Answer:
it may have an even chance
An object was launched off the top of a building. The function f(x)=-16x^{2}+16x+96f(x)=−16x
2
+16x+96 represents the height of the object above the ground, in feet, xx seconds after being launched. Find and interpret the given function values and determine an appropriate domain for the function.
maximum height reached by the object is 100 feet.
Height of the building is 96 feet.
Appropriate domain is 0 ≤ x ≤ 3.
Given,
function for the height of the object above from ground is
[tex]f(x)=-16x^{2}+16x+96[/tex]
The domain can be determined for x for which the value of f(x) = 0
Therefore, when [tex]-16x^{2}+16x+96=0[/tex], we get;
[tex]-16x^{2}+16x+96=0\\\\-16(x^2-x-6)=0\\\\x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\(x+2)(x-3)=0\\\\x=-2 or x=3[/tex]
The minimum value of time, x is 0 and when x = 3, the object is on the ground.
Therefore;
The appropriate domain is 0 ≤ x ≤ 3The maximum value of f(x) = a·x² + b·x + c, is given at [tex]x=-\frac{b}{2a}[/tex]
Therefore;
[tex]x=-\frac{16}{2*-16}=\frac{1}{2}[/tex]
Substituting 'x in f(x) we get,
[tex]f(1/2)=-16(\frac{1}{2} )^{2}+16(\frac{1}{2} )+96\\=-4+8+96=100[/tex]
The maximum height reached by the object, = 100 feetThe height of the building is given when the time, x = 0, as follows;
Height of building, [tex]f(0)=-16(0)^{2}+16(0)+96=96[/tex] feet.Hence, the appropriate domain of the function is 0 ≤ x ≤ 3.
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i am greater than 320 you say my number if you start at 324 and count by 10a i have the same number of tens and ones
Number which is greater than 320 and starts at 324 and count by multiple of 10 and have same number of tens and ones is given by 344.
As given in the number,
Condition for required number is given as follow:
Required number is greater than 320Number should be start at 324.Number should by count by multiple of 10Number should have same number of tens and ones.Start at 324 and count by multiple of 10 are:
324 →334 but in this case tens is 3 and ones is 4 , so it is not a valid number.
324 → 334 →344
This number satisfy all the condition of required number.
It is a valid number.
Therefore, number which is greater than 320 and starts at 324 and count by multiple of 10 and have same number of tens and ones is given by 344.
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Please help me I will give out brainliest.
Answer:
(4,6)
Step-by-step explanation:
PLS MAKE BRAINLIEST
Here are four triangles.
58°
C
23°
9 cm
23°
58°
9 cm
58°
B
D
9 cm
23°
Which two triangles are congruent
23⁰°
9 cm
58°
Total marks
Answer:
they will not be able to change the other owner of the property
Step-by-step explanation:
and the magazine costs m dollars Write down and other expenses for the ping by you
Mario's pizzeria charges $264 for 24 pizzas. What is the restaurant's price for one pizza?
Answer:
The price for one pizza would be $11
Step-by-step explanation:
If its $264 for 24 pizzas you divide
264/24=11
6. A new hi-tech 3D Printer valued at $ 27,800 depreciates exponentially at a rate of 5% yearly. Write the logarithmic equation How long will it take until the machinery has value of $13,900
The logarithmic equation for the time taken until the machinery has a value of $13,900 is x = log₁₉/₂₀ 1/2
Given,
A new hi tech 3D printer valued at $27,800 depreciates exponentially at a rate of 5%.
we are asked to determine the logarithmic equation for the time taken until the machinery has the value of $13,900 = ?
based on the conditions, we formulate:
27800 × (1 - 5%)ˣ = 13900
solve the equation.
27800 × (1 - 0.05)ˣ = 13900
calculate the sum or difference.
27800 × 0.95ˣ = 13900
Divide both sides of the equation by the coefficient of variable.
0.95ˣ = 13900/27800
Reduce the fraction.
0.95ˣ = 1/2
convert exponential to logarithm form.
x = log₀.₉₅ 1/2
cross out the common factor.
x = log₉₅/₁₀₀ 1/2
x = log₁₉/₂₀ 1/2
hence we get the required equation.
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A. EVALUATE Read each number. Then, write it in words. 1. 9.05 6. 76.120 7. 2.705 8. 4. 4.0739 9. 5. 48.002 10. 2. 3. Write 25.8366 17.3 2.8751 123.04 0.008
1. nine hundredths and five hundredths
2. seventy-six hundredths and twelve hundredths
3. two and seven hundred and fifty thousandths
4. four thousand seven hundred thirty-nine tenths
5. five hundred and eighty-two thousandths
6. twenty-five thousand three hundred sixty-six thousand tenths
7. 17 and three tenths
8. two million seven hundred fifty-one hundredths
9. nine hundred and twenty-three hundredths
10. eight thousandths of a percent
How can you put a decimal number into words?1. Write down the complete number.
