Answers
Answer:
f(96) = 85
Step-by-step explanation:
f'(95) gives us the slop of 6, which can be used to estimate the increase
of the next number.
Ex) f(95) = 79 & f'(95) = 6 so
f(96) = 79 + 6 = 85
Related Questions
Rosa is using a recipe that serves six and uses one and three quarters cups of pasta. Choose the amount of pasta she will use if she wants to make eight servings. (2 points)
two and one third cups
three and three quarters cups
four and one quarter cups
two and one quarter cups
Answers
Answer: To calculate the amount of pasta needed for eight servings, we need to multiply the original amount of pasta in the recipe by 8/6.
So, 1.75 cups * 8/6 = 2.3 cups of pasta.
Therefore, Rosa will use 2.3 cups or four and one quarter cups of pasta if she wants to make eight servings.
Step-by-step explanation:
Two cars leave towns 320 kilometers apart at the same time and travel toward eachother. One car's rate is 12 kilometers per hour less than the other's. If they meet in 2 hours, what is the rate of the slower car?
Do not do any rounding.
Answers
Answer:
74 kilometers per hour.
Step-by-step explanation:
Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).
The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:
x + (x - 12) = 2x - 12
According to the problem, they meet after 2 hours of travel, so the total distance they cover is:
distance = speed × time
For the faster car, the distance it covers is:
distance = x × 2
For the slower car, the distance it covers is:
distance = (x - 12) × 2
Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):
x × 2 + (x - 12) × 2 = 320
Simplifying this equation:
2x + 2x - 24 = 320
4x = 344
x = 86
Therefore, the speed of the faster car is 86 kilometers per hour.
To find the speed of the slower car, we can use the expression we found earlier:
x - 12 = 86 - 12 = 74
Therefore, the speed of the slower car is 74 kilometers per hour.
Please can someone help me!!!?
Answers
Answer:
inertia
equilibrium
free body diagram
net force
force
Step-by-step explanation:
Reema bought pencils for school in august. She gave 1/2 of them to her friends. She used 3/4 of what she had left for the first month of school. She now had 3 pencils left. How many pencils did she buy in august?
Answers
Answer:
24 pencils
Step-by-step explanation:
Let's call total number of pencils T.
she gave 1/2 to friends. Now she has (1/2)T.
she then used 3/4 of those, leaving her with only 1/4 of what she had AFTER giving them to friends. That is 1/2 X 1/4 = 1/8.
She now has 3 pencils. 3 pencils = 1/8.
Multiply both sides by 8 to get 24 pencils = 1 (whole ie T).
Total number of pencils, T, bought in August is 24.
Two students share 3/4 of a pound of peanuts. How much of a pound does each person get
Answers
Step-by-step explanation: 3/4 divided by 2 or .75/2
What is the range of the given function?
Answers
Answer:
D
Step-by-step explanation:
Look at the y-values for both dots, the open circle is -7 and the closed circle is 5. The closed circle means y is going to be equal to, so the greater than sign is made to be equal.
5х2 +х — 4
Factor completely
Answers
Answer:
(5x-4)(x+1)
Step-by-step explanation:
For Mean = 73.19, Mode = 79.56 and Variance = 16, the Karl Pearson's Coefficient of Skewness will be -0.0256 -1.64 0.0256 0
Answers
Answer:
To calculate Karl Pearson's coefficient of skewness, we need to use the formula:
Skewness = 3 * (Mean - Mode) / Standard Deviation
Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.
Standard Deviation = √Variance = √16 = 4
Now we can substitute the values into the formula:
Skewness = 3 * (73.19 - 79.56) / 4
Skewness = -6.37 / 4
Skewness = -1.5925
Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.
Based on the pattern, what are the next two terms of the sequence?
Answers
Answer:
33 , 39
Step-by-step explanation:
given
9 , 15 , 21 , 27
there is a common difference between consecutive terms, that is
15 - 9 = 21 - 15 = 27 - 21 = 6
to obtain terms in the sequence add 6 to the preceding term
27 + 6 = 33
33 + 6 = 39
the next two terms are 33 and 39
15-9=6
21-15=6
27-21=6
That means we are adding 6 at every step. Therefore the next two elements must be
27+6=33 and 33+6=39
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm
Answers
Answer:
\(\dfrac{dV}{dt}=502.65\ mm^3/s\)
Step-by-step explanation:
The volume of a sphere is given by :
\(V=\dfrac{4}{3}\pi r^3\)
The rate of change of volume means,
\(\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}\)
We have, \(\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm\)
So,
\(\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s\)
So, the volume is increasing at the rate of \(502.65\ mm^3/s\).
Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
Answers
Hay dos rectángulos posibles que satisfacen las condiciones dadas: uno de 2 cm de largo y 6 cm de ancho, y otro de 6 cm de largo y 2 cm de ancho.
5⁶ • 5 how do i simplify
Answers
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619, $379, $895, $1,256, $1,052
a. What is the median of the first half of the data? (first quartile)
Answers
The price of the refrigerators that is the median for the first half of the data is $498.
