it
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Linear function f(x) = 2/7x - 2
It has no domain or range restrictions, so both of them include all real numbers.
Doman x ∈ ( - ∞, + ∞),Range y ∈ ( - ∞, + ∞).The graph is attached
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 − 2x2 − 15x
x =
Answers
Answer:
-3, 0, 5
Step-by-step explanation:
You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.
Factored formWe notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:
P(x) = x(x² -2x -15)
To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...
P(x) = x(x +3)(x -5) . . . . factored form
ZerosThis product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...
x = 0
x +3 = 0 ⇒ x = -3
x -5 = 0 ⇒ x = 5
The zeros of P(x) are -3, 0, 5.
25, -34, -2, 56, 8,-7 greatest to least
Answers
To arrange this from the greatest to the least
we will first look out for the positive numbers
Among the positive numbers, 56 comes first
then 25 and finally 8
Then we move to the negative numbers
-2 comes first
then -7 and then -34
Hence
56, 25, 8, -2, -7, -34
help I'm practicing
Answers
We have the next formula to find the volume of a triangular prism-
[tex]V=B\times h[/tex]where
B= area of the base
h= height
in our case
B=18 square inches
H= 5 inches
[tex]V=18\times5=90in^3[/tex]the volume of the triangular prism is 90 cubic inches
If there are 40 seats per row how many seats are in 90 rows?
Answers
Answer:
3,600 seats
Step-by-step explanation:
If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.
-Hope this helps
Answer:
Step-by-step explanation:
3600
If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!
Which of the followingrepresents this inequality?|4x – 61 > 10
Answers
Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
1. There are three car manufacturing factories A, B and C, and they are producing the same type
of cars. They are employing 1000, 2000 and 3000 men and producing 10, 15 and 25 cars per
month respectively. Find the labor productivity of each firm and the production of each firm
per year.
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Can someone help me with this please and thank you
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The histogram is skewed to the left, the mean is less than the median.
The point P is on the unit circle. If the y-coordinate of P is −3/5, and P is in quadrant IV, then
x = _________
Answers
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],
so x can be positive or negative 4/5,
and we know that x coordinate of any point in quadrant IV is positive,
so x = 4/5.
In the diagram below, FG is parallel to CD. If the length of CD is the same as the length of FE, CE = 26, and FG = 11, find the length of FE. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answers
Answer:
The length of FE is √286 units.
Explanation:
Let the length of FE = x
Since FG is parallel to CD, then triangles EFG and ECD are similar triangles.
The ratio of the corresponding sides are:
[tex]\frac{FE}{CE}=\frac{FG}{CD}[/tex]Substitute the given values from the diagram above:
[tex]\frac{x}{26}=\frac{11}{x}[/tex]We then solve the equation for x.
[tex]\begin{gathered} \text{ Cross multiply} \\ x^2=26\times11 \\ \text{ Take the square root of both sides} \\ x=\sqrt{26\times11} \\ x=\sqrt{286} \\ \implies FE=\sqrt{286}\text{ units} \end{gathered}[/tex]The length of FE is √286 units (in simplest radical form).
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
If the price of gas was on average $2.85 per gallon, and thus was $1.36 cheaper than a year before, what is the percent of decrease in price?
Answers
The price of gas = $2.85 per gallon
It was $1.36 cheaper than a year before.
So, the price before = 2.85 + 1.36 = $4.21
So, the percent of decrease = 1.36/4.21 = 0.323 = 32.3%
18)Betsy is collecting data on the amount of time shoppers spend inside of a particular large department store. She stands outside the department store and surveys every 10th shopper who exits. What type of sampling is used? Explain your answer.
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Consider the 5 main types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.
In the case of systematic sampling, every kth element of the data set is taken.
In our case, consider all the shoppers and imagine that they can be ordered in a line; then, Betsy selected the 10th shopper in the line, the 20th one, and so on.
This is analogous to systematic sampling; the answer is systematic sampling.write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas
Answers
Here, we want to write ratios in part to part and in part to whole ratio
For the part to part
Writing carrot to peas, we have;
[tex]142\colon97[/tex]For the parts to whole ratio, we have;
[tex]\begin{gathered} \text{Carrot} \\ \frac{142}{250}\text{ = 142:250} \\ \text{Peas} \\ \frac{97}{250}\text{ = 97:250} \end{gathered}[/tex]