Both statements can be included in the exact numbers category.
Maple provides two kinds of numbers: exact and inexact. If you do arithmetic with exact numbers (and they aren't too large) the answer that you get back is exactly right. If you do arithmetic with inexact numbers (and they aren't too large or too small) the answer may have a small amount of roundoff error. Although we'll treat this distinction at length in future lessons, it is convenient to take a preliminary look right now.
consider the four bicycles in the family have been ridden for a total of 250 mi.
The above statement can be categorized into exact numbers as 4 and 250 are countable.
Now, consider a child fell and had a 4-cm laceration that required 12 stitches.
The above statement can be categorized into exact as the numbers 4 and 12 are countable.
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rolling a fair dice, what is the probability that before you getting an odd number, you have got all the even numbers
The probability is [tex]\frac{1}{2}[/tex].
To solve this problem we need to recognize the idea of probability.
To calculate the probability we need to divide the desired final results with the aid of the overall number of consequences.
here, it is asked to locate the chance of having all even numbers earlier than getting an strange variety.
We know that the whole number of results when we roll a dice is 6.
We realize there are three odds and three even in the cube. So, the required
probability of getting even = [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex]
The required probability is equals to [tex]\frac{1}{2}[/tex].
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3. Exponential Function:
Bacteria grows on food by doubling every hour.
If the bacteria initially covers 10% of the food, it will
cover the entire food source in 3.3 hours.
Answer:
[tex]y=0.1(2)^x[/tex]
where x is time in hours, and y is the number of bacteria in percent in decimal form.
Step-by-step explanation:
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.Define the variables:
Let x = time (in hours)Let y = number of bacteria (in percent in decimal form)If the bacteria grows on food by doubling every hour then the growth rate b = 2.
If the bacteria initially covers 10% of the food then y = 10% when x = 0.
Therefore, a = 10% = 0.1.
Therefore, the equation is:
[tex]y=0.1(2)^x[/tex]
Substitute x = 3.3 into the found equation:
[tex]\begin{aligned}x=3.3 \implies y & =0.1(2)^{3.3}\\& =0.9849155307...\\& =1.0\:\sf (nearest\:tenth)\end{aligned}[/tex]
As 1.0 = 100%, this justifies the claim.
[tex]\begin{array}{|c|c|c|}\cline{1-3} x & y & y \\\cline{1-3} 0 & 10\% & 0.1\\\cline{1-3} 1 & 20\% & 0.2\\\cline{1-3} 2 & 40\% & 0.4\\\cline{1-3} 3 & 80\%\ & 0.8\\\cline{1-3} 4 & 160\% & 1.6\\\cline{1-3}\end{array}[/tex]
•The total surface Areas of a cone of base radius r and perpendicular height h, his given by s=πr ² +πr√(r²+h²). iF r and h are each increasing at the rate of 0.5m/s and 0.2m/s respectively, find the rate at which s is increasing at the instant when r=3m and h =4m
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
What is the rate of change of the surface area of a cone?
In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:
ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]
If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:
ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]
ds / dt ≈ 18.473 m² /s
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
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Help please. I cant figure this one out.
Answer:
x =52
Step-by-step explanation:
The angles shown are same side interior angles, and when the lines are parallel, same side interior angles add to 180 degrees
< 1 + <2 = 180
x+23 + x+53 = 180
Combine like terms
2x+ 76 = 180
Subtract 76 from each side
2x+76-76 = 180 -76
2x = 104
Divide by 2
2x/2 = 104/2
x =52
Answer:
x = 52
Step-by-step explanation:
Angle 1 and angle 2 are on the same side, and on the inside of the interior. This means that when added together they = 180
We can set up an equation
x+23+x+53 = 180
Simplify: 2x + 76 = 180
Subtract 76 from both sides
2x = 104
Now divide by 2
x = 52
The teacher is handing out note cards to her students. She gave 48 note cards to the first student, 54 note cards to the second student, 60 note cards to the third student, 66 note cards to the fourth student, and 72 note cards to the fifth student. If this pattern continues, how many note cards will the teacher give to the sixth student?
Answer:
She will give 78 students to the sixth student.
Step-by-step explanation:
The pattern is adding 6 each time.
How do you do these problems and solve
These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.
1) r + 12 = 36
r = 36 -12
r = 24
2) 22+ m = 24
m = 24 - 22
m = 2
3) -27 = n - 29
n = 2
4) -5 = b -26
b = 21
5) -17 = x -23
x = 5
6) v - 26 = - 4
v = 22
7) x+12 = 38
x = 26
8) 8= -12+ a
a = 20
9) b- 21 = 4
b = 25
10) 2 = x - 23
x = 25
11) x + 25 = 46
x = 21
12) -18 = x - 22
x = - 4
These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.