What is the median of the first half of the data?Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
The prices arranged in ascending order is: $379, $498, $619, $777, $895, $1052, $1256
The first half of the prices are $379, $498, $619,
Median = $498
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find two functions f and g
a. f(x) =
b. f(x) =
Answers
The functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.
Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.
Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:
(fog)(x) = f(g(x)) = f(x + a)
b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.
Substituting the expressions for f(x) and g(x) into (fog)(x), we have:
(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)
Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
Using these functions, we can verify the composition (fog)(x):
(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)
Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.
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Twice a number n is no less than 10 units from −1.
Answers
Answer:
n ≥ 4.5 or n ≤ - 5.5===========================
Twice a number n is no less than 10 units from −1:
Twice a number n ⇒ 2n,no less than ⇒ ≥,10 units from −1 ⇒ - 1 ± 10.The inequality becomes an absolute value and translates as:
" The difference of 2n and - 1 is equal or greater than 10"| 2n - (-1) | ≥ 10| 2n + 1 | ≥ 102n + 1 ≥ 10 or 2n + 1 ≤ - 102n ≥ 10 - 1 or 2n ≤ - 10 - 12n ≥ 9 or 2n ≤ - 11n ≥ 4.5 or n ≤ - 5.5The room has a width of 8 feet, a length of 12 feet, and a height of 9 feet. What is the greatest possible distance between two points on the walls in the room?
Answers
Answer:
The greatest possible distance between two points on the walls in the room is 17 feet.
Step-by-step explanation:
The room can be modelled as a rectangular prism with the following dimensions:
width = 8 ftlength = 12 ftheight = 9 ftThe greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.
This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.
The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room. To calculate the diagonal of the floor, use Pythagoras Theorem.
\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)
Substitute a = 8, b = 12 and c = y into the formula and solve for y:
\(\implies 8^2+12^2=y^2\)
\(\implies 64+144=y^2\)
\(\implies y^2=208\)
\(\implies y=\sqrt{208}\; \sf ft\)
Therefore, the diagonal of the floor (y) is √(208) feet in length.
We can now use Pythagoras Theorem again to find the length x.
Substitute a = y, b = 9 and c = x into the formula:
\(\implies y^2+9^2=x^2\)
Substitute the found value of y and solve for x:
\(\implies (\sqrt{208})^2+9^2=x^2\)
\(\implies 208+81=x^2\)
\(\implies 289=x^2\)
\(\implies x=\sqrt{289}\)
\(\implies x=17 \sf \; ft\)
Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.
The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
Answers
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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Someone help me with this please!!!! LOOK at attached a picture.
is the piecewise graph below a function?
Answers
Answer: yes
Step-by-step explanation:
2
1
-1
-2
Determine the period.
2 4
6 8 10 12 14
Acellus
Answers
According to the information we can infer that the period of the graph is 8.
How to determine the period of the graph?To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.
In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.
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Classify the triangle
Answers
Answer:
Equilateral triangle
Step-by-step explanation:
When all sides of a triangle are equal or all angles of the triangle are 60 degree then the triangle is called an equilateral triangle
Literal equations
Show work
Solve for x
-3(x + n) = x
Answers
Answer:
x=-3/4n
Step-by-step explanation:
first, remove the parenthesis.
-3(x + n) = x
-3x -3n = x
collect like terms.
-3x - x = 3n
divide both sides.
-4 = 3n
and therefore,
x= -3/4n
Find the value of x . (Do not round until the final answer . Then round to the nearest tenth as needed .)
Answers
According to the given image, x is the radius of the circle.
So, we can find x using Pythagorean's Theorem in the following right triangle.
Where x is the hypothenuse.
\(\begin{gathered} x^2=5.3^2+4^2 \\ x=\sqrt[]{28.09+16} \\ x=\sqrt[]{44.09}\approx6.6 \end{gathered}\)Hence, x is 6.6, approximately.
Penelope goes out to lunch. The bill, before tax and tip, was $16.05. A sales tax of 3% was added on. Penelope tipped 18% on the amount after the sales tax was added. How much tip did she leave? Round to the nearest cent.
Answers
Answer:
2.98
Step-by-step explanation:
First find 3% of 16.05 which is 0.48.
Then add 0.48 to 16.05 which is 16.53.
Then multiply .18 by 16.53 which gets you 2.98
Hope it helps
Answer:
To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:
Sales tax = 0.03 x $16.05 = $0.48
To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:
Total bill = $16.05 + $0.48 = $16.53
To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:
Tip = 0.18 x $16.53 = $2.98
Rounding to the nearest cent, Penelope left a tip of $2.98.
Step-by-step explanation:
PLEASE HELP! 40 points!!
3000 gallons of oil are to be transported to a destination 1000 miles away.
The only delivery truck available has a load capacity of 1000 gallons max. Additionally the truck consumes 1 gallon per mile from its load.
