The scale of a map is the relationship between the distance on the map and the actual distance. In this case, the scale of the map is 1:4000, which means that 1 unit on the map represents 4000 units in the actual distance. To find the actual distance that is represented by 6.4 cm on the map, we need to convert the distance on the map to the same unit as the actual distance. Since 1 cm is equal to 0.01 m, 6.4 cm is equal to 6.4 * 0.01 = 0.064 m.
Now we can use the scale of the map to convert the distance on the map to the actual distance. We can set up the following proportion:
0.064 m / 1 = x / 4000
Where x is the actual distance in metres. Solving for x, we get:
x = 0.064 m * 4000 = 256 m
Therefore, the actual distance represented by 6.4 cm on the map is 256 m.
what is the derivative of 2x X 5x to the 5th power?
The answer is 0because the second derivative will make it 1
Answer:
Below
Step-by-step explanation:
(2x * 5x)^5 = (10x^2)^5 = 100 000 x^10
derivative is 1 000 000 x^9
piecewise linear functions common core algebra 2 homework answers
Piecewise linear functions, f(x) as common core algebra, Evaluate each of the following :
(1) f(-3) = 12
(2) f(4) = 2
(3) f(0)= 8
(4) f(3)= 8
What is Piecewise linear functions ?A piecewise linear function is a function defined on the interval [xₘᵢₙ ,xₘₐₓ]. A piecewise linear function is a function that consists of straight line segments. This is a piecewise function whose pieces are affine (linear) functions. Graphs of piecewise linear functions consist of line segments and rays.
We have given that,
f(x) = 5x - 3 ; x< -2
= x+8 ; -2≤x< 3
= 1/3(x) + 7 ; x ≥3
we see here that , f(x) is a piecewise linear function defined on interval [-2,3).
Now, we solve the following
(1) f(-3) , here x = -3< -2 i.e we take f(x) =5 x -3
=> f(-3) = 15 - 3 = 12
(2) f(4) , x= 4 >3 so, f(x) = 1/3(x) + 7
=> f(4) = 1/3(4) + 7 = 14/7 = 2
(3) f(3) , x = 3 so, f(x) = 1/3(x) + 7
=> f(3) = 1/3(3) + 7 = 8
(4) f(0) , x = 0 or -2 < x < 3 so, f(x) = x+8
=> f(0) = 0+8 = 8
Hence, we evaluate the given functions.
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Complete question:
piecewise linear functions common core algebra 2 homework answers
5x - 3 x<-2 1. For f (x) = x+8 -25x<3 answer the following questions. -x+7 x23 (a) Evaluate each of the following by carefully applying the correct formula: (1) f ( -3 ) (ii) f (4) (iii ) f ( 3 ) (iv ) f (0 )
Find a polynomial function of degree 3 such that f(0)=17 and the square root of f(x) are 0,5 and 8
Answer:
f(x)=x^3 - 13x^2 + 40x + 17
Step-by-step explanation:
x-0=0 x-5=0 x-8=0
x=0 x=5 x=8
y=x(x-5)(x-8)+b ==> b is what's going to be used to find the equation so that
y=17 when x=0
17=0(0-5)(0-8)+b ==> plugin 0 for x and 17 for y
17=0*(-5)*(-8)+b ==> simplify
17=0+b ==> anything multiplied by 0 is 0.
b=17
Hence, the equation is:
y=x(x-5)(x-8)+17 ==> expand this equation
y=x*(x-5)(x-8) + 17
y=x*(x(x - 8) - 5(x - 8)) + 17 ==> distribute x-8 to x and -5
y=x*(x*x - 8x - 5x - (8)(-5)) + 17 ==> distribution property
y=x*(x^2 - 13x - (-40)) + 17 ==> simplify
y=x*(x^2 - 13x + 40) + 17 ==> subtracting a negative number is equivalent to
adding a positive number
y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the
distribution property.
Answer: f(x)=x^3 - 13x^2 + 40x + 17
Answer: Okay, lets explain.
Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)
= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.
Natalie is using Triangle Tiles to create a design. She finds two congruent scalene triangles, flips one over, and places two vertices together that have the same angle, as shown.
