Megan spent 2 1/12 hours dancing both yesterday and today
How to calculate the number of hours Megan spent dancing ?Megan is involved in a musical production
Yesterday, she practiced for 2 3/4 hours
Today she practiced for 3 1/2 hours
The first step is to calculate the total number of hours she spent at the practice
2 3/4 + 3 1/2
= 11/4 + 7/2
The LCM between both fractions is 4
11/4 + 7/2
11 + 14/4
= 25/4
Megan spent 25/4 hours yesterday and today practicing
Out of this 25/4 hours, she spent 1/3 hours dancing
Therefore the hours she spent dancing can be calculated as follows
= 25/4 × 1/3
= 25/12
= 2 1/12
Hence Megan spent 2 1/12 hours dancing yesterday and today
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Solve 5(x + 2) = 26 - 3x
x = ...
an exponential function f has a 3-unit growth factor of 1.55. what is the 1-unit growth factor for f ? what is the 2-unit growth factor for f ? what is the 1 2 -unit growth factor for f ?
Given that 3 unit factor growth is 1.65
Then 1 unit growth factor = (1.65)^1/3 = 1.181
2 unit growth factor of F = 1.396
And 1/2 unit growth factor = (1.65)^0.5/3 = (1.65)^0.53/3 = (1.65)^1/6
= 1.0875
or 1/2 unit growth of factor f = 1.0875
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The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H . A wall of uniform height that is 16 feet long is constructed using 280 bricks. What is the height, in feet, of the wall?
The height of the wall in feet is 2.5 feet.
According to the question,
We have the following information:
The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H .
A wall of uniform height that is 16 feet long is constructed using 280 bricks.
So, we have:
B = 280 and H = 16
Putting these values in the given expression:
B = 7LH
280 = 7*L*16
L = 280/(7*16)
L = 280/112
L = 2.5 feet
Hence, the height of the wall in feet is 2.5 feet.
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Can anyone help me with this?
Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x2 +rx+1)
is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
All real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero are given as r = -1
A real number is a quantity of a continuous number that can express a distance along a line in mathematics.
Hence the workings for the above result are indicated as follows:
Expanding the brackets, we see that we want the following three inequalities to be true.
a ≥ 0 (constant term) (1)
ar + 1 ≥ 0 (coefficient of x) (2)
a + r ≥ 0 (coefficient of x²) (3)
If r ≥ 0, then any a ≥ 0 meets the requirement of (1), (2), and (3).
It remains to address r < 0. In this case, note that (3) immediately suggests (1)
Hence, we only need to look at (2) and (3). Given that r < 0, inequalities (2) and (3) are equivalent to the following.
a ≤ − 1/r (4)
a ≥ − r (5)
Therefore, we seek all values of r < 0 such that there is exactly one real number satisfying the expression −r ≤ a ≤ −1/r (6)
Thus −r = −1/r ,
This implies r = ±1.
Given that r < 0 we have r = −1.
This implies that the only corresponding value of a is a = 1.
It only remains to follow that (x + 1)(x² − x + 1) = x³ + 1, which has no negative coefficients.
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Full Question:
Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
WILL GIVE BRAINLY Given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
[tex]\begin{cases} f(x)=3x-1\\\\ (f\circ g)(x) = x^2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\circ g)(x)\implies f( ~~ g(x) ~~ )~~ = ~~3( ~~ g(x) ~~ ) - 1\implies \stackrel{(f\circ g)(x)}{x^2}~~ = ~~3g(x)-1 \\\\\\ x^2+1=3g(x)\implies \cfrac{x^2+1}{3}=g(x)[/tex]
Pleaseee help will give brainliest to best and most detailed answer!
f(x) = x3 + 5x2 –32x – 7 is divided by x – 4
I really need help on this, and please show me every step!
Answer:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
[tex]\textsf{Dividend: \quad $x^3+5x^2-32x-7$}[/tex]
[tex]\textsf{Divisor: \quad $x-4$}[/tex]
[tex]\large \begin{array}{r}x^2+9x+4\phantom{)}\\x-4{\overline{\smash{\big)}\,x^3+5x^2-32x-7\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-4x^2)\phantom{-b))))))..)}}\\9x^2-32x-7\phantom{)}\\-~\phantom{(}\underline{(9x^2-36x)\phantom{)))..}}\\4x-7\phantom{)}\\-~\phantom{()}\underline{(4x-16)\phantom{}}\\9\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the divisor is divided.
Quotient: The result of the division.
Remainder: The part left over.
If line m is parallel to line n then determine the value of x.
If line m is parallel to line n then determine the value of x= 65°
2x+50° = 180°
2x = 180° - 50°
2x = 130°
x = 130°÷2
x = 65°
What are parallel to line?Parallel lines are lines that do not cross or meet at any point in the plane. They are always parallel and equidistant from each other. Parallel lines are non-intersecting lines. We can also say that parallel lines meet at infinity.
Properties of Parallel Lines
They are always straight equidistant from each other. These are coplanar lines. They never cross, no matter how much you try to stretch them in any direction. If there is a transversal that intersects two parallel nets at two different points, it forms angles at each point.To learn more about parallel to line, refer;
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The value of x is 25. It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.
What is parallel?Parallel lines are coplanar straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.
Parallels, paralleling, and paralleled are all word forms. a countable noun A parallel is something that is similar to something else but exists or occurs in a different place or at a different time.
Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees).
Two different interior angles.
- (2x - 10)°
- (65 - x)°
Because lines m and n are parallel and because of the alternate angles theorem.
We can see that.
2x - 10 = 65 - x
2x + x = 65 + 10
3x = 75
x = 75/3
x = 25
Hence, the value of x is 25.
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f(x) = 4x³ + 6x² – 3x − 4
g(x) = 4x - 3
Find (f - g)(x).
Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of variables, coefficients and constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.
Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4
and the value of g(x) is equal to 4x-3.
Subtracting g(x) from f(x) we get,
(f-g)(x)= 4x³+6x²-3x-4-4x+3
4x³+6x²-7x-1
Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.
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Solve for x: -4x - 4 = -4(x + 2)
Oo
O-4
O All real numbers
O No solution
Please answer this with an explanation:
Answer:
-2
Step-by-step explanation:
PT = TQ
3x + 4 = 5x - 8
-3x -3x
4 = 2x - 8
-8 -8
-4 = 2x
÷2 ÷2
x= -2
sooo
3 times -2 +4 = -2
v/8 - 3.1 = -15.9 solve for v
[tex]\frac{v}{8} -3.1=-15.9[/tex]
Simplify equation:
[tex]\frac{1}{8}v+-3.1=-15.9[/tex]
[tex]\frac{1}{8} v-3.1=-15.9[/tex]
Add 3.1 to both sides:
[tex]\frac{1}{8} v-3.1+3.1=-15.9+3.1\\[/tex]
[tex]\frac{1}{8} v=-12.8[/tex]
Multiply both sides by 8:
[tex]8\times(\frac{1}{8} v)=(8)\times(-12.8)\\-102.4[/tex]
[tex]\fbox{v=-102.4}[/tex]
A Construction worker needs to pour a rectangular slab 29 feet long 16 feet wide and 6 inches thick how many cubic yards of concrete does the worker need
We have a rectangular slab.
The volume of concrete is equal to the volume of this rectangular prism.
The volume of this prism is equal to the product of its length, width and thickness.
Then, we can write:
[tex]\begin{gathered} V=L\cdot W\cdot t \\ V=29ft\cdot16ft\cdot6in \\ V=29ft\cdot16ft\cdot(6in\cdot\frac{1ft}{12in}) \\ V=29\cdot16\cdot\frac{6}{12}ft^3 \\ V=232ft^3 \end{gathered}[/tex]We convert the thickness from inches to feet by multiplying it by a unit ratio 1 ft / 12 inches, which has a value of 1, as 1 ft = 12 inches, but let us change the units from inches to feet.
When we have all the measures in feet we can have the volume in cubic feet.
Answer: 232 cubic feet.
Translate "the sum of m and 2.33 multiplied by s is 77.77" into an algebraic equation.
Although part of your question is missing, you might be referring to this complete question "Translate the sum of m and 2.33 multiplied by s is 77.77 into an algebraic equation. Do not solve the equation."
Translated equation is m + 2.33s = 77.77
An algebraic equation is the equality of two expressions formulated by applying a set of variables such as addition, subtraction, multiplication, division, raise to power, etc. The phrase " the sum of a and b" into an algebraic expression is determined as a+b. It deals with symbols and these symbols deal with each other through variants.
Hence, the equation translated is a linear equation of algebraic equations. m+ 2.33s = 77.77
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Question 1 1 pts If g and h are both positive numbers, which statement is true about the x-intercepts of the function f(x) = (x - g)(x - h). the function has no x-intercepts both x-intercepts are negative one x-intercept is negative and one x-intercept is positive both x-intercepts are positive
for the function
f(x) = (x -g)(x - h)
To get the x-intercept, we can equate the function to zero
f(x) = (x -g)(x - h) = 0
so (x - g) = 0
which gives x = g
And (x - h) = 0
which gives x = h
Since we have been told that g and h are positive, then it follows that both intercepts are positive
for a between-subjects experiment, any factor that increases the variance within treatments also increases the likelihood of finding a significant difference between treatments.
The answer is FALSE. The likelihood of discovering a substantial difference between treatments does not increase with any factor that makes treatments more variable.
In experiments, you create situations where several treatments (such a are used in order to investigate the impact of an independent variation.
Every participant in a between-subjects or between-groups design only experiences one condition, and group differences between participants in various conditions are compared. In contrast, no participant in a within-subjects design is exposed to every condition.
As a result, the likelihood of discovering a substantial difference between treatments is not increased by factors that enhance variation within treatments.
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Sophie opened a picture of a tree on her cell phone screen and zoomed in 2.5 times. The new scale of the photograph became 1:168. What would be the scale if Sophie zoomed the image in 4 times?
Moores law predicts that the number of transistors that can be fit on a microchip will increase 40% every year. If microchips from a given year could hold about 922,200 transistors, how many transistors could fit on a microchip 19 years later?
If necessary, round your answer to the nearest whole number.
[tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.
Moore's law predicts that the number of transistors that can be fit on a microchip will increase 40% every year.
So the expected increment every year [tex]40\%[/tex].
Microchips from a given year could hold about [tex]922,200[/tex] transistors.
We have to find ow many transistors could fit on a microchip [tex]19[/tex] years later.
From the question total years are [tex]19[/tex].
Since the number of transistors is increased every year so number of transistors of previous year added. So we can see that the number of transistors that can be fit on a microchip is increased compound. We can find the total number of transistors by multiplying number of transistors with the rate assembled by one. So we can use the formula
So the number of transistors could fit on a microchip 19 years later.
Number of transistor = Microchips from a given year could hold about transistors(1 + increment rate)^total years
Number of transistor [tex]=922,200(1+\frac{40}{100})^{19}[/tex]
Number of transistor [tex]=922,200(1+\frac{2}{5})^{19}[/tex]
Number of transistor [tex]=922,200(\frac{5+2}{5})^{19}[/tex]
Number of transistor [tex]=922,200(\frac{7}{5})^{19}[/tex]
After evaluating the expression using the calculator we get
Number of transistor [tex]=551134751.094269[/tex]
Number of transistor [tex]=5.51134751094269\times10^8[/tex]
Hence, [tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.
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Halp me with this 1 question Brainliest to correct answer
Answer:
A is correct.
[tex]g = \frac{p}{6} - 15[/tex]
Step-by-step explanation:
[tex]p = 6g + 90[/tex]
[tex]6g = p - 90[/tex]
[tex]g = \frac{p}{6} - 15[/tex]
So A is correct.
Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
Leah can run 320 yards in 2 minutes at the same rate as she can run 720 yards in 4.5 minutes. The correct option is B. 320.
To find out how many yards Leah can run in 2 minutes at the same rate, we can use the concept of proportionality.
Let's set up a proportion based on the information given:
720 yards / 4.5 minutes = x yards / 2 minutes
To find the value of x, we can cross-multiply:
4.5 minutes × x yards = 720 yards × 2 minutes
Now, divide both sides by 4.5 to solve for x:
x yards = (720 yards × 2 minutes) / 4.5 minutes
x yards = 320 yards
So, Leah can run 320 yards in 2 minutes at the same rate.
The correct answer is B. 320.
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The point (-2, K) lies on the circle x^2 +y^2= 20. Find the values of k. Show all the steps
I will plug in the POINTS including k in the equation each point in its place either x or y.
[tex]( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4[/tex]
ATTACHED IS THE SOLUTION
AB=AD and BC=DC What is y equal to? Please show your work of how you got the answer.
The measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.
What is quadrilateral?It is defined as a four-sided polygon in geometry having four edges and four corners. The kite is quadrilateral, having two pairs of congruent sides and it has one pair of opposite congruent angles.
The kite is given in the picture.
AB = AD
BC = DC
∠DBC + ∠CBD + ∠C = 180
From the property of kite: ∠DBC = ∠CBD
y + y + 82 = 180
y = 98/2
y = 49 degrees
Thus, the measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.
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Johnny drew a scale drawing of an apartment. The scale he used was 8 inches : 3 feet. In the drawing, the broom closet is 16 inches long. What is the length of the actual closet?
The actual closet has a length of 6 feet
How to determine the length of the actual closet?The scale of the drawing is given as
Scale = 8 inches : 3 feet.
Also, we have the length of the closet to be
Length = 16 inches
So, we have
16 inches : Actual length = 8 inches : 3 feet.
Multiply the ratio by 2
So, we have
16 inches : Actual length = 16 inches : 6 feet.
By comparison, we have
Actual length = 6 feet
Hence, the length of the actual closet is 6 feet
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What is the inverse of function f?
f(x)=10/9x+11
Lance the alien is 5 feet tall. His shadow is 8 feet long. At the same time of day, a tre shadow is 24 feet long. What is the height of the tree?
Answer:
15 ft
Step-by-step explanation:
5:8
?:24
8x3=24 SO 5x3=15
If the water level rises 12 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change of the given relation is 1.7142 the value of y is 36 centimeters.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given question,
The water level rises 12 centimeters every 7 minutes.