What is the maximum gallons of oil that can reach the destination when taking into account the truck consumption?
Answers
Answer:
0 gallon
Step-by-step explanation:
Given: 1 gallon per mile
total amount = 3000 gallons
capacity of truck = 1000 gallons
total number of trips = 3000/1000 = 3
total oil to reach the destination = 3000-3000=0
I hope this helps.
The maximum gallons of oil that can reach the destination when taking into account the truck consumption equals to zeroes.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is 3000 gallons of oil are to be transported to a destination 1000 miles away. The only delivery truck available has a load capacity of 1000 gallons max. Additionally the truck consumes 1 gallon per mile from its load.
The maximum number of gallons of oil that can reach the destination when taking into account the truck consumption can be calculated as follows.
In one trip of 1000 miles, The amount of oil transferred will be -
1000 - 1 x 1000
0 Gallons.
Similarly, in all the trips the total gallons of oil reaching the destination will be zero.
Therefore, the maximum gallons of oil that can reach the destination when taking into account the truck consumption equals to zero gallons.
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What ratio is equivalent to 8/6
Answers
Answer:
3rd option: 32/24
Step-by-step explanation:
8/6 = 4/3
1st option: Now let's change the denominator to 24:
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
2nd option: Now let's change the numerator to 24:
4/3 ==> 24/?
4/3 =
4*6 / 3*6 = 24/18, not 24/32
24/32 = 3/4, not 4/3 ==> don't get confused by this
3rd option: 32/24 is correct [Look at the explanation for 1st option]
4/3 ==> ?/24
4/3 =
4*8 / 3*8 = 32/24, not 3/24.
Hence, the 3rd option is correct.
What percent of 20 is 4?
Answers
Answer:
4 is 20% of 20
Step-by-step explanation:
4/20 × 100
20%
Otto builds and sells model cars. He made a graph to compare the number of days to the number of model cars. Three of the points form a proportional relationship, but one does not. Which point does not fit in the proportional relationship? Coordinate plane with Number of Days on the x-axis and Number of Model Cars on the y axis. 4 points are plotted in the plane: 2, 1; 4, 2; 6, 2; and 8, 4. A (2, 1) B (4, 2) C (6, 2) D (8, 4)
\
Need HELP ASAP
Answers
Answer:
I have attached a really rough graph!!
Step-by-step explanation:
The point that does not fit in the proportional relationship is (6,2) when we plot the other three points and join the points they will give us a staright line but the point (6,2) isnt lying on that staright line.. Therefore, it does not fit in the proportional relationship!
Answer:
(6,2)
Step-by-step explanation:
Laws of Exponents, urgent please need the answers right away, thank you!!
solve it both and show the step by step!
Answers
The values of the expressions are;
z³³
d⁻¹⁶
How to simply the exponentsNote that index forms are described as forms used in the representation of numbers or variables too large or small.
Some rules of index forms are;
Add the exponents when multiplying like basesSubtract the exponents when dividing like basesThen, from the information given, we have that;
(z⁻⁴/z⁶ × z⁵/z⁻⁶)⁻¹¹
Subtract the exponents, we have;
(z⁻² × z⁻¹)⁻¹¹
expand the bracket
z²² ⁺ ¹¹
z³³
(d⁴)⁻³/(d⁶)⁻² ÷ (d⁴/d⁶)⁻⁸
expand the brackets
d⁻¹²/d¹² ÷ (d⁻²)⁻⁸
subtract the exponents
d⁰ ÷ d¹⁶
d⁻¹⁶
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Select whether each of these factors was a reason for or against American neutrality. US trade with Europe was worth almost one billion dollars. for against Intro
________________________
Sunny ko behan mil gayi sonali ✨
Answers
The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.
Why did American neutrality benefit from commerce with Europe?Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.
The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.
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2. The speed of light is 1.08 x 10⁹ k/h. Express this in (a) SI units (b) millimetres per nanosecond
Answers
The speed of light is 1.08 x 10⁹ k/h Express this in SI units is 3 x 10⁸ m/s and in millimeters per nanosecond is 0.3 mm/ns.
How to calculate the speed of light in SI units and millimeters per nanosecond(a) To express the speed of light in SI units, we can convert kilometers to meters and hours to seconds.
1 km = 1000 m
1 h = 3600 s
Therefore,
1.08 x 10⁹ k/h = (1.08 x 10⁹) x (1000 m/km) / (3600 s/h) = 3 x 10⁸ m/s
So the speed of light in SI units is 3 x 10⁸ m/s.
(b) To express the speed of light in millimeters per nanosecond, we need to convert meters per second to millimeters per nanosecond.
1 m = 10⁶ mm
1 s = 10⁹ ns
Therefore,
3 x 10⁸ m/s = (3 x 10⁸) x (10⁶ mm/m) / (10⁹ ns/s) = 0.3 mm/ns
So the speed of light in millimeters per nanosecond is 0.3 mm/ns.
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