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Bella has a bag that contains pineapple chews, lemon chews, and watermelon chews. She performs an experiment. Bella randomly removes a chew from the bag, records the result, and returns the chew to the bag. Bella performs the experiment 58 times. The results are shown below:
A pineapple chew was selected 53 times.
A lemon chew was selected 2 times.
A watermelon chew was selected 3 times.
the probability is pinapple 53/58
lemon 2/58
watermelon 3/58
The given values are
A pineapple chew was selected 53 Times
A lemon chew was selected 2 times
A watermelon chew was selected 3 times
The probability that you Bella remove from the bag is pineapple chew.
Probability is which we can't predict actual it is usually about the prediction
As we know
Probability - expected outcome/total outcome
The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58
The probability of Bella pick chew of lemon -2/58
The probability of Bella pick watermelon is - 3/58
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Use the point slope form to write the equation of a line that passes through the point (1,-17) with slope 4
The equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
What is the slope intercept form of a line ?
The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
The equation of a line which is passing through point (1 , -17) with slope m = 4 can be found by using the slope intercept form which is given by :
y = mx + c
Here ; m is the slope and c is the y - intercept of the line.
So ;
The point given is (x , y) = (1, -17) and slope m = 4. Let's use these values to find out the equation of the line. But before that let's find out the value of y-intercept (c).
-17 = (4 × 1) + c
c = - 17 - 4
c = -21
Hence , the equation of line passing through (1, -17) will be :
y = 4 × x + (-21)
or
y = 4x - 21
Therefore , the equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
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HELPPPPPPPPPPPPPPPPPPPPPPPPP! whats 1+1
What clockwise angle rotations, if any, between 0 degrees and 360 degrees make the figure rotate onto themselves?
A clockwise 360 degrees angle rotation will make the figure rotate onto themselves.
Any angle rotations other than a 0 degree or a 360 degree will change the figure and so does not rotate onto themselves.
To rotate onto themselves, which means the figure should not be changed after the rotation transformation, we have to rotate it 360 degrees.
We are asked for a clockwise angle rotation, so the require angle rotation is of 360 degrees.
0 degree angle rotation will not make a rotation. So we will go with a 360 degree rotation. Any figure after a 'full circle' clockwise rotation will goes onto themselves.
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Find the value of x and y.
Question 2(Multiple Choice Worth 5 points)
(Irrational Numbers LC)
Describe in words where √60-11 would be plotted on a number line.
O Between -3 and -4, but closer to -3
O Between -3 and -4, but closer to -4
O Between 7 and 8, but closer to 8
O Between 7 and 8, but closer to 7
The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.Given: √60 - 11
The value of √60 - 11 is given as: √60 - 11 = 7.2 (approx.) - 11 = -3.2
Thus, as seen from the calculation of the value of the given number, √60 - 11 will lie between -3 and -4, but closer to -3 as -3.2 is closer to -3 than to -4.
Hence, The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
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Avani is making smoothies. Each smoothie uses cup of yogurt. How many cups of
yogurt does she need to make 17 smoothies? Express your answer in simplest form.
5
16
Answer type: Mixed number
Submit Answer
Avani needs 6 cups of yogurt.
To find the amount of yogurt required for specified number of smoothies, simple multiplication operation needs to be performed.
For 1 smoothie, the required amount of yogurt = 3/8 cups
So, the required amount of yogurt for 17 smoothies = (3/8) × 17
Performing multiplication and division to find the amount of yogurt required
Amount of yogurt required = 51/8 cups
Converting the fraction into fraction into decimal -
Amount of yogurt required = 6.375 cups
Rounding off the number of cups to convert it in simplest form -
Number of cups of yogurt required = 6 cups
Hence, the amount of yogurt for making 17 smoothies is 6 cups.
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The complete question is -
Avani is making smoothies. Each smoothie uses 3/8 cups of yogurt. How many cups of yogurt does she need to make 17 smoothies? Express your answer in simplest form.
use the foil method to evaluate the expression: left parenthesis 2 plus square root of 3 right parenthesis left parenthesis square root of 3 minus 7 right parenthesis
-5√3 - 11 is value of expression.
What do math Surds mean?