If (equation shown in the picture), what is the value of x?
The value of x in the triangle is 70°
How to find the value of x in the triangle?Given:
the equation m<A + m<B = 130°
We know that:
m<A + m<B + m<C = 180° (sum of angles in a triangle)
Since m<A + m<B = 130°, we have
130° + m<C = 180°
m<C = 180° - 130°
m<C = 50°
Considering the middle triangle, let the unlabeled angle be y:
m<C + m<C + y + 40° = 180° (sum of angles on a straight line)
50 + 50 + y + 40 = 180°
y = 180° - 140° = 40°
x + x + y = 180° (sum of angles in a triangle)
2x + y = 180°
2x + 40° = 180°
2x = 140°
x = 140/2
x = 70°
Thus, the value of x is 70°
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Solve for y
6/8 = 15/y
Answer:
The answer is 20
Step-by-step explanation:
6/8 = 15/y
(6) × y = (8) × (15)
6y = 120
6y/6 = 120/6
y = 20
Thus, The value of y is 20
Answer:
[tex] \sf \: y = 20[/tex]
Step-by-step explanation:
Given equation,
[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]
Now the value of y will be,
[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]
[tex] \sf \rightarrow \: 6y = 15 \times 8[/tex]
[tex] \sf \rightarrow \: 6y = 120[/tex]
[tex] \sf \rightarrow \: y = \frac{120}{6} [/tex]
[tex] \sf \rightarrow \boxed{ \sf y = 20}[/tex]
Hence, the value of y is 20.
Remata it’s 3 more than 6 times as old as her daughter Isabella. The sumo their ages is 38. What are Renata and Isabella’s ages, respectively.
Answer:
The answer to you question is 18 and 20
18 and 20
A well-mixed cookie dough will produce cookies with a mean of 7 chocolate chips apiece. What is the probability of getting a cookie with no more than 4 chips? Round
your answer to four decimal places
Answer:
I have solved this on Paper and attached an image in the explanation part!
Step-by-step explanation:
Andre has a summer job selling magazine subscriptions. He earns $25 per week plus $3 for every subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats.
Write an inequality to describe the number of subscriptions Andre must sell to reach his goal.
The inequality to describe the number of subscriptions Andre must sell to reach his goal is 3s + 25 ≥ C.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.
∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.
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which equation is equivalent to 32x−4y 1=0?
y = 3/8x + 1/4 is equation of linear equation .
What in mathematics is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.
The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.
There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.
3/2x -4y+1=0
-4y = -3/2x - 1
y = 3/8x + 1/4
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The complete question is -
Which equation is equivalent to 3/2x -4y+1=0
How do you find how many times greater something is in scientific notation
Answer: The number it is a power too
To determine how many times greater something is in scientific notation, you need to compare the exponents of the numbers and calculate the ratio between them.
In scientific notation, a number is expressed as the product of a coefficient (a decimal number between 1 and 10) and a power of 10. The exponent represents the number of places the decimal point has been moved.
To find how many times greater one number is than another, you compare the exponents of the powers of 10. If the exponent of the first number is n and the exponent of the second number is ᵃ, you can calculate the ratio by dividing 10ⁿ by 10ᵃ.
The result of this division will give you the factor by which the first number is greater than the second number. For example, if the result is 100, it means the first number is 100 times greater than the second number.
In summary, to determine how many times greater something is in scientific notation, compare the exponents of the powers of 10 and calculate the ratio between them.
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Erica recorded the number of sales she made during each of the first 4 months when
she began her new career. Erica plotted the data on a coordinate grid, and she noted
that the data correlate to an exponential equation, as shown.
What is the domain of the function shown in the graph?
The domain for the given graph is obtained as {1, 2, 3, 4}.
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
From the graph of the given exponential function,
The set of ordered pairs can be written as follows,
{(1, 10), (2, 20), (3, 40), (4, 80)}
Since the domain is the set of first elements for a given pair of ordered set.
The domain is given as {1, 2, 3, 4}.
Hence, the domain obtained from the given graph is {1, 2, 3, 4}.
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The graph missing in the question is attached here.