2. Enter "and" as the decimal point.
3. The decimal part should be written exactly like a whole number.
4. Write down the place value of the last digit.
What exactly is a decimal?For both integer and non-integer numbers, the decimal numeral system is the most often used representational scheme. Non-integer values have been added to the Hindu-Arabic numeral system. The word "decimal notation" refers to the method through which decimal numbers are represented.
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A universtiys freshman class has 8600 students. 1634 of those students are majoring in econmics. What percentage of the freshman class are econmics majors.
Answer:
19%
Step-by-step explanation:
number of economics students/total students in class * 100
1634/8600 * 100
1634/86
817/43
19%
Over the last semester, Mr. Finch kept track of the number of student
absences, Now that the semester is over, he wants to see if there is a linear
relationship between the number of absences and a student's grade for the
semester. The data he collected are given in the table.
A scatter plot of the data is shown in the image attached below.
An equation for the least squares regression line (trend line) is y = -3.49x + 93.14
How to determine a line of best fit for the data?In order to determine a linear equation for the least squares regression line (trend line) that models the data points contained in the table (see attachment), we would have to use a scatter plot.
In this scenario, the number of absences would be plotted on the x-axis of the scatter plot while the algebra grade would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the number of absences and algebra grade in the table, a linear equation for the least squares regression line (trend line) in terms of the problem is given by:
y = -3.49x + 93.14
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What situation is best represented by the following equation
68.50x +127.95=
Answer:
Independent and dependent
Step-by-step explanation:
68.50 would stand as the independent as x could stand for anything such as months or days. 127.95 acts like a static number as it will never change regardless.
A 9ft ladder lens against the side of a house the bottom of the ladder is 6ft from the side of the house how high is the top of the ladder from the ground round the answer to the nearest tenth
Answer:
6.7 feet
Step-by-step explanation:
You want to know the height of a 9 ft ladder above the ground where it leans against a house, and its base is 6 ft from the house.
Pythagorean theoremThe Pythagorean theorem relates the side length of a right triangle. The geometry of this problem can be modeled by a right triangle with hypotenuse 9 ft and one leg 6 ft.
a² +b² = c² . . . . sum of the squares of the legs is the square of the hypotenuse
6² +b² = 9²
b² = 81 -36 = 45
b = √45 ≈ 6.708
The top of the ladder is about 6.7 feet above the ground.
Twice a number n
Help
Lol
Answer:
2n
Step-by-step explanation:
2 x n = 2n
A shop sells bottles of mango juice for
£1.80, but will take 20% off the total
cost when you buy more than 20
bottles. How much does it cost, in
pounds (£), to buy 40 bottles of
mango juice?
It cost £57.6 pounds to buy a 40 bottles of mango juice after 20% discount.
What is discount?
The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Here the cost of one bottle mango juice is £1.80 .
Then cost of 20 bottles mango juice = 20*1.80 = £36.
Now here we can get 20% discount then ,
=> cost of 20 bottles - 20% of cost of 20 bottles
=> 36- 20% of 36
=>36- [tex]\frac{20}{100}[/tex]*36
=>36-7.2
=>£28.8
Now here we have to buy 40 bottles then,
Cost of 40 bottles after 20% discount = 2*28.8=£57.6
Hence cost of 40 bottles of mango juice is £57.6.
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[(114−34)⋅(−23)3]÷(−4)
If you dealt 4 cards from a shuffled deck of 52 cards without replacement, what is the probability that all 4 cards are face cards?.
The probability that all 4 cards are face cards is 0.00182842367.
The face cards are the King, Queen, and Jack (sometimes known as the Knaves). There are 12 face cards in the 52-card deck of playing cards.
The cards are drawn without replacement,
The probability of getting a face card in first draw is 12/52.
As it is without replacement, in the second draw the probability is 11/51.
In third draw, it is 10/50.
In the fourth draw the probability is 9/49.
We have to draw all the four cards, so we multiply the probabilities, to get the final probability.
=12/52x 11/51 x 10/50 x 9/49
=0.00182842367.
Therefore, the probability that all 4 cards are face cards is 0.00182842367.
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The question is in the image, please answer all parts of the question. My brain is empty and I need help desperately!
Answer:
The y2 is over the number of x2 because y has to be larger then x because this says that o and p are both 0,0 so it is a slope angle through M.
Step-by-step explanation:
y2-2, x2-2, 2-25=23divided by 2 so its 11.5
One card is selected from a deck of playing cards. What is the probability the card is not a diamond? (Your answer should be in fraction form.)
Multiply.
3√2•2√8•√3•√6
Enter your answer, in simplest radical form, in the box.