An expression with a square root, cube root, or other root symbol is called a surd. Since the decimals of irrational numbers do not finish or recur, they cannot be expressed properly in decimal form. Surds are used to write irrational numbers precisely.( 2 + √3) (√3 - 7)
First = 2√3
outer = 2(-7) = -14
inner = √3 √3 = 3
last = √3 (- 7)
= 2√3 + (- 14) + 3 + ( - 7√3)
= -5√3 - 11
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martin s cat weighs 12.37 pounds. what is this weighs written as a mixed number
Answer:
your mixed fraction would be 12 37/100
Step-by-step explanation:
The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.
You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.
HELP- pleaseeee I’m beggginnngg
The ending number is related to the starting number by n + 9.
To start with this magic number puzzle, let us take a positive number and a negative number. After that we have to perform some simple mathematical operations,
Taking positive number as 10 and negative number as -8.
Now, performing the mathematical operations as described in the next steps.
First starting with positive number which is 10.
Step-1. Add 10
So, 10+10 = 20
Step-2. Multiply by 2
So, 20×2 = 40
Step-3. Subtract 2,
So, 40 - 2 = 38
Step-4. Divide by 2,
So, 38/2= 19
Number chosen in the starting was 10 and at the end it became 19. The number 9 got added to 10.
Now, performing the steps on our negative number which is -8,
Step-1. Add 10
So, 10-8=2
Step-2. Multiply by 2
So, 2×2 = 4
Step-3. Subtract 2
So, 4-2 = 2
Step-4. Divide by 2
So, 2/2 = 1.
Number chosen in the starting was -8 and after performing the steps it became 1.
Now, for any number 'n',
Step-1. Adding 10
So, n+10
Step-2. Multiply by 2
So, 2(n-10) = 2n+20
Step-3. Subtract 2
So, 2n+20-2 = 2n+18
Step-4. Divide by 2.
So, (2n+18)/2 = n+9
The number taken in the starting was n and now it became n+9.
So the ending number becomes 9 times more in the end then the starting number.
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Geometry question!!
Please help i’ll give points!
Answer:
63°
Step-by-step explanation:
[tex]m\angle OZQ=m\angle OZP+m\angle PZQ \\ \\ 125^{\circ}=62^{\circ}+m\angle PZQ \\ \\ m\angle PZQ=63^{\circ}[/tex]
Area of Circles Area of Circles Area of Circles
The area of the circle with the radius is 192 square feet
How to calculate the area of the circle?The figure represents the given parameter
On the figure, we have the radius (r) to be
r = 8 ft
The area of a circle is calculated as
A = πr^2
Where π is given as
π = 3
So, we have
A = 3 * 8^2
Evaluate the exponent
A = 3 * 64
Evaluate the product
A = 192
Hence, the area of the circle with the radius is 192 square feet
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the area of the circle is 201.06
1. 3x-2x² = 7
2. 5-2x² = 6x
3. (x+3)(x + 4) = 0
4. (2x+7)(x-1)=0
5. 2x(x-3) = 15
Answer:
No 3
2x+4x+3x+12=0
9x+12=0
9x=0_12
9x=-12
divide by 9
x=1.333
25. ALGEBRA Angle E and Angle F are supplementary. The measure of angle E is 54 more than the
measure of Angle F. Find the measures of each angle.
The measure of each angle is , ∠E = 117° and ∠F = 63°
What is an angle ?In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.
What are supplementary angles?Angles which are on the same line are supplementary angles. The sum of supplementary angles are always equals to 180 degree.
Some common terms related to angles :
Endpoint : It is the point where the rays met to each other.Ray : Ray is the side or line segment on which angle is formed.Curve : It is a line but not straight i.e. a bended line.Tangent : A line which touches the surface of curve.In the given question:
Let measure of ∠E = x
and, measure of ∠F = y
as ∠E and ∠F are supplementary angles therefore their sum is 180
i.e. m∠E + m∠F = 180
=> x + y =180
also, m∠E is 54 more than m∠F
=> y+54 + y = 180
=> 2y + 54 = 180
=> y = 180-54 / 2 = 63
and , x = y + 54 = 63 + 54 = 117
Hence, ∠E = 117 degree and ∠F = 63 degree
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PLEASE HELP!!!
Solve.
-2x+3y-z=-2
3x + y = 4
-2y+2z=4
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Step-by-step explanation:
the second equation gives us right away
y = 4 - 3x
we can use that now in the 3rd equation :
-2(4 - 3x) + 2z = 4
-8 + 6x + 2z = 4
6x + 2z = 12
3x + z = 6
z = 6 - 3x
now we use both in the 1st equation :
-2x + 3(4 - 3x) - (6 - 3x) = -2
-2x + 12 - 9x - 6 + 3x = -2
-8x + 6 = -2
-8x = -8
x = 1
y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1
z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3
so,
(1, 1, 3)
suppose that 10% of people are left handed. if you pick two people at random, what is the probability that they are both left handed? express your answer as a decimal rounded to three decimal places.
