The double inequality describing the length of time (in minutes) that Liz spends on her phone each night is 45 ≤ f(x) ≤ 120.
What is double inequality?Double inequality is a mathematical expression that has two inequalities.
Double inequality is also known as a compound inequality. because there is more than one inequality in the expression
The form of double inequality is always written as: a ≤ f (x) ≤ b.
This double inequality gives the value of x as more than a and less than b.
The least number of minutes spent by Liz on her phone = 45 minutes
The maximum number of minutes spent by Liz on her phone = 120 minutes
Inequalities:Inequality 1: 45 ≤ f(x)
Inequality 2: f(x) ≤ 120
Thus, this double inequality 45 ≤ f(x) ≤ 120 shows Liz's time on the phone every night.
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I need this for today !!!
Answer:
1. reflection
2.translation
3.rotation
4.translation
5.translation
6.reflection
7.rotation
8.reflection
Hope this helps
have a good day
God bless you!
There are 40 students in class. 12 like pink best, 4 like yellow and the rest blue. What fraction of the class likes blue?
Solve the equation for y in terms of x
8x=1-3y
enclose numerator and denominators in parentheses
The value of y in the equation in term of x is y= (1-8x)/(3)
What are algebraic equations?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. For example, 8x = 1-3y is an algebraic equation with two variables x and y with coefficient 8 and 3 respectively and 1 is the constant.
The value of y can there be solved by firstly making 3y the subject of formula
3y= 1-8x
dividing both sides by 3
3y/3= (1-8x)/3
therefore y= (1-8x)/(3)
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The quotient of 8 and the cube of a number.
By using division, it is obtained that
The Quotient of 8 and cube of 2 is 1
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division.
Divisor x Quotient + Remainder = Dividend.
Let the number be 2
cube of 2 = [tex]2^3 = 8[/tex]
Quotient of 8 and 8 = [tex]\frac{8}{8}[/tex] = 1
The Quotient of 8 and cube of 2 is 1
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Please i need help urgently thanks
Answer:
Step-by-step explanation:
rate of change
[tex]=\frac{f(b)-f(a)}{b-a} \\=\frac{f(9)-f(1)}{9-1} \\=\frac{28-20}{8} \\=\frac{8}{8} \\=1[/tex]
Question
Find the rate if a principal of $1,100 earned $1,089 interest in 12
years.
Answer:
Step-by-step explanation:
Intrest = PRT\100
$1089. =. ($1100x12xR)\100
$1089. = 132R
Divide through by 132.
R. =. 8.25%
calculate the distance between two points a(-9,-10) and b(0,-10)
Answer:
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates
Step-by-step explanation:
HELP PLS!!
Determine if this table represents a linear function
Answer: im pretty sure the answer is c
Step-by-step explanation:
if the answer is not c im sorry but i hope this helps! Have a good day!
2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions
What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?
Work to Support Your Answer (Required for Credit!)
The equation of the parabola, in vertex form is
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]
6. MJ is creating a graph of the equation
2x + 4y = -8. Which of the following points will
lie on the line?
a. (2,4)
b. (-2,-1)
c. (2, 1)
d. (4,4)
Which parabola will have one real solution with the line y=x-5?
The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4
What is the standard form of the equation of a parabola?The standard form of the equation of a parabola is y = a·x² + b·x + c
The equation of the line is; y = x - 5
The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;
Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;
y = x² + x - 4 = x - 5x² + x - 4 - x + 5 = 0
x² + 1 = 0
x² = -1
x = ±√(-1) (Complex solution)
y = x² + 2·x - 1 = x - 5x² + x + 4 = 0
The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)
x² + 6·x + 9 = x - 5x² + 5·x + 14 = 0
The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)
x² + 7·x + 4 = x - 5x² + 6·x + 9 = 0
The discriminant, b² - 4·a·c is 6² - 4 × 1 × 9 = 0 One real solution;The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;
y = x² + 7·x + 4
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i need someone to help me with my math test 24 questions please
Answer:
Add the picturess!!!!!