The simple radical form is 72√2.
What is simple radical form?
If we know the prime factorization of 32, we can write the simplest radical form of the square root of 32. Thus, the prime factorization of 32 is 2 × 2 × 2 × 2 × 2. If it is written in the radical form, then the simplest radical form of the square root of 32 is 4√2. Square Root of 32 in Radical Form: 4√2.
Given,
3√2•2√8•√3•√6
= 3×√2×2×√8×√3×√6
as we know √ab = √a√b
we can write, √8 = √2√4 and √6 =√2√3
we get,
=3×√2×√2×√4×√3×√3×√2
=3×2×2×3×√2
=72√2
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. Answer questions (a – f) based on the following graph.
a. When x = -1, what is the value of y?
b. When y = 7, what is the value of x?
c. What is the y-intercept of the graph?
d. What is the x-intercept of the graph?
e. What is the slope of the line?
f. What is the equation of the line?
Answer:
are you asking for all the answers to this
Step-by-step explanation:
How can I solve 2 divided by 3/11 using the giant one method
Answer:
we use to work out dividing a fraction by a whole number.
Jacob can wax 1/4 of the floor in 1 hour. Working together, Jacob and his younger brother can wax the entire floor in 40 minutes. How long would it take Jacob’s brother to wax the floor by himself?
Answer:
48 minutes
Step-by-step explanation:
Jacob can wax 1/4 of the floor in 1 hour so we need to find how much he can do in 40 minutes
Since 40 in 2/3 of an hour we multiply 1/4 by 2/3
1/4*2/3
2/12
1/6
Jacob can do 1/6 of the floor in 40 minutes so that means his brother can do 5/6 of the floor in 40 minutes
we need to find that 1/6 more of floor he needs to do by dividing 5/6 by 5 and 40 by 5
5/6/5
5/6*1/5
5/30
1/6
40/5
8
It takes 8 minutes for his brother to do 1/6 of the floor so we add that to the original
40+8
48 minutes it takes for jacob’s brother to do the entire floor
Hopes this helps please mark brainliest
Someone please explain this to me.
The new coordinate points of the line will be -
Point X' → (-4, 2)
Point Y' → (3, -4)
What do you mean by Translation of figure ?
Translation is s transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation.
We have -
The transformation rule : (x, y) → (x − 1, y + 1).
Coordinates of the vertices of the line -
Point X → (-3, 1)
Point Y → (4, - 5)
After the translation, the coordinate points will become -
Point X' → (-4, 2)
Point Y' → (3, -4)
Hence, the new coordinate points of the line will be -
Point X' → (-4, 2)
Point Y' → (3, -4)
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Write 5√12 in the form √a where a is an integer to be found.
Answer:
a = 300
[tex]5 \sqrt{12} = \sqrt{25} \sqrt{12} = \sqrt{25 \times 12} = \sqrt{300} [/tex]
Find the mode of the following number of paper clips found by each participant during a scavenger hunt.
15,12,20,19,20,15,7,12,7,19,15
The mode of the data set is 15.
What is the mode?A data set's mode or modal value is the value that appears the most frequently.
The given data are:
15, 12, 20, 19, 20, 15, 7, 12, 7, 19, 15.
Note that the number 15 occurs 3 times in the data set which is highest than the occurrence of any other number in the data set.
Hence, the mode of the data set is 15.
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find the domain of
4x^2/x^3
The domain of the expression [tex]\frac{4x^2}{x^3}[/tex] is (-∞,0) ∪ (0,∞)
The given expression is
[tex]\frac{4x^2}{x^3}[/tex]
The expression is the mathematical statement that consist of different variables, numbers and mathematical operator. The mathematical operators are addition, subtraction, multiplication and division. The expression does not contain equal sign and inequality signs
The given expression is
[tex]\frac{4x^2}{x^3}[/tex]
First we have to solve the given expression and make it in simplest form and find the domain of the expression
[tex]\frac{4x^2}{x^3}[/tex] = 4/x
The set of all possible input of the expression are called domain.
Here 0 is not the part of domain
The domain = (-∞,0) ∪ (0,∞)
Hence, the domain of the expression [tex]\frac{4x^2}{x^3}[/tex] is (-∞,0) ∪ (0,∞)
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Help me solve this please!
Movie Tickets
Tickets to a 3D movie cost $13 for an adult and $10 for each child. A total of $859 was collected in ticket sales for the 7:15PM show.
Write a linear equation in general form to represent this situation. Let C represent the number of children's tickets and A represent the number of adult tickets sold.
Equation:
If 53 adult tickets were sold, how many children were there?
There were children at the movie.
The linear equation is 10C+13A=859 and number of children ticket is 17.
What is linear equation ?
A linear equation is also known as a one degree equation. The linear equation's highest power is 1. Linear equations are equations with variables on both sides that are multiplied by a constant.