Factor the polynomial
below completely:
10m5n² + 25m³n³
(Show work please)
Answer:
[tex]5mn^{2} (2+ 5m^{2} n)[/tex]
Step-by-step explanation:
I assumed the polynomial is [tex]10mn^{2} +25m^{3}n^{2}[/tex]
FIRST: Highlight the common factors{ 5 , m and[tex]n^{2}[/tex])
[tex]5mn^{2} (2+ 5m^{2} n)[/tex]
An assumption made about the value of a population parameter is called a A. confidence
B. hypothesis
C. significance D. normal curve
An assumption made about the value of a population parameter is called a hypothesis.
What is null hypothesis?
In inferential statistics, the null hypothesis is that 2 possibilities are an equivalent. The null hypothesis is that the determined distinction is because of likelihood alone. mistreatment applied mathematics tests, it's doable to calculate the chance that the null hypothesis is true.
Main Body:
As we need to make an assumption about population , it could be done by using a hypothesis test. so , the incorrect options are identified below:
The confidence, significance and normal curve cannot be used to make the assumptions about the value of a population parameter.
Hence , An assumption made about the value of a population parameter is called a hypothesis.
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27. The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations Graph C Graph B Graph A 200 Sample Means h of the following is the correct ordering of the graphs from least value of n to greatest value of n? 200 200 0 Sample Means Sample Means A A, C, B (B) B. A, C (C) B. C, A (D) C. A, B (E) C, B, A
Previous question
The correct ordering of the graphs from least value of n to greatest value of n is A, B, C.
The three graphs, A, B, and C, represent the results of three simulations of a sampling distribution of a sample mean. Graph A has a value of n of 200, Graph B has a value of n of 200 and Graph C has a value of n of 0. Thus, the correct ordering of the graphs from least value of n to greatest value of n is A, B, C. To understand this, it is important to note that as the value of n increases, the sample means will be more representative of the population. Therefore, Graph A with the lowest value of n would have the least representative sample means, followed by Graph B and Graph C with the highest value of n having the most representative sample means.
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Frances can complete 91 oil changes in 7 days.
How many oil changes can Frances complete in 11 days?
Answer:
143. Divide 91/7 = 13, then take the number of oil changes per day and times it by 11. 13 x 11 = 143.
Step-by-step explanation:
Answer:
113.75
Step-by-step explanation:
Since 11 days is only 4 days away from 11, divide 91 / 4 = 22.75. Add this number to 91 to get the answer.
A line is parallel to the line 3y-15x+11=0 and passes through the point (5, 3). Which equation models the line?
A: x-5y+10=0
B: x+5y-20=0
C: y=5y+12
D: 5x-y-22=0
The equation for such line is 5x - y - 22 = 0, using properties of parallel line and slope of a line.
What are the properties of two parallel line ?
1. These lines never intersect each other.
2. These lines have same slope .
General Equation for a line :
y = mx +c
Where m is slope of a line and c in constant .
As in que , we are given one line ,
so we can find slope of that line , using differentiation
3dy/dx - 15 = 0
slope : (1dy/dx) = 5
From 2nd property :
Slope of another line = 5 and passing point is (5,3)
Put all these information in general equation for a line:
3 = 5*5 + c
c = -22
So, the equation for a line with slope (m):5, constant(c):(-22) is
y = 5x - 22
or 5x - y - 22 = 0
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How many cups are in 1/2 a gallon?
A gallon which is a liquid measuring unit of US in cooking measurements, there are eight cups in half of a gallon.
A gallon is the most commonly used unit of measure for measuring the volume of liquids. US gallons are legally defined as 231 cubic inches, or exactly 3.78 liters .
Ounces : fluid ounces (fl oz, fl. oz ) is a unit of volume commonly used to measure liquids. To convert from gallons to ounces, multiply the value in gallons by 128. So, 1/2 gal = (1/2) × 128 = 64 oz or ounces, 1/2 gallons = 64 ounces. Now, let's measure a cup in gallons, 1 cup is equal to 8 ounces ,then 8 cups are 64 ounces. From the above discussion we conclude that 8 cups = 64 ounces = 1/2 gallon. So, 8 cups is 1/2 gallon.