Step-by-step explanation:
Find m<1, m<2 and m<3 86 degree 12 and 3
The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
How to determine the measure of each angle?The possible diagram that completes the question is added as an attachment
From the attached diagram, we have the following representation
<1 + <2 = 180 degrees --- by the theorem of supplementary angles
Also, we have the following angle measure
Given that
<1 = 86 degrees
Substitute the known values in the above equation
So, we have the following equation
86 + <2 = 180
Evaluate the like terms
<2 = 94
Also, we have
<3 = <1 --- by the theorem of vertical angles
Substitute the known values in the above equation
<3 = 86
This is so because <1 = 86 degrees
Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
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a musician buys a guitar for $46 and a guitar amplifier. the guitar amplifier costs $1.54 more than$1.26 times the cost of the guitar. how much does the amplifier?
Answer:
$26.33
Step-by-step explanation:
Solve for x
150µ=0.694(x+7.2K)*10^-9
[tex]x=2.16*10^{11}u-7.2k[/tex].
Side note: This answer could be more precise if made usage of more significant figures. For practicality reasons, in this solution we reduced the amount of significant figures to use.
Step-by-step explanation:1. Write the expression.[tex]150u=0.694(x+7.2K)*10^-9[/tex]
2. Solve the parenthesis using the distributive property of multiplication.[tex]150u=[(0.694*x)+(0.694*7.2K)]*10^-9\\\\150u=[0.694x+4.9968k]*10^-9\\ \\150u=10^-9*0.694x+10^-9*4.9968k[/tex]
3. Subtract "10^-9*0.694x" from both sides of the equation.[tex]150u-10^-9*0.694x=10^-9*0.694x-10^-9*0.694x+10^-9*4.9968k\\ \\150u-10^-9*0.694x=10^-9*4.9968k[/tex]
4. Subtract "150µ" from both sides of the equation.[tex]-150u+150u-10^-9*0.694x=10^-9*4.9968k-150u\\ \\-10^-9*0.694x=10^-9*4.9968k-150u[/tex]
5. Divide both sides by "-10^-9*0.694".
[tex]\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k-150u}{-10^-9*0.694} \\ \\\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k}{-10^-9*0.694}-\frac{150u}{-10^-9*0.694} \\ \\x=-7.2k-(-2.16*10^{11} u)\\ \\x=-7.2k+2.16*10^{11}u\\ \\x=2.16*10^{11}u-7.2k[/tex]
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Boxes of Valentine’s Day chocolate truffles come in a variety of sizes. The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches. If each truffle in this box has a volume of 2 cubic inches, how many truffles are included in the box?
The no. of truffles than can be included in the box is 135.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.
∴ The volume of the box is,
= (15×12×1.5) inches³.
= 270 inches³.
Given each truffle has a volume of 2 iches³.
∴ No. of truffles than can be included in the box is,
= (270/2).
= 135.
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Find all x ∈ R that are solutions to this equation:
0 = ( 1- X- X^2-...) (2- X- X^2-...)
The solution of the geometric equation is x = 1/2 or x = 1
What is an equation?An equation is a mathematical expression that shows the relationship between variables.
What is a geometic series?A geometric series is the sum of a geometric sequence.
How to find the solution to the equation?Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p
So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).
0 = (1 - [X + X²+...) (2 - [X + X²+...).
Substitute x + x² + ... = p. So,
0 = (1 - [X + X²+...) (2 - [X + X²+...).
0 = (1 - p)(2 - p).
So, (1 - p) = 0 or (2 - p) = 0
p = 1 or p = 2
Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.