0 minutes → 0 cm
7 minutes → 12 cm
14 minutes → 24 cm
21 minutes → 36 cm.
Since, (21,y) best match with the above condition.
So, 21 minutes is the time taken while 36 cm is the level of water.
Slope or rate of change = 12/7 cm/minutes.
And, 36/21 = 12/7 (proved)
Hence "The rate of change of the given relation is 1.7142 the value of y is 36 centimeters".
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Handmade socks, knitted using pure cashmere wool, are very expensive to buy. Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 . She pays her sister £8 to knit each pair of socks. 135g of cashmere wool is used to knit each pair of socks. Rowena sells 40 pairs of cashmere socks at £18.95 per pair. What is her percentage profit? Give your answer correct to 2 significant figures.
The percentage profit for the so is that were made is 40.32%.
How to calculate the profit?From the information, Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 and she pays her sister £8 to knit each pair of socks. The cost will be:
= (£1.42 × (20 + 135) + (40 × £8)
= £220.1 + £320
= £540.1
The selling price will be:
= £18.95 × 40
= £758
Therefore, the percentage profit will be:
= Profit / Cost price × 100
= (758 - 540.1) / 540.1 × 100
= 217.9 / 540.1 × 100
= 40.32%
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1. The number of miles a car can travel on a gallon of gasoline is related to its fuel
efficiency. Fuel efficiency depends on many factors including the speed of the car.
Driving at very slow or very fast speeds uses more gas than driving at a moderate
speed, which means fuel efficiency can often be modeled by a quadratic function.
For a certain model of car the fuel efficiency is maximized at 32 miles per gallon
with a speed of 55 mph. At 65 mph the car can get 31 miles per gallon.
The quadratic equation that models the fuel efficiency of the car is given by:
y = -0.01(x - 55)² + 32.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the parameters of the equation are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficientFor a certain model of car the fuel efficiency is maximized at 32 miles per gallon with a speed of 55 mph, hence the vertex is given by:
(h,k) = (55,32).
Hence the rule is:
y = a(x - 55)² + 32
When x = 65, y = 31, hence we can find the leading coefficient a as follows:
31 = a(65 - 55)² + 32
100a = -1
a = -0.01.
Hence the equation is given by:
y = -0.01(x - 55)² + 32.
What is the missing information?The problem is incomplete, hence we suppose that it asks for the quadratic model of the car's fuel efficiency.
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Suppose a sample of 1762 floppy disk is drawn. Of these disks, 70 were defective. Using the data estimate the proportion of disks which are defective. Enter your answer as a fraction or decimal number rounded to three decimal places.
In order to find the proportion of disks that are defective, we can divide the number of defective disks by the total number of disks in the sample:
[tex]p=\frac{70}{1762}=\frac{35}{881}[/tex]Therefore the proportion is 35/881.
the following data were obtained for days required to reach 230 lb and backfat thickness of a sample of 10 pigs: pig no. days to 230 lb, days backfat thickness, in 1 164 1.0 2 180 1.1 3 158 1.2 4 160 1.4 5 198 1.2 6 172 1.3 7 186 1.1 8 178 1.3 9 178 1.4 10 186 1.0 calculate the covariance between days to 230 lb and backfat thickness.
The covariance value between two variables says, days to 230 lbs and backfat thickness, is 0.48..
The covariance value between any two variables is used to determine whether the variables are changing in the same direction. It relates the two variables if they are from different data sets.
Let X and Y be two data sets with different values. Then the covariance between X and Y is given by
Cov ( X,Y) = ∑ ( X ᵢ– u) ( Yⱼ-v ) /n
Where are Xᵢ's elements in the X data set
Yⱼ→ elements of the Y set
μ → mean of X data set
ν→ mean of Y set
n→ total number of observations
As we have given two sets of data, let days to 230 lbs and backfat thickness be sets X and Y, respectively.
Now, we shall calculate the mean value for X and Y sets.
Mean of X set = (164+158+180 + +160+198+172+186+178+178+186)/10= 176
The mean of Y set =
(1.0+ 1.1+ 1.2+ 1.4+1.2+1.3++1.1+1.3+1.4+1.0)/10 = 1.2
Xᵢ– μ - 12 -18 4 -16 22 -4 10 2 2 10
Yⱼ– ν -.2 - .1 0 .2 0 .1 -.1 .1 .2 -.2
(Xᵢ - μ)(Yⱼ- ν) 2.4 1.8 0 - 3.2. 0 0.4 1 4.4 -2
∑ (Xᵢ - μ ) ( Yⱼ - ν) = 4.8
put all the values of variables in above formula we get,. Cov( X, Y) = 4.8 / 10 = 0.48 ..
So, the Covariance between the days of 230lb and backfat thickness is 0.48 ..
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