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Your cell phone plan costs $24.99 per month plus $0.16 for each text message you send or receive. You have at most $30 to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next month?
Please use an inequality equation
Answer:
Step-by-step explanation:
ok
Which statement explains how the lines x + y = 2 and y = x + 4 are related? (1 point)
The product of the slope of the lines is negative 1. Then both lines are perpendicular to each other.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equations are given below.
x + y = 2 ...1
y = x + 4 ...2
The slope of the first line is -1 and the slope of the second line is 1.
The product of the slope of the lines is negative 1. Then both lines are perpendicular to each other.
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g neptunium-239 has a half-life of 2.35 days. how many days must elapse for a sample of 239np to decay to 0.100% of its original quantity? 0.0427 days 1.491 days 2.04 days 23.4 days
23.5 days must elapse for a sample of 239np to decay to 0.100% of its original quantity.
Given is the equation for radioactive decay.
N equals N0exp(-λt). We have to determine the λ decay constant.
λ= -(lnN/N0)/t where t = Neptunium-239's half-life, 2.35 days,
and N/N0 = 1/2 where N = Amount of Neptunium-239 after half-life,
and N0 = Amount of Neptunium-239 at the beginning.
Consequently,
λ = (-ln(1/2))/2.35 = 0.294/day.
Neptunium-239 will now degrade to 0.100% of its original value.
N/N₀ × 100 % = 0.100%
N/N₀ = 0.100/100
N/N₀ = 0.001
We calculate the time it takes for Neptunium-239 to decay to this value using the equation for radioactive decay. Making t the formula's subject,
-(lnN/N0)/ = -(ln(0.001))/0.294/day.= 23.5 days
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A certain quadratic function has x-intercepts at 2 and 3. What is the x-coordinate of its vertex?
Answer: [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The vertex is halfway between the [tex]x[/tex]-intercepts.
So, the answer is [tex]\frac{2+3}{2}=\frac{5}{2}[/tex].
let s be the set of integers from 100 through 999. some integers in s have a digit in common. for example, 256 and 530 have the digit 5 in common. how many integers from 100 through 999 must you pick in order to be sure that at least two of them have a digit in common?
In order to achieve at least two integers with common digits, we must choose at least 10 integers.
What is meant by an integer?A whole number that can be positive, negative, or zero is called an integer. It is not a fraction.
All three-digit integers in the range of 100 to 999 are taken into consideration.
The ten numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are all feasible.
In the worst case, there are no common digits among the nine chosen integers. It is feasible, for instance, that no two of the nine integers 111, 222, 333, 444, 555, 666, 777, 888, and 999 share any digits.
There is only one digit that was not stated in the previous nine integers, therefore if we choose a tenth three-digit integer, it must share at least one digit with the first nine integers. However, a three-digit integer cannot start with a 0, so the first digit must be something else.
One of the previous nine integers must have also used the three-digit integer. In order to achieve at least two integers with common digits, we must choose at least 10 integers.
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a person buying a personal computer system is offered a choice of three models of the basic unit, three models of keyboard, and four models of printer. how many distinct systems can be purchased?
The person can buy a total of 36 distinct systems from three models of the basic unit, three models of keyboard, and four models of printer.
Given, a person buying a personal computer system is offered a choice of three models of the basic unit, three models of keyboard, and four models of printer.
we have to find the number of distinct systems that can be purchased.
Using the concept of Permutations and Combinations, we get
Choose One model of basic unit from three models, Choose one model of keyboard from three models of keyboards and also choose one model of printer from four models of printers.
C(3 , 1)×C(3 , 1)×C(4 , 1)
= 3×3×4
= 36
So, the total of 36 systems can be purchased.
Hence, the total of 36 systems can be purchased.
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What is the volume of a box that is 14 inches long,7 inches wide, and 10 inches high?
Answer:
The volume equals 980
Step-by-step explanation:
Volume = L x W x H
14 x 7 x 10 = 980
Brianna is working two summer jobs, making $16 per hour lifeguarding and $11 per hour tutoring. Brianna must earn no less than $130 this week. Write an inequality that would represent the possible values for the number of hours lifeguarding, ll, and the number of hours tutoring, tt, that Brianna can work in a given week.