The probability that they are both left-handed is 0.01
Probability is the number of ways of achieving success.
the total number of possible outcomes.
Probability takes values between 0 (no chance) and 1 (certain) inclusive.
Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .
Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .
Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)
For both, the persons selected at random are left-handed
10 % out of 100 % are left-handed.
Hence the probability that the person is left-handed
P(L) = 10 /100 = 1 / 10 = 0.1
where P(L) is the probability that the person is left-handed.
Therefore both the persons selected are left-handed
= 0.1 * 0.1
= (0.1)^2
= 0.01
Hence the probability that they are both left-handed is 0.01.
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circles with centers $(2,1)$ and $(8,9)$ have radii $1$ and $9,$ respectively. the equation of a common external tangent to the circles can be written in the form $y
The value of b in the equation of common external tangent to both the given circles is 3.75.
A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.The equation of a circle with a centre at (2,1) and a radius of 1 is : (x - 2)² + (y - 1)² - 1² = 0.The equation of a circle with a center at (8,9) and a radius of 9 is : (x - 8)² + (y - 9)² - 9² = 0.The equation of the common external tangent is :y = mx + b, where m < 0If m < 0, then the circles touch each other.We will get the equation of the common external tangent by equating the equations of both the circles.(x - 2)² + (y - 1)² - 1² = (x - 8)² + (y - 9)² - 9²(y - 1)² - (y - 9)² = (x - 8)² - (x - 2)² + 1² - 9²(2y -10)(8) = (2x - 10)(-6) + 1 - 8116y - 80 = -12x + 60 - 8016y = -12x + 60y = (-3/4)x + (15/4)y = -0.75x + 3.75y = mx + bOn comparison, we get b = 3.75.To learn more about tangent, visit :
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the density of a certain material is such that it weighs 3 grams per fluid ounce of volume. express this density in ounces per liter.
The density of the material in ounce per liter is 0.1059 ounce per liter.
How to express the density in ounce per liter?The ounce per liter conversion selector on this page selects the density measurement unit to convert to starting from ounces per liter (oz/L).
Given that,
Density = 3 grams per fluid ounce
Convert grams to ounce.
1 grams = 0.0353 ounce
Then
Density = 3 * 0.0353 ounce per fluid grams
= 0.1059 ounce per fluid grams
Convert fluid gram to liter
Density = 0.1059 ounce per 1000 liter
= 0.0001059 ounce per liter
Hence, the density in ounce per liter is 0.0001059 ounce per liter.
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Choose one value that is in the domain of both y(x) = x² and y² = x and that is greater than
0. Substitute that value into y(x) = x² and y² = x and then simplify. Explain how your answers
help to show that the graph on the left represents a function while the graph on the right
represents a relation. Show your work and use function notation where possible
I
We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.
Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for
y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)
[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)
A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.
Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.
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HI, I need help!! I'm so lost on how to solve this.
Answer:
3⁹
Step-by-step explanation:
you can use a calculater and it will give 19683 and 3⁹ gives 19683
Determine the inverse function of f(x)=1/7x-1/7
The inverse of the function → y= f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
We have -
y = f(x) = x/7 - 1/7
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question, the equation given is as follows
y = f(x) = x/7 - 1/7
Replace 'y' with 'x', we get -
x = y/7 - 1/7
Now, solve for y -
y/7 = x + 1/7
y = 7(x + 1/7)
y = 7x + 1
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = 7x + 1
Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
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Write 2.5 as a mixed number and as an improper fraction. Write your answers in simplest form.
Answer:5/2 and 2 1/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
2.5 as a mixed number is 2 1/2 since 1/2 = 0.5
2.5 as an improper fraction is 5/2
Simplify the fraction 24/56 until it is in simplest form.
explain
Answer: 3/7
Step-by-step explanation:
You would divide this by the number 8.
8*3 = 24
8*7 = 56
Therefore the answer is 3/7
Hey there!
24/56
= 24 ÷ 8 / 56 ÷ 8
= 3/7
Therefore, your answer should be:
3/7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
which of rthe following goups of scores would hav ethe smallest standard deviation 20, 40, 60, 80, 100
In dataset 60 is the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation.
n dataset C, the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation
Standard deviation is 60
What do you mean by standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.
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