The length KM is equivalent to 8.61 ft.
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
Given is that JKLM is a parallelogram such that JN = 5 ft and KN = 7 ft.
We can write that -
KM² = JN² + KN²
KM² = 5² + 7²
KM² = 25 + 49
KM² = 74
KM = √74
KM = 8.61
Therefore, the length KM is equivalent to 8.61 ft.
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if x+y=7/10 and x-y=5/14 then x^2-y^2=?
Add both
2x=1x=1/2=0.5Put in first one
y=0.7-0.5y=0.2Find
x²+y²(0.5)²+(0.2)²0.25+0.040.29A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3840 MB. How many downloads of the standard version were there?
Step-by-step explanation:
s = number of standard downloads
2s = number of high-quality downloads
2.8s + 4.6(2s) = 2760
2.8s + 9.2s = 2760
12s = 2760
s = 230
The standard version was downloaded 230 times and the high-quality version was downloaded 460 times.
The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answer:
(-1,-2)
Step-by-step explanation:
Hello!
The solution to the system is at the intersection between the two graphed lines.
Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.
The coordinate is (-1, -2).
he graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units
We conclude that the graph of f(x) is the graph of g(x) translated 3 units upwards.
How do relate the graphs of f(x) and g(x)?Here we have the functions:
[tex]f(x) = log(x) + 3\\\\g(x) = log(x)[/tex]
And we want to find a relation between them.
Remember that a vertical translation of N units (the sign of N defines the direction of the translation) is written as:
[tex]f(x) = g(x) + N[/tex]
In this case, we can see that N = 3, it is positive, so the translation is upwards. (This means that the whole graph of the function f(x) is translated upwards 3 units in the coordinate axis)
Then we conclude that the relation between the graphs of the given functions is that the graph of f(x) is the graph of g(x) translated 3 units upwards.
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Question 2: 11 pts
A coin is tossed three times. Find the probability that 2 heads and 1 tail turn up in any order.
Answer:
3/8 or 0.375 or 37.5%
Step-by-step explanation:
So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3 combinations or 8 combinations. But we can also use Binomial Distribution Formula.
Binomial Distribution Formula:
[tex]P(x)=(^n_x)p^xq^{n-x}[/tex]
Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials
Combination Formula:
[tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]
So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.
So let's plug the values into the equation:
[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]
Rewrite 0.50 as a fraction
[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]
Cancel out values in fraction, and also square the fraction
[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]
Multiply fractions
[tex]P(x)=3*\frac{1}{8}[/tex]
Multiply the two values
[tex]P(x)=\frac{3}{8}[/tex]
This means the probability is 3/8 or 0.375 or 37.5%
I also provided a diagram on how to just draw out each scenario/combination
oscar bought some markers notebooks and packs of sticky notes for his office he bought the same number of markers as notebooks he bought three more packs of sticky notes than markers and notebooks combined he paid $1.05 for each marker $2.25 for each notebook, and the packs for sticky notes were $1.95. how many of each kind of office supply did oscar buy if he paid $49.05 in all?
The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.
Calculation of total office supplyThe number of markers he bought = X
The number of notebooks he bought= y
The number of sticky notes he bought= z= 3 + X+y
The amount he paid for markers = $1.05*X
The amount he paid for notebooks = $2.25*y
The amount he paid for sticky notes= $1.95 (3 + X+y)
The total amount he paid is = $49.05
That is;
$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)
$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y
$49.05 - $5.85 = 3x + 4.2y
$43.2 = 3x + 4.2y
Make X the subject of formula,
3x = 43.2 - 4.2y
X = (43.2 - 4.2y)/3
y= (43.2-3x)/4.2
z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3
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What is the length of BC?
Answer:
75/4
Step-by-step explanation:
Assuming BA and ED are parallel, we know thay the two triangles are similar.
So,
[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]
For a normal distribution, find the probability of being (a) Between −1 and +1 (b) Between 3 standard deviations below the mean and 2 standard deviations above the mean (c) More than 3.5 standard deviations away from the mean Use the Standard Normal Table in your textbook or Excel to obtain more accuracy.
Using the normal distribution, the probabilities are given as follows:
a) 0.6826 = 68.26%.
b) 0.9759 = 97.59%.
c) 0.0004 = 0.04%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The probability is the p-value of Z = 1(0.8413) subtracted by the p-value of Z = -1(0.1587), hence:
0.8413 - 0.1587 = 0.6826
Item b:
The probability is the p-value of Z = 2(0.9772) subtracted by the p-value of Z = -3(0.0013), hence:
0.9772 - 0.0013 = 0.9759.
Item c:
This probability is P(|Z| > 3.5), which is 2 multiplied by the p-value of Z = -3.5, which is of 0.0002.
Hence:
2 x 0.0002 = 0.0004 = 0.04%.
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The rectangular part of the field shown below is 160 yd long and the diameter of each semicircle 12 yd. How much will it cost to fertilize the field at 0.25 per square yard? Use π = 3.14 and round to the nearest cent.
It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Given that the field is 160 yards long and the diameter is 12 yards and charge of 1 square yard of fertilizing is $0.25.
We are required to find the total cost of fertilizing the field.
The total cost of fertilizing the field will be the product of the cost of 1 square yards and the area of the field.
When we will observe the field carefully then we will say that the diameter of the semi circle is equal to the breadth of the rectangle. There are two semicircles so we have to just find the area of 1 circle and the area of 1 rectangle.
Area of the field=Area of rectangle+Area of circle
=length* breadth+π[tex]r^{2}[/tex]
=160*12+3.14*[tex]6^{2}[/tex]
=1920+3.14*36
=1920+113.04
=2033.04 [tex]yards^{2}[/tex]
Cost of fertilzing the field=2033.04*0.25
=$508.26
Hence It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Question is incomplete as the figure which is attached should be included.
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The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table
6 steps
The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607
How to determine the regression equation?The table of values is given as:
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Next, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 305Sum of Y = 15.5Mean X = 61Mean Y = 3.1Sum of squares (SSX) = 34Sum of products (SP) = -14.5r = -0.9607Regression Equation = ŷ = bX + a
b = SP/SSX = -14.5/34 = -0.42647
a = MY - bMX = 3.1 - (-0.43*61) = 29.11471
So, the regression equation is
y = -0.42647x + 29.11471
And the correlation coefficient is -0.9607
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At a cost of R55 per box how much would it cost to tile the training room
The total cost needed to tile the training room with an area of 100 m² is R110.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:
number of box needed = 100 m² / 50 m² = 2
Total cost = R55 per box * 2 box = R110
The total cost needed to tile the training room with an area of 100 m² is R110.
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what are the restricted values for??
Considering the domain of the function, it is restricted for:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
A fraction cannot have a denominator of zero, hence:
[tex]4x^2 - 12x \neq 0[/tex].[tex]-x^2 + 5x - 6 \neq 0[/tex].We solve these two inequalities to find the restrictions, hence:
[tex]4x^2 - 12x \neq 0[/tex]
[tex]4x(x - 3) \neq 0[/tex]
[tex]4x \neq 0 \rightarrow x \neq 0[/tex]
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
[tex]-x^2 + 5x - 6 \neq 0[/tex].
[tex]x^2 - 5x + 6 \neq 0[/tex]
[tex](x - 3)(x - 2) \neq 0[/tex]
[tex]x - 2 \neq 0 \rightarrow x \neq 2[/tex].
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
Hence the correct option is:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
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Express the following function, F(x), as a composition of two functions, f and g:
Answer:
There are many different answers to this question but here is one that I thought of.
g(x)=x^2
f(x)=x/(x+4)
f(g(x))=F(x): plug in x^2 into each of the x in f(x) and and answer should equal F(x)
Step-by-step explanation:
since the function F(x) had 2 x^2 in it, I thought that g(x) could easily be x^2 that way u can subsitute the x in f(x) later to x^2 and get the right answer.
Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
The solution to the system of inequalities is given as Graph II.
A group of two or more inequalities in one or more variables is referred to as a system of inequalities.
When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilized.
What is the calculation leading to the above solution?The system of inequality,
2x - y < 4
x + y < -1
First we draw the graph of both line. So make table of each line
For line 2x - y < 4
x : -1 0 1
y : -6 -4 -2
Test point (0,0)
0 - 0 < 4
0 < 4
True (Shade towards origin)
For line x + y < -1
x : -1 0 1
y : 0 -1 -2
Test point (0,0)
0 + 0 < -1
0 < -1
False (Shade away from origin)
Plot the points graph.
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Full Question:
The graphs associated with the question are attached.
If you spend $50 (including shipping) at an online store, you recieve a $10 gift card. You want to purchase CDs that cost $12 each. If shipping cost $5, write and solve an inequality to find the number of Cds you must to receive the giftcard.
Four CDs must be bought to receive a gift card from an online store.
How to determine the least number of CDs to be bought to receive a gift card
The total costs are equal to the sum of the shipping cost and the total related to the number of acquired CDs (n). The number of gift cards (m) is equal to the total costs divided by minimum spent money, that is, $ 50. We need to solve the following inequation to find the minimum quantity of CDs:
(12 · n + 5)/50 > 1
12 · n + 5 > 50
12 · n > 45
n > 45/12
n > 3.75
Four CDs must be bought to receive a gift card from an online store.
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Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
This is multiple choice pls help
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
What is the probability of flipping a coin once and getting heads if you have gotten 5 tails in a row before that?
a. 1/32
b. 1/5
c. 1/4
d. 1/2
Answer:
Answer is..... D
Step-by-step explanation:
every single flipping may two results, head or tail.So last one has equal chance.