16h + 11t ≥ 130
16*5=80, 16*4=64
11*5=55, 11*6=66
80x+55y>130
64x+66y>130
The possible values for the number of hours lifeguarding, is 5,4 hours and the number of hours tutoring, is 5,6 hours that Brianna can work in a given week.
What does a mathematical inequality equation mean?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to depict the relationship between two expressions. An inequality sign has non-equal expressions on both sides.
Write an inequality equation in what format?Use these steps to resolve an inequality: Eliminate fractions in Step 1 by multiplying all terms by the total fractions' lowest common denominator. On both sides of the inequality, combine like phrases to simplify in Step 2. To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts.
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the area of a triangle 10cm 8cm 21cm 17cm
The area of the triangle given in this problem is of:
A = 84 cm².
How to calculate the area of the triangle?The area of a triangle of base b and height h is given by the multiplication of these two dimensions divided by two, which is equivalent to the multiplication of these measures by 0.5, hence:
Area = 0.5 x base x height.
For the triangle given at the end of the answer, these dimensions are given as follows:
Base: 21 cm.Height: 8 cm. (height equivalent to the base of 21 cm).Then the area of the triangle is obtained by the multiplication as follows:
Area = 0.5 x 8 x 21 = 4 x 21 = 84 cm².
Missing InformationThe triangle from which we calculate the area is given by the image shown at the end of the answer.
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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2013, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the number of new cases would reach 604.
The linear regression equation that represents this set of data is given as follows:
y = -27.3x + 843.2.
The estimate of the calendar year in which the number of new cases would reach 604 is of:
2019.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.
From the table given at the end of the answer, the points of the function are given as follows:
(0, 832), (1, 827), (2,800), (3,750).
Inserting these points into the calculator, the equation is given as follows:
y = -27.3x + 843.2.
The number would reach 604 when:
y = 604
-27.3x + 843.2 = 604
x = (843.2 - 604)/27.3
x = 8.7
2011 + 8.7 -> during the year of 2019.
Missing InformationThe table is given by the image shown at the end of the answer.
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Ximena needs to order some new supplies for the restaurant where she works. The restaurant needs at least 333 spoons. There are currently 255 spoons. If each set on sale contains 6 spoons, which inequality can be used to determine ss, the minimum number of sets of spoons Ximena should buy?
In linear equation, Joshua should buy is 255 + 6s ≥ 333.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let the sets of spoons be represented by s
The restaurant needs at least 333 spoons.
Each set on sale contains 8 spoons
There are currently 333 spoons.
At least as an inequality is ≥
Hence:
255 + 6 × s ≥ 333
255 + 6s ≥ 333
Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is
255 + 6s ≥ 333
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Which of the following is a solution to both y= 4x - 8 and y = 8x - 4? A. (-12, -1) B. (3, 4) C. (1, 4) D. (-1, -12)
(-12, -1) is a solution to both y= 4x - 8 and y = 8x - 4.
What is meant by solution of equation?Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is considered a solution to the problem. Finding the solution or solutions to an equation is known as solving it.
What are three types of solution?Unique, infinitely many solutions and no solutions are three types of solution.
If we put x=-12 and y=-1 in both of the given equation we will get L.H.S=R.HS . So (-12, -1) is the required solution.
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The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
70 times smaller is the bacterial cell than the amoeba cell.
What is 10^n?
As a result, a power of 10 is represented in long form as the number 1 followed by n zeros, where n is the exponent and is bigger than 0; for instance, 10⁶ is represented as 1,000,000. The number 1 n places after the decimal point represents the power of 10 when n is less than 0; for instance, 10⁻² is represented as 0.01.
Given that, the length of a bacterial cell is about 5 x 10⁻⁶ m, and the length of an amoeba cell is about 3.5 x 10⁻⁴ m.
To calculate times of smaller, divide the length of amoeba cell with bacterial cell.
Therefore, (3.5 x 10⁻⁴)/(5 x 10⁻⁶) = 70.
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Answer:
so the experts answer is correct but its not in scientific notation the answer is: 7 x 10^1
Step-by-step explanation:
