Answer:
I = 17deg, II = 73deg
Step-by-step explanation:
Let's say first angle is x, and then respectively, the second angle is 4*x + 5.
Their sum is 90 degrees, so:
x + (4*x+5) = 90
5x + 5 = 90
5x = 85 | :5
x = 17 degrees ==> first angle
4*x+5 = 73 degrees ==> second angle
Hey i dont know leave step by step
The exponential function f (t) = e is a mathematical function that describes a relationship between a number and its power.
What is the value for b?It is also known as the exponential growth function, as it models the continuous growth of a quantity over time.The exponential function f (t) = e can be expressed in the form f (t) = b, where b is a constant. The constant b is the base of the exponential function and determines how quickly the quantity grows or decays. The value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function. The Taylor series is an infinite sum of terms, where the terms are the derivatives of the exponential function at the origin.The value of b for the exponential function f (t) = e is important because it helps to determine the rate of growth or decay of a quantity over time. Knowing the value of b for the exponential function allows us to easily calculate the value of a quantity at a given time, given its initial value. In summary, the value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function and is used to determine the rate of growth or decay of a quantity over time.To learn more about The exponential function refer to:
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unit 1 geometry basics homework 2 segment addition postulate
The geometry questions attached are: UV = 67, x = 67, BD = 88, BC = 26 and CD = 61
What is meant by line segment?In contrast to a line, which can be extended endlessly on both ends, a line segment has endpoints.
An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment.
A line segment, in geometry, is a portion of a straight line that is constrained by two clearly defined end points and contains every point on the line that is situated in between those endpoints. The Euclidean distance between two line segments' ends determines the length of the segment.
5.)
UW = 6x - 35
UW = UV + VW (total length of a line segment)
UV = 19
VW = 4x - 20
6x - 35 = 19 + 4x - 20
simplifying the above equation, we get
6x - 4x = 19 - 20 + 35
2x = 34
x = 34 / 2
x = 17
UW = 6x - 35 = 6(17) - 35 = 67
6.)
HJ = 7x - 27
HJ = HI + IJ (total length of a line segment)
Substitute the values in the above equation, we get
7x - 27 = 3x - 5 + x - 1
simplifying the above equation, we get
7x - 3x - x = - 5 - 1 + 27
3x = 21
x = 21 /3
x = 7
7.)
BD = 7x - 10, BC = 4x - 29 and CD = 5x - 9
BD = BC + CD (total length of a line segment)
7x - 10 = 4x - 29 + 5x - 9
simplifying the above equation, we get
7x - 4x - 5x = - 29 - 9 + 10
-2x = - 28
x = 14
Therefore, the geometry questions attached are:
BD = 7(14) - 10 = 88
BC = 4(14) - 29 = 27
CD = 5(14) - 9 = 61
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What is the value of K in the polynomial 3x2 2kx 3?.
A formula with just one phrase where the unknown is squared and no terms where the unknown is raised to a power greater than 2 assumed: 3x* + 2kx+ 3= when compared to the quadratic equation ax2 + bx + c = 0, a = 3 b= 2kc= 3.
Given that the equation's roots are genuine and equal D=0 Discriminant, hence D = b2 - 4ac = 0 (2k) - 4.3.3 = 0 4k -36 = 0 4k -36 = 0 4k2 = 36 k'=9 taking square root on both sides k=3 or k=-3 as a result, the roots of the quadratic equation are real and equal for the values of k of 3, and -3.
When a polynomial is evaluated at x=2, the outcome is zero if the polynomial is divisible by (x-2). Therefore, we can substitute x = 2 into the polynomial 2kx-kx-8 and solve for k to find the value of k.
2k(2)^-k(2)-8 = 0 2
k(0.25) - 8 =0\s
k(0.25) = 8\sk=32 = 4
Therefore, k must be equal to 4 for the polynomial 2kx-kx-8 to be divisible by (x-2).
Complete question:
What is the value of K in the polynomial 3x2 2kx 3 The roots of the quadratic equation 3x2 2kx 27 are real and equivalent.
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The value of k when x = (-1/2) is a solution of the quadratic polynomial 3x² + 2kx - 3 = 0 is -2.