What is the sum to infinity of a geometric series?The sum to infinity of the geometric series is given by
S = a/(1 - r) where
a = first term and r = common ratioFor the given series,
a = x and r = xSo, S = a/(1 - r)
= x/(1 - x)
Since S = p, we have that
x/(1 - x) = 1 or x/(1 - x) = 2
So, x = 1 - x or x = 2 - x
x + x = 1 or x + x = 2
2x = 1 or 2x = 2
x = 1/2 or x = 2/2
x = 1/2 or x = 1
So, the solution is x = 1/2 or x = 1
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Identities and properties of logarithms
[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]
Abigail is studying for the school spelling bee. She already knows 150 words from the vocabulary list. Each day, she learns 50 additional words from the vocabulary list.
Which equation can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days?
A. y = 50x + 150
B. y = 50(x + 150)
C. y = 50x - 150
D. y = 150x + 50
The equation that can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days is A. y = 50x + 150
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Abigail already knows 150 words from the vocabulary list and each day, she learns 50 additional words from the vocabulary list.
Let x be the number of days.
y = vocabulary list
The equation will be:
y = 150 + 50x
Therefore, the correct option is A.
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A 150-pound person uses 5.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at:
this speed to use at least 220 calories?
A person must walk for at least
(Round up to the nearest minute.)
minutes in order to use at least 220 calories.
The person must walk 2.61 miles to use 220 calories with speed of 4mph.
What is speed?
The pace at which an object's position changes in any direction is known as its speed. The distance traveled relative to the time it took to travel that distance is how fast something is moving. Due to its lack of magnitude and only having a direction, speed is a scalar quantity.
Here, At 4 mph 5.6 calories are used in = 1 minute
So, at 4 mph, 220 calories are used in,
=> 220/5.6
=> 39.28 minutes
Hence, a person must walk for 39.28 minutes to burn 220 calories.
To find the distance a person should walk, when the speed is 4 miles per hour.
In 60 minutes a person is walking = 4 miles
So, in 39.28 minutes a person will walk = 4/60*39.28
= 2.61 miles
Therefore The person must walk 2.61 miles to use atleast 220 calories.
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Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
a. The current ratio is 1.3125
b. The acid test is 1.09375.
c. The average day collection is 37 days.
d. The asset turnover is 1.28.
e. The profit margin on sales is 14.63%.
How to calculate the current ratio?a. The current ratio will be:
= Current asset / Current liability
= 21000 / 16000
= 1.3125
b. Acid test quick ratio will be:
= (Current asset - Inventory) / Current liability
= (21000 - 3500) / 16000
= 1.09375
c. Average day collection will be:
= Account receivable / (Net sales / 360)
= 4200 / (41000 / 36)
= 4200 / 114
= 37 days.
d. Asset turnover will be:
= Net sales / Total asset
= 41000 / 28000
= 1.28
e. Profit margin will be:
= Net income / Net sales
= 6000 / 41000
= 14.63%
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I need answer asap thank you
The measure of ∠QTS = 58°
Given; A triangle QPR
PQ = PR
this means that ∠ Q = ∠ R
and QR = QT this means ∠ R = ∠ T
And ST ║ QR
and QT is the transversal
From the above mentioned information we can conclude that
∠QTS = ∠TQR -------------- 1
Thus since ∠ Q = ∠ R
by using angle sum property of triangle we can conclude that
∠ Q + ∠ R = 116 [ exterior angle sum property ]
2 ∠ Q = 116
∠ Q = 58°
this means ∠ TQR = 58°
And from 1 we know that this angle is equal to angle QTS
Thus ∠QTS = ∠TQR = 58°
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A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze. How long does it take the water to fall and reach the flames?
The required time that would it takes to reach the flames is 2.78 sec.
Given that,
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze how long it takes the water to fall and reach the flames is to be determined.
Here,
According to the question,
The initial velocity of the water is u = 0, and s = 38
Speed gain by the water is due to the acceleration due to gravity g = 9.8.
The time for water to reach to the ground is given by the second equation of motion.
s = u²t + 1/2gt²
Substitute the values in the above equation,
38 = 1/2(9.8)t²
(9.8)t² = 76
t = √(76/9.8)
t = 2.78 sec.
Thus, the required time that would it takes to reach the flames is 2.78 sec.
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
please help?!
The angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
What is described as the trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship here between angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.The ramp is the hypotenuse of a right angle triangle formed by the doorway, the ground, and the ramp.
The ramp's elevation angle is the angle Ф it makes with the ground.
Apply the tan function;
Tan Ф = length of doorway/ distance along ramp of building
Tan Ф = 1/5
Ф = 11°
Thus, the angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
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Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.
How to determine the total possibilities?Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.
Hence,
Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)
Total possibilities = 26^4 × 10^5
Total possibilities = 456976×100000
Total possibilities = 45,697,600,000
Therefore we can assume that the total possibilities is : 45,697,600,000.
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Please help!
Find the amount of money( future value) in an account where 8,800 is deposited ( present value) at an interest rate 6.5% per year compounded continuously and the money is left in the account for 7 years.
The final amount is $ ?
Round your answer to 2 decimal places.
By using the formula for amount of money in a compound interest, it can be calculated that
Amount received after 7 years is $13675.08
What is a compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then
amount = [tex]p(1+\frac{r}{100})^n[/tex]
Difference between amount and principal gives the compound interest.
Principal = $8800
Rate = 6.5 %
Time = 7 years
Amount received = [tex]8800(1 + \frac{6.5}{100})^7[/tex]
$13675.08
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What is the equation of the line that passes through the point (8, 2) and has a slope of -3/4
The equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
In the given question we have to find the equation of line that passes through the point (8, 2) and has a slope of -3/4.
The given points are (8, 2).
The slope(m) = -3/4
The standard equation of slope intercept form is
y-y(1) = m(x-x(1))
From the question; x(1) = 8 and y(1) = 2.
Putting the value
y-2 = -3/4(x-8)
Add 2 on the both side, we get
y = -3/4(x-8)+2
Hence, the equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
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Suppose that f(x)= −4x^2+5.
(A) Find the slope of the line tangent to f(x) at x= 1.
(B) Find the instantaneous rate of change of f(x) at x= 1.
(C) Find the equation of the line tangent to f(x) at x= 1. y=
The slope of the line tangent to f(x) at x = 1 is -8
The instantaneous rate of change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
What is a tangent to a curve?The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.
so the slope of a line at that point is the slope of the curve at that point.
f(x) = -4[tex]x^{2}[/tex] + 5
To find the slope, we differentiate f(x) with respect to x
dy/dx = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)
= -8x + 0
dy/dx = -8x
The slope = -8x
at x = 1,
the slope becomes, -8(1) = -8
The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8
The slope of the line is -8
to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.
one of the coordinates x = 1, to find y, we substitute x into f(x)
f(x) = -4[tex](1)^{2}[/tex] + 5
f(x) = 1
so the point is (1, 1)
so equation of straight line
[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m
y - 1/x - 1 = -8
by cross multiplying
y - 1 = -8(x - 1)
y - 1 = -8x +8
y = -8x + 9
In conclusion,
The slope o the line tangent to f(x) at x = 1 is -8
The instantaneous rate off change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
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a coin is tossed 5 times. find the probability that none are tails
Answer:
[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]
Step-by-step explanation:
The probability of "not a tail" is 1/2. The five tosses are independent, so the probability of "not a tail" 5 times in succession is
[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]
As part of a major renovation at the beginning of the year, Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash. The original cost of the shelves was $7,000 and they had been depreciated on a straight-line basis over an estimated useful life of 15 years with an estimated residual value of $1,300.
Record the sale of the shelving units.
Cash 2300
Accumulated Depreciation 4940
Gain one of fixtures 240
Store fixtures 7000
From the question, we have
Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.
Accumulated Depreciation = (7000-1300)/15*13
=4940
Gain one of fixtures = 240
Store fixtures = 7000
Multiplication:
Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.
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