Has a base of 3, is reflected over the y-axis, has a horizontal shift right by 5 and an asymptote of y=-3
The equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
How to determine the equation?An exponential equation is represented as:
y = b^x
Where b represents the base.
The base is 3.
So, we have:
[tex]y = 3^x[/tex]
When reflected over the y-axis, we have:
[tex]y = 3^{-x[/tex]
When shifted right by 5 units, we have:
[tex]y = 3^{-x -5[/tex]
Lastly, the function has an asymptote of y=-3
So, we have:
[tex]y = 3^{-x -5} - 3[/tex]
Hence, the equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
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Hurry please help!!!!
Determine which statement is true about the zeros of the function graphed below.
An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units.
A.
Function f has exactly two complex solutions.
B.
Function f has exactly one real solution and no complex solutions.
C.
Function f has exactly two real solutions.
D.
Function f has one real solution and one complex solution.
Answer:
A. Function f has exactly two complex solutions.
Step-by-step explanation:
The function will have real solutions where the graph crosses the x-axis. It will always have a total number of solutions equal to its degree. The ones that are not real are complex.
ApplicationThe graph has its vertex above the x-axis and extends upward from there. It never crosses the x-axis, so there are no real solutions. That means both solutions are complex.
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''. Which of the following statements is true for ΔABC and ΔA''B''C''?
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.
Hence:
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
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Melissa is driving at a constant speed. She catches up to a minivan half a mile ahead of her that is
moving at 50 miles per hour in 50 seconds. How many miles per hour is the speed of the sports
car?
The speed of the sports car is 53.6 miles per hour
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Distance covered by Melissa = 0.5 miles + Distance covered by minivan
Let speed of Melissa be x miles per second
x. 50 = 0.5 + 50x50/3600
x .50 = 0.5 + 25/36
x = 1/100 + 1/72
x = 0.001 + 0.013
x = 0.014 miles per second
x = 3600 x 0.014 = 53.6 miles per hour
Thus the speed of the sports car is 53.6 miles per hour
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A text message plan costs $9 per month plus $0.39 per text. Find the monthly cost for x text message The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.) *
Answer:
The monthly cost = $9 + $0.39x
Step-by-step explanation:
The lengths of the sides of a pentagons are 2'', 6'', 10'' , 14'', and 24''. calculate the lengths of the sides of a similar pentagon if the shortest side is 5'' .
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"How to get the lengths of the sides of a similar pentagon?
All the measures must be multiplied by the same scale factor to get a similar pentagon.
If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:
5" = k*2"
5"/2" = k = 2.5
Then the scale factor is 2.5
To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"If you want to learn more about similar figures:
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The measure of dispersion that measures how much the data differ from the mean is called the.
The measure of dispersion that measures how much the data differ from the mean is called the standard deviation.
What is standard deviation?Standard deviation is a statistical measure of dispersion as opposed to the measure of central tendency like mean, median and mode.
The standard deviation is a measure of how spread out data values are around the mean.
It is defined as the square root of the variance and represented with the Greek letter σ.
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Rational expressions are often used in combining rates of work.
Rational expressions are often used in combining rates of work. Therefore, it's true.
What is rational expression?It should be noted that a rational expression is simply defined by a rational fraction.
They're are used in combining rates of work. Fir example, if Mr John performs 1/2 of his work and does 1/3 on another day. This can be expressed as:
= 1/2 + 1/3
= 5/6
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Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
Using the binomial distribution, we have that:
The mean is of [tex]\mu = 6[/tex].The standard deviation is of [tex]\sigma = 2.05[/tex].What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]\mu = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are:
n = 20, p = 0.3.
Hence:
[tex]\mu = np = 20 \times 0.3 = 6[/tex][tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20 \times 0.3 \times 0.7} = 2.05[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
please give answer to these fractions give STEPS
no scam 30 points + BRAINLIEST
1/2 × 3/5 ÷ 9/15 - 6/4 ÷ 4/1
Answer:
1/8
Step-by-step explanation:
Look at the screen shots
will give brainliest !!!!
Finding the inverse function of [tex]f(x) = 5\sqrt{x + 3} - 2[/tex], it is best described by graph B.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
[tex]f(x) = 5\sqrt{x + 3} - 2[/tex]
[tex]y = 5\sqrt{x + 3} - 2[/tex]
Exchanging x and y:
[tex]x = 5\sqrt{y + 3} - 2[/tex]
Working through the function to isolate y:
[tex]5\sqrt{y + 3} = x + 2[/tex]
[tex]\sqrt{y + 3} = \frac{x + 2}{5}[/tex]
[tex](\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2[/tex]
[tex]y + 3 = \frac{(x + 2)^2}{25}[/tex]
[tex]y = \frac{(x + 2)^2}{25} - 3[/tex]
[tex]f^{-1}(x) = \frac{(x + 2)^2}{25} - 3[/tex]
Which is best represented by graph B.
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