To find the value of k, we can substitute the value of x = (-1/2) into the equation and solve for k. So, we have:
3 * (-1/2)² + 2k * (-1/2) - 3 = 0
Expanding the square and substituting the value of x gives us:
-3/4 + k * (-1/2) - 3 = 0
Simplifying the left-hand side of the equation gives us:
k * (-1/2) = 3/4 + 3
Finally, solving for k by dividing both sides by -1/2 and simplifying gives us:
k = -2
Hence, the value of k when x = (-1/2) is a solution of the quadratic equation 3x² + 2kx - 3 = 0 is -2.
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Complete Question:
If x=(− 1/2), is a solution of the quadratic equation 3x^2 +2kx−3=0, find the value of k.?
Suppose that y varies jointly with w and x and inversely with z and y = 150 when w = 5, x = 15 and z = 3. Write the equation that models the relationship. Then find y when w = 3, x = 2 and z = 2.
sorry for bad handwriting :)
What is the formula to find the nature of the roots of a quadratic equation?.
The roots of the quadratic equation are x and if they are the values of x that fulfill the quadratic equation. The equation (-b(b2-4ac))/2a yields roots. The discriminant determines the kind of roots.
Mathematical algebra includes solving quadratic equations. The equations that have at least one term that is squared or in square form are known as quadratic equations. The equation of the second degree is another name for quadratic equations.
The standard form of the quadratic equation is ax2 + bx + c = 0, where a, b, and c are real numbers or constants that do not equal 0, and x is an unknown variable whose value can only be determined by solving the equation using a variety of methods for solving quadratic equations. The two powers of x are equal to the square on x, and the nature of the roots can be real, estimated, or assumed.
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What percent of the 8th graders estimated they spend less than an hour a day on social media? Round your answer to the nearest tenth of a percent.
The percent of 8th graders estimated they spend less than an hour a day on social media 47% .
What do you mean by percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is basically denoted using the percent sign, "%". For example, 45% means 45 out of 100, or 0.45. Percentage can be used to express how much of something is present or has been completed.
From the given table,
For 7th grade,
26 / 37 * 100
= 70%
For 8th grade,
26/55 * 100
= 47% (approx)
Total ,
52 / 92 * 100
= 5200 / 92
= 57 %
Hence, the percent of 8th graders estimated they spend less than an hour a day on social media 47% .
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One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take the two hoses to fill the pool working together?
Answer: I believe it would be 25 minutes
Step-by-step explanation: longest amount of time minus shortest amount of time.
Grant is at a basket ball game and wants to buy as many 3 hotdog and 4 Sodas as he can. If grant has 38 and wants to buy as many sets of one hot dog and one soda as he can how can he
The number of sets of one hot dog and one soda he can buy is; 5 sets
How to solve Algebra Word problems?We are given;
Cost of hotdog = $3
Cost of soda = $4
Total amount grant has = $38
Now, we are told that he wants to buy same set of hotdog as that of sodas. Thus, let the amount be x and we have the algebraic expression;
3x + 4x = 38
7x = 38
x = 38/7
x = 5³/₇
We will pick the whole number to get 5 sets
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Complete question is;
Grant is at a basket ball game and wants to buy as many $3 hotdog and $4 Sodas as he can. If grant has $38 and wants to buy as many sets of one hot dog and one soda as he can how can he buy?
How do you find the inverse of a function in standard form?.
The inverse of a function in standard form can be determined by substituting the function in the standard form
Every function does not have an inverse. A function needs to be a one-to-one function, which means there can't be repeated output for distinct inputs, in order to have an inverse. When a quadratic function is in vertex form, if the leading coefficient (a) is not zero, the function has an inverse. The various steps to find the inverse of a function in standard form can be noted as -
The function should first be written in standard form as follows: y = f(x) = a*x + b, where a and b are constants.Substituting y for x and x for y in the equation: x = f(y)(a*y + b)(y)Isolate y on one side of the equation and solve for it: y = (x-b)/aIf required, make the equation simpler.The original function f(x) = a*x + b is now the inverse function f-1(y) = (x-b)/a.Read more about standard form on:
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Determine if each expression is or is not equivalent to −0.5g + 2.5.??
where is the expressions?
y=_x + _
what is the slope?
Answer:
slope: -3y-intercept: +7equation: y = -3x +7Step-by-step explanation:
You want to know the slope and y-intercept of the line shown in the graph.
InterceptThe line crosses the y-axis at y = 7. This is the y-intercept, the added constant in the equation. That is, b = 7.
SlopeIn addition to passing through the point (0, 7), the line can also be seen to pass through the point (1, 4). This means the line has a "rise" of -3 for the corresponding "run" of +1.
The slope is ...
m = rise/run = -3/1 = -3
EquationThe slope-intercept equation for the line is ...
y = mx + b
y = -3x +7
__
Additional comment
We chose to determine the y-intercept first, because it usually is found on a grid intersection. For determining slope, it is convenient to find two points on grid intersections. That way, the slope can be most precisely determined. It can be less accurate to interpolate values when determining points that are not on grid intersections.
Since the y-intercept is a grid intersection point, we only need to find another point where the line crosses a grid intersection to make our slope calculation as simple and accurate as possible.
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How do you find the median of a modal class in class 10?.
In such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution ,
income distribution, wealth assessment, mean loses its representation of the data.
Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.
We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)
0to10. 3. 3
10 to 20. 7 10
20to 30. 10 20
30 to 40 8 28
40 to 50. 6. 34
Total. 34
N=34
N/2 = 34/2 =17
MEDIAN class=20 to 30
C =10
L lower boundary of MEDIAN class =20
f=10
m=10
MEDIAN =L +( N/2 -- m) ×c) /F
=20+ (17-10)×10. /10
= 20+ 7=27
MEDIAN=27
It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.
In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.
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Answer:
Step-by-step explanation:
In such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution , income distribution, wealth assessment, mean loses its representation of the data.
Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.
We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)
0to10. 3. 3
10 to 20. 7 10
20to 30. 10 20
30 to 40 8 28
40 to 50. 6. 34
Total. 34
N=34
N/2 = 34/2 =17
MEDIAN class=20 to 30
C =10
L lower boundary of MEDIAN class =20
f=10
m=10
MEDIAN =L +( N/2 -- m) ×c) /F
=20+ (17-10)×10. /10
= 20+ 7=27
MEDIAN=27
It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.
In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.
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so like i nee help asap
Step-by-step explanation:
[tex] {h}^{2} + {r}^{2} = {l}^{2} \\ {h}^{2} = {l }^{2} - \: {r}^{2} \\ {h }^{2} = {13}^{2} - {12}^{2} \\ {h}^{2} = 169 - 144 \\ {h}^{2} = 25 \\ h = 5[/tex]
:. h = 5 in ...
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Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary.
The value of each variable in a parallelogram can be found by measuring the lengths of the sides, the angles between the sides, and the area of the shape. The measurements should be rounded to the nearest tenth, if necessary.
The value of each variable in a parallelogram can be determined by taking measurements of the various components of the shape. The first step is to measure the lengths of the sides. These are typically labeled as a, b, c, and d. The angles between the sides can then be measured, which are typically labeled as A, B, C, and D. The area of the parallelogram can be calculated using the formula A=ab sin C. All of these measurements should be rounded to the nearest tenth, if necessary. Once all of the measurements have been taken, the values of the variables can then be determined. This is done by using the values found to solve for the unknowns in the formula. For example, if the lengths of the sides are known, the angles can be calculated using the Law of Cosines. Knowing all of the measurements of the parallelogram can allow you to solve for the values of the variables.
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The complete question is
Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary labeled as A,B,C and D.
How do you plot 3 coordinates?.
We'll begin with a three-dimensional coordinate system where the x-axis comes toward us on the left.
The y-axis moves out toward the right, and the z-axis is absolutely vertical in order to plot points in three-dimensional coordinate space. When we need to take into account negative values of x, y, or z, then we should be aware that the negative x-axis moves out to the left.
The negative y-axis moves out to the right, and the negative z-axis is absolutely vertical and extends out below the positive z-axis.
In three-dimensional space, up until we reach our coordinate point, we advance along the x-axis, then parallel to the y-axis, then parallel to the z-axis.
Similar to how we find our point by going parallel to the y-axis after moving outside along the x-axis to our x value in two-dimensional coordinate space.
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What is the difference between the largest 6 digit number and smallest 4 digit number?.
The difference between the largest 6-digit and the smallest 4-digit numbers is 998999.
The aim is to find the smallest 4-digit and largest 6-digit numbers, and then we need to determine the difference between these two values.
Let's start by finding the smallest 4-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.
Thus, we can create the required 4-digit smallest number with 0 and 1.
