The histogram for the stickers from the small package is distributed as follows:
Normally.
How to obtain the distribution of the histogram?To obtain the distribution of the histogram, we must correctly identify the mean and the median of the distribution.
Hence the distribution is defined as follows:
Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedThe ordered distribution is given as follows:
13, 15, 18, 19, 22, 24.
Hence the median is of:
(18 + 19)/2 = 18.5.
The mean is of:
(13 + 15 + 18 + 19 + 22 + 24)/6 = 18.5.
They are equal, hence the histogram is normal = symmetric;
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Brenna is considering which brand of cereal to buy. She knows some brands contain a lot of sodium, or salt, which she is trying to avoid. Crispee Flakes has 0.23 grams of sodium per cup. Corn Puffers has 0.28 grams of sodium per cup. Energy Doodles has 0.26 grams of sodium per cup.
How many of the brands have less than 1\4
of a gram of sodium per cup?
Using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Basic arithmetic operations or calculations, such as addition, subtraction, multiplication, and division, are covered in Fundamentals of Mathematics and are concepts we learn in primary school.
Students will eventually study fundamental ideas like algebra, geometry, factors, ratios, etc. in upper classes.
So, we have that:
Crispy Flakes have 0.23 grams of sodium per cup.
Corn Puffers have 0.28 grams of sodium per cup.
Energy Doodles have 0.26 grams of sodium per cup.
Now, brands that have less than 1/4 gram of sodium per cup:
100 * 1/4 = 25
Then, 1/4 of 1.00 = 0.25
0.23 > 0.25
Therefore, using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.
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The maximum resistance for a new spark plug wire is 840 ohms per inch. A 25-in. wire had a resistance of 20,250 ohms. Does this fall within the acceptable limit?
Answer:
Yes
Step-by-step explanation:
Let's calculate the resistance of one inch for our wire and compare it with the maximum:
20250 / 25 = 810 Ohm
810 < 840 ? Yes!
Yes, this is within the acceptable limit. Wire can be used.
Here is a completed box challenge puzzle. If you look at it closely, you'll see that the umber at the top is the product of the two numbers on the left and right, and the number at the bottom is the sum of the two numbers on the left and right. *** 18 15 3x15=45 3+15= 18
The product of the two numbers 45, is the highest number, and the sum of the two numbers 18, is the lowest number follow symmetry .
what is symmetry ?When an object is split into two identical, mirrored components, it is said to have symmetry in mathematics. What does "axis of symmetry" refer to? An "axis of symmetry" is a fictitious line that has the ability to fold or split a thing into two identical mirror parts. Any object is symmetrical if two parts fit together. To determine the shape's symmetry, draw a mirror line across the center, making sure that all parts are identical. Another way of putting it is that symmetry is when two objects are facing one another or when two items have mated components that circle around an axis.
given
The two numbers on the left and right are multiplied together to create the number at the top.
The two digits on the left and right add up to the number at the bottom.
middle number + top number = 3 * 15 = 45 ( top number )
3+15 Equals 18 ( lowest number ) ( bottom number )
The product of the two numbers on the left and right, 45, is the highest number, and the sum of the two numbers on the left and right, 18, is the lowest number.
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The complete question is :-
Here is a completed box challenge puzzle. If you look at it closely, you'll see that the number at the top is the product of the two numbers on the left and right, and the number at the bottom is the sum of the two numbers on the left and right.
which of the following tests analyze the difference between the means of two independent samples?
a. Correlated T Test
B. T test for independent groups
c. sign test
d. all the above
T-test for independent groups analyzes the difference between the means of two independent samples. Hence, option B is the correct answer.
B. T-test for independent groups is the test that analyzes the difference between the means of two independent samples. This test assumes that the two samples are drawn from populations that have normal distributions and that the variances of the two populations are equal. The T-test for independent groups compares the means of the two samples and determines if there is a statistically significant difference between them. This test is also known as a two-sample T-test or independent T-test.
The other options A and C are not the correct ones.
A. Correlated T-Test is used when comparing means of dependent samples, it's also known as a dependent t-test
C. Sign test is a non-parametric test that is used to compare two dependent samples.
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Select the correct answer. The given equation has been solved in the table. Step Statement 1 2 3 x − 9 = − 13 2 2 3 x − 9 + 9 = − 13 + 9 3 2 3 x = − 4 4 3 2 ⋅ 2 3 x = 3 2 ⋅ ( − 4 ) 5 x = − 6 In which step was the addition property of equality applied? A. step 2 B. step 3 C. step 4 D. The addition property of equality was not applied to solve this equation.
In step 2 the addition property of equality was applied. Thus, the correct option is A.
What is addition property of equality?When the same amount is added to both sides of an equation, according to the addition property of equality, the equation remains the same. An equation that reads as A = B still holds true if a number x is added to both sides. The equation is A + x = B + x in mathematics.
When the same amount is added to both sides of an equation, the equation remains true, which is known as the addition property of equality. One of the basic characteristics of equality in mathematics, it is also very significant. The division, multiplication, and addition properties of equality are the additional characteristics.
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Full question:-
Select the correct answer. The given equation has been solved in the table. (see attachment)
Solve equation 7x+8=43
x = 5
7x+8=43
First, we want to separate the variable, so we subtract 8 from both sides:
7x=35
Then we divide both sides by 7 to get x all by itself:
x=5
This is because 35/7=5
Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does
the line with equation y = x + 1 intersect the circle with radius 4 and center (0, 1)?
The point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center [tex](0,1)[/tex] is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.
How to find the point in the first quadrant?The equation of a circle with center (h, k) and radius r is:
[tex](x - h)^2 + (y - k)^2 = r^2.[/tex]
The equation of the line is given as [tex]y = x + 1[/tex].
Given the center of the circle is (0,1) and the radius is 4, the equation of the circle is [tex](x-0)^2 + (y-1)^2 = 4^2[/tex]
This can be simplified as [tex]x^2 + y^2 - 2y + 1 = 0[/tex]
Now we can substitute [tex]y = x + 1[/tex] in the circle equation:
[tex]x^2 + (x+1)^2 - 2(x+1) + 1 = 0\\x^2 + x^2 + 2x + 1 + 2x + 1 = 0\\2x^2 + 4x = -2\\x^2 + 2x = -1\\(x+1)^2 = 0\\x = -1[/tex]
Now that we have the value of x, we can substitute it in the equation [tex]y = x + 1[/tex] to find the corresponding y value:
[tex]y = -1 + 1\\y = 0[/tex]
So, the point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center (0,1) is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.
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Subtract.
(5y − 3) - (-2y - 7) =
Greatest common factor 10x2+28x-6
Answer:
The equation 10x2+28x-6 can be simplified using a few steps. Firstly, the greatest common factor (GCF) needs to be identified. The GCF of this equation is 2, which can be identified by factoring out the coefficient of the first term, 10. After factoring out 2, the equation becomes -3 + -14x + 5x2.
The next step is to factor the remaining polynomial. This can be done by multiplying the coefficient of the first term by the constant and then finding two factors whose sum equals the coefficient of the middle term. In this case, the multiplication of the coefficient of the first term (5) and the constant (-3) gives -15. Then, two factors of -15 whose sum adds up to -14 must be found. These factors are -15 and 1. Therefore, the equation can be rewritten as 5x2 - 15x + 1x - 3.
Afterwards, the four terms in the equation can be added up in pairs, pulling out like factors. This results in (5x+1)(x-3), which is the desired factorization. Finally, the expression can be written as 2(x-3)(5x+1). Thus, the GCF of 10x2+28x-6 is 2.
Step-by-step explanation:
Answer:
2 is the answer .
if u r not sure u can try doing it yourself
the answer will be the same as I told
The higher your credit score, the
A) lower your savings interest rate
B) higher your car loan rate
C) lower your mortgage interest rate
D) higher risk you are to a creditor
Answer: c lower your mortgage interest rate
Step-by-step explanation
The higher your credit score, the less risk you represent for a lender.
My dad taught me this.
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.
What is the actual area of the park? Show how you know.
The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure? Show your reasoning.
Answer:
Step-by-step explanation:
L = 4 in real life = 4*30 =120 miles
W=6 in real life =6*30=180 miles
actual area = 120*180 = 21600sq miles
to fit into a 6sq in paper it'll need to shrink to 2x3 inches, 1/2 of what it was before, so the scale becomes 1" for every 60miles.
Solve for y. Assume the equation has a solution for y. py + qy = -4y + 8
Answer:
y = [tex]\frac{8}{p+q+4}[/tex]
Step-by-step explanation:
py + qy = - 4y + 8 ( add 4y to both sides )
py + qy + 4y = 8 ← factor out y from each term on the left side
y(p + q + 4) = 8 ← divide both sides by p + q + 4
y = [tex]\frac{8}{p+q+4}[/tex]
1) Health officials routinely check sanitary conditions of restaurants. Assume you visit a popular tourist spot and read in the newspaper that in 3 of every 7 restaurants checked, there were unsanitary health conditions found. Assuming you are planning to eat out 10
times while you are there on vacation, answer the following questions:
a) How likely is it that you will eat at three restaurants with unsanitary conditions?
b) How likely is it that you will eat at 4 or 5 restaurants with unsanitary conditions?
c) Explain how you would compute the probability of eating in at least one restaurant with unsanitary conditions. Could you use the complement to solve this problem?
d) What is the most likely number to occur in this experiment?
e) How variable will the data be around the most likely number?
f) Is this is a binomial distribution?
g) If it is a binomial distribution, does that mean that the likelihood of success is always
50% since there are only two possible outcomes?
a) The probability of eating at a restaurant with unsanitary conditions is 3/7. If you plan to eat at 10 different restaurants, the probability of eating at exactly 3 restaurants with unsanitary conditions is given by the binomial probability formula:
P(X = 3) = (10 choose 3) * (3/7)^3 * (4/7)^7 = 120 * (0.42857)^3 * (0.57143)^7 = 0.1437
So, the likelihood of eating at three restaurants with unsanitary conditions is 14.37%.
b) The probability of eating at 4 or 5 restaurants with unsanitary conditions can be found by summing the binomial probabilities for each case:
P(X = 4) = (10 choose 4) * (3/7)^4 * (4/7)^6 = 210 * (0.42857)^4 * (0.57143)^6 = 0.1735
P(X = 5) = (10 choose 5) * (3/7)^5 * (4/7)^5 = 252 * (0.42857)^5 * (0.57143)^5 = 0.1428
P(X = 4 or X = 5) = P(X = 4) + P(X = 5) = 0.1735 + 0.1428 = 0.3163
So, the likelihood of eating at 4 or 5 restaurants with unsanitary conditions is 31.63%.
c) The probability of eating in at least one restaurant with unsanitary conditions can be found by subtracting the probability of eating in no restaurants with unsanitary conditions from 1. The probability of eating in no restaurants with unsanitary conditions is given by the binomial probability formula:
P(X = 0) = (10 choose 0) * (3/7)^0 * (4/7)^10 = 1 * (1) * (0.57143)^10 = 0.0139
P(X >= 1) = 1 - P(X = 0) = 1 - 0.0139 = 0.9861
So, the probability of eating in at least one restaurant with unsanitary conditions is 98.61%.
d) The most likely number is 3, as it has the highest probability of occuring.
e) The data is not very variable around the most likely number, as the probability of the other numbers is relatively low.
f) Yes, this is a binomial distribution as the experiment has only two possible outcomes, "success" (eating at a restaurant with unsanitary conditions) or "failure" (eating at a restaurant with sanitary conditions) and the number of trials is fixed (10)
g) No, the likelihood of success is not always 50% in a binomial distribution. The probability of success is given by the proportion of successful trials in the population, which in this case is 3/7.
2. The graph of the basic quartic function m(x) = x is shown. a. The function h(x) = 3x - 6)" is a transformation of m(x). Complete the table. Reference Corresponding Points on m(x) Points on h(x) (-2, 16) (-1,1) (0,0) (1,1) (2.16) b. Graph the function h(x) = (x - 6)* on the same coordinate plane as mix). c. Is the function h(x) even, odd, or neither? Explain your reasoning.
1. The complete table is shown below.
2. The graph is attached below.
3. the function h(x) is an odd function.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
m(x)=[tex]x^4[/tex]
and, h(x)= [tex]1/4 (x-6)^4[/tex]
So, the -6' in the h(x) there is Horizontal transformation on right side by 6 units, i.e., (x, y)--->(x +6, y)
and, 1/4 in h(x) shows there is Vertical stretch in h(x).
So, (x, y)--->(x, y/4)
Now, Points on m(x) points on h(x)
(x, y) (x+6, y/4)
(-2, 16) (4, 4)
(-1, 1) (5, 1/4)
(0, 0) (6, 4)
(2, 16) (8, 4)
2. The graph is attached below.
3. Replace h(x) by h(-x) we get
h(-x) = [tex]1/4 (x-6)^4[/tex]
h(-x) = [tex]1/4 (-x-6)^4[/tex] will give an odd function.
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Lara puts pictures of the same size on each page in a scrapbook.
. She has 48 large pictures, and each page can fit 3 large pictures.
. She has 24 small pictures, and each page can fit 6 small pictures.
Which equation shows how to find p, the greatest number of pages Lara can fill in the scrapbook?
OA. 48 24+6÷3=p
OB. 48-6 +24÷3=p
OC. 48 x 3 + 24 x 6=p
OD.
48+3+24+6=p
Reset
Next
Answer:
d
Step-by-step explanation:
I think the a answer is d
Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–21
–4
11
27
The value of b in the Line JK passes through points J(–4, –5) and K(–6, 3) is
b = –21
How to find the value of bThe graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The slope, m of the linear function is calculated using the points J(–4, –5) and K(–6, 3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (3 + 5) / (-6 + 4)
m = (8) / (-2)
m = -4
equation passing through point K(–6, 3)
(y - y₁) = m' (x - x₁)
y - 3 = -4(x + 6)
y - 3 = -4x - 24
y = -4x - 24 + 3
y = -4x - 21
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Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in a row so that the product of any two adjacent numbers is even or a multiple of 3
Answer:
3,10,8,5,4,1,7,2,9,6
Step-by-step explanation:
Use the number line below, where RS=4y+4, ST=3y+8, and RT=54.
a. What is the value of y?
b. Find RS and ST.
The value of y is 6 and the length of RS and ST are 28, 26 respectively.
What is a line ?
line is a straight one dimensional figure having no thickness is called as the line.
Given , number lines
RS = 4y+4
ST = 3y+8
RT = 54
From the given figure ,
RS+ST = RT
4y+4+3y+8 = 54
7y+12 = 54
7y = 54-12
7y = 42
y =42/7
y = 6
The RS = 4y+4 = 4*6+4 = 28
ST = 3y+8 = 3*6+8 = 26
Hence, The value of y is 6 and the length of RS and ST are 28, 26 respectively.
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You spend 100 minutes in 2 classes. How many minute will you spend in 3 classes?
Answer:150
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
since half of 100 is 50, 2 classes will have 50 minutes. If you add 100+50 you get 150. So therefore ur answer is 150!
A sample proportion of 0.62 is found. To determine the margin of error for this statistic, a simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62.
The minimum sample proportion from the simulation is 0.73, and the maximum sample proportion from the simulation is 0.97.
What is the margin of error of the population proportion using an estimate of the standard deviation?
A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.
What is margin of error?Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error.
A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
However, the official definition goes a little bit beyond. The range of values in a confidence interval that lie below and above the sample statistic is known as the margin of error.
The confidence interval is a tool for displaying the level of uncertainty surrounding a certain statistic (i.e. from a poll or survey).
According to our question-
Because the sample proportions' range is 0.97-0.73 = 0.24
Calculate the standard deviation:
Range = 6* (s-bar)
= 0.24
s-bar = 0.04
S/Sqrt (100) then equals 0.04
and s = 0.4
S.D = 0.04 + 0.04
= 0.08
Hence, A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.
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A person invested $230 in an account growing at a rate allowing the money to double
every 7 years. How long, to the nearest tenth of a year would it take for the value of
the account to reach $390?
It would take 28.6 years for the value of the account to reach $390.
The equation reads A(t) = Ao (2) Where
A(t) = 3902, Ao = 230, and t =?, k = 7 years
Hence, 3902 = 230 × (2)
^t/7
We divide 230 on both sides (3902/230 = 230) (2)
^t/7/230
16.965217391 = (2) (2)
^t/7
Calculate the ln of both sides:
16.965217391 = ln (2)t/7
ln 16.965217391 = t/7 ln (2) (2)
In 16.965217391/ln 2 = t/7
t = 4.0874628413× 7
t = 28.612239889 years
Approximately = 28.6 years
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Find the x intercepts of the graph y= 2/pie squared
The x-intercept is the point where the graph of a line intersects the x-axis. The y-intercept is the point where the graph of a line intersects the y-axis.
What is the formula for x-intercept form?Take into account a line with the slope intercept form y = mx + c, an intercept of (c, 0), and a slope of m. To find the x-intercept, enter y = 0 in the equation.Yb = m (xa), where m is the line's slope and (a,b) is a point on the line, is the point-slope form of a straight line. You may find the line's x-intercept by entering y = 0 and x-intercept = (amb)/m.Where the line crosses the x-axis is known as the x-intercept. Because the point won't be on the x-axis if y doesn't equal 0, you must always use a value of 0 for y when calculating the x-intercept.Given data :
y = ( 2 / π )²
y = 2² / π²
y = 4 / π²
Here i attached the graph of x interception
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1
1
the graph.
a. y = 3x - 2
b. y = 3x-2
c. y = 3x+2
d. y = 3x + 2
e. y = ( )* - 2
Answer:
e
Step-by-step explanation:
Which of the following sets of numbers could represent the three sides of a triangle? { 12 , 27 , 39 } {12,27,39} { 12 , 18 , 29 } {12,18,29} { 5 , 9 , 16 } {5,9,16} { 9 , 24 , 33 } {9,24,33}
The sets of numbers that could represent three sides of a triangle is given as follows:
{12, 18, 29}.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
Hence the set in this problem is given as follows:
{12, 18, 29}.
The larger measure is of:
29.
The sum of the two smaller measures is given as follows:
12 + 18 = 30.
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Which is the rate of change for the interval between –6 and –3 on the x-axis?
The rate of change for the interval between –6 and –3 on the x-axis is; 2
How to find the rate of change of the graph?To find the rate of change for the interval between –6 and –3 on the x-axis, we will first identify the ordered pairs at those two points. The ordered pairs from the graph would be (3, -2) and (6, 4).
Using the slope formula with those two points, we can find the rate of change as;
slope; m = (y₂ - y₁)/(x₂ - x₁)
m = (4 + 2)/(6 - 3)
m = 6/3
m = 2
This value of m represents the rate of change
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-2 is the answer i cant exaplin it bc i jsut guessed and got it right
HOW FAR FROM HOME PLATE
TO SECOND BASE?
The catcher at home plate often needs
to make a quick throw to second base.
According to the measurements shown on
the baseball diamond, the exact distance
is √16,200 feet. How far is that in decimal
form? (Round to the nearest hundredth.)(please hurry )
The exact distance from home plate to second base on a baseball diamond is √16,200 feet. To convert this distance to decimal form, we must first understand the concept of a square root and how it relates to the distance formula.
A square root is a mathematical operation that represents the value whose square is equal to a given value. In this case, the square root of 16,200 is equal to the distance from home plate to second base.
To find the decimal form of the square root of 16,200, we can use a calculator or we can use the long division method. With a calculator, we simply input √16,200, which will give us the result of 126.84955592153876
To round to the nearest hundredth we look at the hundredths digit (8) if it's 5 or above we round up otherwise we round down so 126.84955592153876 rounded to the nearest hundredth is 126.85
The distance from home plate to second base on a baseball diamond is 126.85 feet in decimal form.
It's worth noting that the distance from home plate to second base is a critical aspect of the game and it's really important for the catcher to make a quick and accurate throw to second base.
22. Represent Real-World Problems The railroad
tracks meet the road as shown. The town will
allow a parking lot at angle Jif the measure of
angle Jis greater than 38: Can a parking lot be
built at angle? Why or why not?
++++
Green
50°
Park
Ave.
Ave.
On observing the provided question, we can say that the the provided equation f(x) = is the basic cubic function.f(x) = 8100
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
basic cubic function is = f(x) = x^2
x = 90
f(x) = 8100
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On solving the provided question, we can say that It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
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????What’s the answer??
one of the most common forms of the equation of lines called slope-intercept form along with derivation.
What is the slope-intercept for the linear function?The linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:
(y – y1) = m(x – x1)
Here, (x1, y1) = (0, c)
Substituting these values, we get;
y – c = m(x – 0)
y – c = mx
y = mx + c
Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
Slope Intercept Form Formula
As derived above, the equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
Usually, x and y have to be kept as the variables while using the above formula
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A nurse sets an intravenous
fluid drip rate at 1000 mL
every 8 hr. How much fluid would the patient receive in
3 hr? Step by step (applications of rational equations)
Answer:
375 mL
Step-by-step explanation:
Let x = Amount of fluid patient receives in 3 hours
Fluid drip rate: 1000 mL --------- 8hr
x --------- 3 hr
Cross multiplication is applied:
(x).(8 hr) = (1000 mL).(3hr)
x = [(1000mL).(3 hr)]/ (8 hr)
x = 375 mL
Determine the dimensions of Nul A and Col A for the matrix shown below. A = [1 0 0 0 4 0 0 0 -5 1 0 0 2 -4 1 0 -4 -3 -3 0 6 -1 -4 0 -1 -6 6 0] The dimension of Nul A is and the dimension of col A is
The dimension of Nul A = 0 and the dimension of Col A = 4. means that the matrix A has no solutions for the homogeneous equation A × x = 0, which means that its null space is trivial, and it has 4 linearly independent columns, which means that its column space is 4-dimensional.
In other words, it is the number of linearly independent vectors x that satisfy the equation Ax = 0.
The dimension of Col A, also known as the column space of the matrix A, is the dimension of the subspace spanned by the columns of the matrix A. In other words, it is the number of linearly independent columns of matrix A.
In general, it is not possible to determine the dimensions of Nul A and Col A of a matrix just by looking at its elements. In order to find the dimensions, we need to perform the row echelon form or reduced row echelon form of the matrix to find the rank and the nullity which is the difference in the number of columns and rank.
For the specific matrix A provided, the rank of the matrix is not provided, thus we can not determine the dimension of the Nul A and Col A.
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