Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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If [tex]$4^x = 3$[/tex], what is [tex]$4^{2x-2}?$[/tex]
[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]
Order these numbers from least to greatest.
1.4 comma space 1.04 comma space 16 over 10 comma space 1 1 half
Answer:
1.04, 1.4, 1.5 (one and a half), 10, 16
Answer:
1.04, 1.4, 1.5, 1.6
Step-by-step explanation:
1 1 half = 1.5
16 over 10 = 1.6
hope this helps!
Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
What is radioactive decay?
The release of energy in the form of ionizing radiation occurs during radioactive decay.
Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.
We know that decay behaves exponentially and follows this model
[tex]m(t) = m_{0} . e^{t/T} \\[/tex]
The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression
T = t1/2 /In2
If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:
τ ≈ 11.541 min
t = -τ .In m(t)/m₀
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
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A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.
Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
n(s)=4
n(e)=1
Probability of choosing a sock, replacing it, and then choosing another sock,
=1/4*1/4
=1/16
Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.
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Find the x- and y-intercepts of the graph of -3x + y = 6. State each answer as an
integer or an improper fraction in simplest form.
Answer:
X-intercept : (-2,0)
Y-intercept : (0,6)
Answer:y-intercept (0,6),x-intercept (-2,0)
Step-by-step explanation:
To find the y-intercept set x=0
-3(0)+y=6
y=6
y-intercept (0,6)
To find the X-intercept set y=0
-3x+0=6
-3x=6
x=-2
x-intercept (-2,0)
when finding 6.1 divided by 0.1 how is the decimal point moved?
well, let's just divide them anyway and check it out.
hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets one "0".
That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61. We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.
please help meeeee!!
Answer:
f(2) = 9
Step-by-step explanation:
to evaluate f(2) substitute x = 2 into f(x) , that is
f(2) = 4(2) + 1 = 8 + 1 = 9
The diameter of a circle is 12 ft. Find its area to the nearest whole number.
Answer:
77.04
Step-by-step explanation:
A=3.14r^2
a=3.14(6)^2
A=3.14(36)
A=77.04
Answer: 113 ft^2
Step-by-step explanation:
A frog in a hemispherical pod (see fig. ) just floats without sinking into sea water with density 1. 35g / c * m ^ 3 if the pod has radius 6 cm and negligible mass, what is the mass of the frog?.
Thus, the mass of the frog is 48.6π grams when it is in a hemispherical pod which just floats without sinking into sea water.
What is meant by buoyancy?The force imposed on a body by a fluid, such as water or air, in which the body is submerged or immersed is known as buoyancy. This force is equivalent to the mass of the fluid that the body has displaced. In mathematics, buoyancy is defined as the sum of the fluid density, gravitational acceleration, and body volume. Archimedes' principle, which asserts that the buoyant force on an item is equal to the weight of the fluid it displaces, is a name for this connection. A key idea in the study of fluid mechanics, buoyancy has many uses, including the construction of boats, planes, and other floating structures.
How to solve?
V = 2/3 * π * r^3,
V = 2/3 * π * 6^3 = 2/3 * π * 216 = 36π.
F = V * d,
F = 36π * 1.35g/c * m^3 = 48.6π g.
F = m + W,
48.6π g = m + 0 g.
m = 48.6π g.
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[tex]10x+6y=0\\\-7x+2y=31[/tex]solve the system by using substitution or elimination
The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
Given that,
The system of equation are 10x+ 6y=0 and 7x+ 2y=31.
We must resolve the equation system.
We know that,
Take the system of equations.
10x+ 6y=0 ------>equation(1)
7x+ 2y=31 ------->equation(2)
Multiply 3 to the equation(2) and subtract with equation(1)
3×(7x+ 2y=31)
21x+ 6y=93
10x+ 6y=0
----------------- (subtract)
11x+0=93
11x=93 (divide)
x=93/11
Substitute x=93/11 in equation(1)
10(93/11)+6y=0
930/11+6y=0
6y=-930/11
y=-155/11
Therefore, The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
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how many ways are there to list the letters of the word mathematics so that no two consecutive letters are the same?
There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the ordering of the selection is irrelevant. You can choose the components of combos in any order.Total number of ways to organize the word "mathematics".
The same letter does not appear twice.
The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.
We will first organize H,E,I,C,S in five different ways;
−H−E−I−C−S−
No, we could arrange 2M, 2T, and 2A as we have 6 gaps;
= 6!/(2!.2!.2!)
So there are a total of;
= 5 x 6!/(2!.2!.2!)
= 22.5
= 22 ways
Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
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42 out of the 84 teachers in a school staff meeting were first-year teachers. What percentage of the teachers in the meeting were first-year teachers? Write your answer using a percent sign (%).
Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. If caroline keeps planting flowers at this rate, how long will it take her to plant all 70 flowers that she has?.
It will take 40 minutes for her to plant all 70 flowers that she has. By using proportions, we can find this value.
How to calculate a word problem using proportions?To calculate a word problem using proportions is as follows:
Consider the details of the word problem in proportions as
a : b = c : d
Here, a: b is the ratio of an event, and c : d is the ratio of another event.
Then, to find the value of c we need to reframe the above proportion into
c = ad/b
This is also said to be a cross formula in terms of word problems.
Calculation:It is given that, Caroline is planting flowers in her garden.
She plants her first 7 flowers in 4 minutes.
After 12 minutes, she planted 21 different flowers.
Then, she takes x minutes for planting 70 flowers.
(Since the rate of planting is the same)
So, we can write
70 : 21 = x : 12
⇒ x = (70× 12)/21 = 40 minutes
Therefore, Caroline takes 40 minutes for planting all 70 flowers.
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Which of the following relations between input numbers and output numbers is NOT a function?
send a picture so i know what its asking for
0.27 times 35 = 9.45 because i just said so bye
Answer:
Yes, you're right.
Step-by-step explanation:
Just by doing the math, 0.27 times 35 is 9.45.
Plugging it in a calculator also says it's 9.45.
If 65% of a number is 208 and 15% of the same number is 48, find 80% of that number.
The number is 320 and 80 % of the number is 256
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation A is
65% of a number is 208 and 15% of the same number is 48
So , 65% of n = 208 be equation (1)
15% of n = 48 be equation (2)
Now , on simplifying the equations , we get
( 15 / 100 ) x n = 48
15n/100 = 48
Multiply both sides by 100 . we get
15n = 4800
Divide by 15 on both sides of the equation , we get
n = 320
The number n can also be determined by
( 65% - 15% ) of n = 208 - 58
50 % of n = 160
So , 100 % on n = 160 x 2
n = 320
Therefore , the number n is 320
Now , the 80 % of the number n is A = 80/100 x 320
A = 320 x 0.8
A = 256
Therefore , the value of A is 256
Hence , The number is 320 and 80 % of the number is 256
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if 14 meter of ribbion cost 19$ how much will 21 meters cost
Answer: 21 meters cost $28.5
Step-by-step explanation:
divide 19 by 14 and multiply by 21
21 meters cost $28.5
write an equation of the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9
An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Here, slope of a line y=-1/5x-9 is m=-1/5.
The slope of a line perpendicular to given line is m1=-1/m2
So, slope =5
Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get
10=5(7)+c
⇒c=-25
Substitute m=5 and c=-25 in y=mx+c, we get
y=5x-25
Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
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If x=6 what is 4x
??????????????
Answer:
24
Step-by-step explanation:
6*4=24
Show your work, (I am stuck on this because I’m not smart lol)
Answer:
She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.
Step-by-step explanation:
(97+78+89+?) divided by 4 at\geq 90
It is divided by 4 because it is the average of 4 test scores.
To Solve: (97+78+89+?) divided by 4 at\geq 90
Multiply by 4 on both sides 97+78+89+? at\geq 360
Isolate variable: ? at\geq 96
The diameter of a circle is 6 cm. Find its area to the nearest whole number.
Answer:
28.26
Step-by-step explanation:
A=3.14r^2
A=3.14(3)^2
A=3.14(9)
A=28.26
Answer: 28 cm
Step-by-step explanation: Area=π·r² and diameter =2r
So if we need to find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.
Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26
Now round to the nearest whole number ⇒ 28.
The general form of an parabola is 4y2 + 40y + 3x + 103 = 0
What is the standard form of the parabola?
The standard form of the parabola is x = -4/3y² -40/3y -103/3
What is parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.
x = -4/3(y +5)² -1
Solve for x.
x = (4y² +40y +103)/(-3)
x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US
__
Taking our clues from the graph*, we can write the vertex form equation as ...
x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places
____
* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...
x = a(y -(-5))² +(-1) = a(y +5)² -1
The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.
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Kona work at a bakery. She baked 3308 muffin. She diplayed the muffin on tray that each hold 12 muffin. How many tray did Kona ue to diplay the muffin?
Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.
So, a tray will be needed to display all the cakes:
The total number of muffins is 3308.
Each tray can have 12 muffins.
The total trays needed are:
3308/12
275.66
Rounding off: 276
Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.
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What is an equation of the line that passes through the point (5, -8) and is
perpendicular to the line 5x - 4y = 16?
The equation of the line which is perpendicular to 5x - 4y = 16 is [tex]y = -\frac{4}{5}x -4[/tex].
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:
The intersection of perpendicular lines is always at a right angle.Two lines will always be parallel to one another if they are perpendicular to the same line.Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.
If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.
As a result, the following is the formula for the perpendicular's slope:
m1.m2 = -1
The equation of the line be "y = mx + c".
Equation of the line Perpendicular to the line is 5x - 4y = 16
Therefore, 4y = 5x - 16
⇒ [tex]y = \frac{5}{4}x -4[/tex]
Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].
Slope of the required ine be m .
Therefore, m * [tex]\frac{5}{4} = -1[/tex]
⇒ [tex]m = -\frac{4}{5}[/tex].
Equation of the line is ,
[tex]y = -\frac{4}{5}x + c[/tex]
The line passes through (5,-8)
Therefore,
[tex]-8 = \frac{-4}{5}*5 + c[/tex]
⇒ c = -4
The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].
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What is the solution of the equation?:
-2(3x+1)-2x=-4(2x)-4
it doesn't have solution
Janet made 7 1/3 pounds of trail mix. If she puts 1 5/6 pounds into each bag, how many
bags can Janet fill?
X is a normally distributed random variable with mean 26 and standard deviation 1.
What is the probability that X is between 24 and 28?
Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.
Answer: give me brainliset
(
X
>
42
)
=
P
(
Z
>
−
1.1429
)
=
1
−
P
(
Z
<
1.1429
)
=
1
−
Φ
(
1.1429
)
=
1
−
0.8729
(from tables)
=
0.1271
Step-by-step explanation:
O
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and
each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a
system of equations that could be used to determine the number of games Nolan
played and the number of rides Nolan went on. Define the variables that you use to
write the system.
Answer: g + r = 17
2.5g + 3.5r = 52.5
Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:
g + r = 17
2.5g + 3.5r = 52.5
We can solve this system of equations using elimination, substitution, or graphing.
Find the equation of the line, in lope-intercept form, containing the point ( 5,2. 2) and (9,2. 6)
The equation of the line, in slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.
What is an example of a slope intercept form?Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.
What is the slope and y-intercept?The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b
Here, m = (y2-y1)/(x2-x1)
So, m = (2.6-2.5)/(9-5)
m= 1/40
m=0.025
Now finding b by using formula y=mx+b using x= 5 and y= 2.5
2.5=(0.025)(5)+b
2.5=(0.125)+b
b=2.375
so equation of line is y=0.025x+2.375 in slope-intercept form.
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what is the probability that an electron will tunnel through a 0.50 nm air gap from a metal to a stm probe if the work function is 4.0 ev?
The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5
The air gap from a metal to a STM = 0.50 nm
The work function = 4.0 eV
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
The value of η = h / [tex]\sqrt{2m(U_0-E)}[/tex]
Substitute the values in the equation
= [tex]\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }[/tex]
Do the arithmetic operation
= 0.0972 nm
The probability = exp (-1 / 0.972)
= 3.4 × 10^-5
Therefore, the probability is 3.4 × 10^-5
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