Hence, the smallest 4-digit number is 1000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Now, find the difference between these two values.
So, we can determine the difference between the smallest 4-digit and the largest 6-digit numbers by subtracting the smallest from the largest.
Thus, we get,
⇒999999−1000
⇒998999
Hence, 9989999 is the difference between the smallest 4-digit and the largest 6-digit numbers.
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Find the missing side length.
The missing length is 14 yards from the given figure.
What is Quadrilateral ?
A quadrilateral is a closed form and a form of polygon that has 4 sides, 4 vertices and 4 angles. it's miles formed via joining four non-collinear points. The sum of indoors angles of quadrilaterals is continually identical to 360 tiers.
The word quadrilateral is derived from the Latin phrases ‘Quadra’ which means four and ‘Latus’ means ‘sides’. It is not essential that every one the four aspects of a quadrilateral are equal in length. therefore, we are able to have distinct kinds of quadrilaterals primarily based on aspects and angles.
Given ,
from the figure,
It was mentioned to find the missing length
As when we add up two sides we get the missing length from the given figure.
missing length = 9 + 5
missing length = 14 yards.
So, missing length is 14 yards
Therefore, the missing length is 14 yards from the given figure.
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work out
a) 7/9×5 2/5 b) 1 3/4×4 1/6
From the work out of the expressions, we have;
a. 4 1/5
b. 7 7/24
Types of fraction?A fraction can be defined as any expression which consists of a numerator and denominator. The three major types are: proper fraction, improper fraction and mixed fraction.
To work out the given expressions;
a. 7/9 × 5 2/5
convert both to a proper fraction,
7/9 x 27/ 5 = (7 x 27)/ (9 x 5)
= 189/ 45
= 4 1/5
b. 1 3/4 × 4 1/6
express in a proper fraction
7/ 4 x 25/ 6 = (7 x 25)/ (4 x 6)
= 175/ 24
= 7 7/24
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Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet
longer than it is wide.
The equation to determine the length and width of the rug is
28 = w² + 12w
Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.
What is a rectangle?
Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
We are given a rectangular rug with an area of 28 square feet.
Also, the rug is 12 feet longer than it is wide.
So,
Let 'l' be the length of the rug and 'w' be the width of the rug
As given, Length is 12 feet longer than its width
Therefore, l = w + 12
We know Area of rectangle = Length * Width and area is given to be 28 square feet.
So,
⇒28 = (w + 12)w
⇒28 = w² + 12w
Hence, the equation to determine the length and width of the rug is
28 = w² + 12w.
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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.
Create an equation to determine the length and the width of the rug.
Which expression is equivalent the one seen in the image
Answer: option 1
Step-by-step explanation: as when you try to simplify you get the values in option 1
Answer: 1
Step-by-step explanation:
Evaluate 0.5^3 and 0.5^-3 as fraction
Answer:
Step-by-step explanation:
0.5^3 = 0.5*0.5*0.5
= 0.125
= 125/1000
= 1/8.
0.5^-3
= 1 / 0.5^3
= 1 / 1/8
= 8.
Why is mole Avogadro's number?.
The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is also called Avogadro's number.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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You know that the general chance that a randomly selected individual got a placebo is. 33208489. You also know that the general chance that an individual did not get the flu is. 93196005. Finally, the chance of both happening is. 27278402. Question 1 Given that they received the vaccine, what is the probability that an individual got the flu
The probability that an individual got the flu given that they received the vaccine is 0.739130435.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Bayes' theorem to solve for the probability that an individual got the flu given that they received the vaccine. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
The probability of event B given that event A has occurred, P(B|A), can be calculated as the general chance of both events happening, which is .27278402.
So, using Bayes' theorem:
P(A|B) = P(B|A) * P(A) / P(B) = .27278402 * .33208489 / .06803995 = .739130435
Therefore, the probability that an individual got the flu given that they received the vaccine is 0.739130435.
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The probability that an individual got the flu is approximately 1.09.