Let us take Number of children's ticket as C and number of adult's ticket as A.
Here cost price of one adult ticket = $13
Cost price of one children ticket =$10
A total of $859 was collected in ticket sales for the 7:15PM show.
Total cost price = cost price of children ticket + cost price of adult ticket
=> Total cost price = 10*C+13*A
=> 859=10C+13A
Hence the linear equation is 10A+13A=859.
Here If number of adult ticket = 53. Then
=> 13*53+10C=859
=>689+10=859
=>10C= 859-689=170
=> C=170/10 = 17.
Hence the number of children ticket is 17.
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Iowa has, on average, 37,785 annual births compared to 30,530 annual deaths. If Maine was proportional to Iowa in annual births to deaths and Maine averages 14,676 annual deaths, how many annual births should Maine expect? Round to the nearest whole number.
The annual births that Maine should expect is about 18,164
Given,
The average annual birth in Lowa = 37,785
The average annual death in Lowa = 30,530
The average annual death in Maine = 14,676
Maine is proportional to Lowa in annual births to deaths.
We have to find the annual births that Maine should expect;
Here,
Maine is proportional to Lowa in annual births to deaths.
That is,
Annual birth in Lowa : Annual death in Lowa = Annual birth in Maine : Annual death in Maine
37,785 : 30, 530 = x : 14,676
x = (37,785 x 14,676) / 30,530
x = 18, 164
That is,
The annual births that Maine should expect is about 18,164
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if sin α=1/3, pi/2 < α < pi and cos β = -1/3, pi < β < 3pi/2 find exact value of: (a) = (b) = (c) = (d) = (e)
The exact values of two trigonometric functions are listed below:
Case A: - 2√2 / 3
Case B: - 2√2 / 3
Case C: 7 / 9
Case D: 4√2 / 9
Case E: ± √6 / 3
How to determine the exact values of the trigonometric functions
In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.
Case A - cos α:
Since sin α > 0 for π / 2 < α < π, then cos α < 0. Then, by the fundamental formula:
cos α = - √(1 - sin² α)
cos α = - √[1 - (1 / 3)²]
cos α = - √(8 / 9)
cos α = - 2√2 / 3
Case B - sin β:
Since cos β < 0 for π < α < 3π / 2, then sin β < 0. Then, by the fundamental formula:
sin β = - √(1 - cos² β)
sin β = - √[1 - (- 1 / 3)²]
sin β = - 2√2 / 3
Case C - cos 2α:
cos 2α = cos² 2α - sin² 2α
cos 2α = (- 2√2 / 3)² - (- 1 / 3)²
cos 2α = 7 / 9
Case D - cos (α + β):
cos (α + β) = cos α · cos β - sin α · sin β
cos (α + β) = (- 2√2 / 3) · (- 1 / 3) - (1 / 3) · (- 2√2 / 3)
cos (α + β) = 2√2 / 9 + 2√2 / 9
cos (α + β) = 4√2 / 9
Case E - sin (β / 2):
sin (β / 2) = ± √[(1 - cos β) / 2]
sin (β / 2) = ± √[[1 - (- 1 / 3)] / 2]
sin (β / 2) = ± √6 / 3
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The height of liberty school is 8.85*10^3m.the height of festus school is 5.89*10^3m.write these in ordinary form,find the difference and write each height value correct to 2 sgf
The height of Liberty School in ordinary form is 8850m and height of Festus school is 5890m , the difference of the height of the schools is 2960m .
In the question ,
it is given that
the height of the Liberty school is 8.85×10³m .
we have to convert this height in the ordinary form ,
8.85 × 10³ = (885/100) × 1000
= 885 × 10
= 8850m
The height of the Festus school is 5.89 × 10³ m
in ordinary form it is
= 5.89×10³
= (589/100) × 1000
= 589 × 10
= 5890m
The difference in the height of the schools = (height of the Liberty school) - (height of Festus school) .
So , the difference = 8850 - 5890
= 2960m
Therefore , the height of Liberty School is 8850m and height of Festus school is 5890m , the difference of the height of the schools is 2960m.
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Find the range of each function, given the domain
h(x) = x - 7; {-8, 0,4}
For the given function, the range of each function would be R = {-15, -7, -3}.
What is the range of the function?
In mathematics, the range of a function can refer to one of two concepts that are closely related: The function's codomain and the function's visual representation A binary relation f between two sets X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.
The given function is: h(x) = x - 7 and the domain = {-8, 0, 4}
Now find the range of each function
h(-8) = -8 - 7 = -15
h(0) = 0 - 7 = -7
h(4)= 4 - 7 = -3
Range(R) = {-15, -7, -3}.
Hence, for the given function, the range of each function would be R = {-15, -7, -3}.
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