Let's call the probability of receiving a placebo "P(placebo)" and the probability of not getting the flu "P(no flu)". Then, using the information given, we have:
P(placebo) = 0.33208489
P(no flu) = 0.93196005
P(placebo and no flu) = 0.27278402
To find the probability of getting the flu given that they received the vaccine (not a placebo), we can use the formula for conditional probability:
P(flu | vaccine) = P(flu and vaccine) / P(vaccine)
Since the individual either received a placebo or a vaccine (but not both), the probability of receiving a vaccine is given by:
P(vaccine) = 1 - P(placebo) = 1 - 0.33208489 = 0.66791511
The probability of getting the flu and receiving a vaccine is equal to the complement of the probability of getting the placebo and not getting the flu, which is:
P(flu and vaccine) = 1 - P(placebo and no flu) = 1 - 0.27278402 = 0.7272159
Finally, substituting these values into the formula for conditional probability, we get:
P(flu | vaccine) = P(flu and vaccine) / P(vaccine) = 0.7272159 / 0.66791511 = 1.09103623
So, the probability of getting the flu given that an individual received the vaccine is approximately 1.09.
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can someone please help me with this math problem it is listed in the picture!
Answer: I think that the answer for that is fh
Step-by-step explanation:
what is The quotient of a number and nine is lessthan the number. In algebraic expressions
Answer:
Step-by-step explanation:
The quotient is the result you get when dividing numbers.
Let the number be n then the expression is:
n / 9 < n.
1. the solution set of an inequality ×-2 ×+3>0 is
A. (2,3) C, (-infinity,-3)U (2,infinity)
B, (-Infinity,3) U (-2,infinity) D, (- ♾, -2) U (3, ♾)
The solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).
What is inequality?
An inequality is a mathematical statement that represents a relationship between two values that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), to describe the relationship between the values.
Isolate the variable x:
x - 2 × + 3 > 0
x - 2 × + 3 - 3 > 0 - 3
x - 2 × > -3
Divide both sides by -2 and reverse the inequality sign:
(x - 2 ×)/(-2) < (-3)/(-2)
x - 2 × < 3
x > 2 × + 3
Test values of x to see which ones make the inequality true:
If x is less than -2, the inequality is false.
If x is between -2 and 3, the inequality is true.
If x is greater than 3, the inequality is false.
So the solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).
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The sum of Georges's age and his father's age is 60 years. In 6 years, George's father will be twice as old as George will be. How old are gorge and his father now?
Answer:
Father:42
Son:18
Step-by-step explanation:
Present ages are father 48–6= 42
son = 24 ‘6 = 18
Shelley drew a scale drawing of the high school. She used the scale 5 millimeters : 3 meters. If the actual width of the parking lot is 42 meters, how wide is the parking lot in the drawing?
We can use the proportion:
measurement in the drawing / scale = actual measurement
We know that the scale is 5 millimeters : 3 meters and the actual width of the parking lot is 42 meters. To find the width of the parking lot in the drawing, we can set up the proportion as:
width in drawing / 5 millimeters = 42 meters / 3 meters
To solve for the width in the drawing, we can cross-multiply and divide:
width in drawing = (42 meters * 5 millimeters) / 3 meters
Converting millimeters to meters:
width in drawing = (42 * 5 * 10^-3) / 3
width in drawing = (210 * 10^-3) / 3
width in drawing = 70 * 10^-3 meters = 0.07 meters
So the width of the parking lot in the drawing is 0.07 meters or 70 millimeters.
can someone help me i don't know how to do this.
Graph −1/2x+1/8y=3/4.
[tex]-\cfrac{1}{2}x+\cfrac{1}{8}y=\cfrac{3}{4}\implies -\cfrac{x}{2}+\cfrac{y}{8}=\cfrac{3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8\left( -\cfrac{x}{2}+\cfrac{y}{8}\right)=8\left( \cfrac{3}{4} \right)} \\\\\\ -4x+y=6\implies y=4x+6[/tex]
Check the picture below.
(05. 01 LC)
The following data et how the pule rate of ome cattle at a farm:
65,68,69,67,69,68,65,69,65,68,67,69,68,67,67,69
Which plot bet repreent the data?
The dot plot that represents the data for pulse rate of some cattle at a farm is shown in the image below.
A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis
How to Construct a Dot Plot?
Given the data as: 65, 68, 69, 67, 69, 68, 65, 69, 65, 68, 67, 69, 68, 67, 67, 69, find the frequency of each data point in the data set as shown below:
65 - 3
67 - 4
68 - 4
69 - 5
Use dots to represent the frequency of each data point.
Thus, the dot plot that represents the data is shown in the image below.
To learn more about dot plot visit : brainly.com/question/22746300
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