Answer:
\( \boxed{\sf x \degree = 62 \degree} \)
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
\( \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree\)
In the given figure, the value of x is 62°.
What is angle ?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
The given angles are,
x°, 38° and 100°.
To find the value of angle x, use exterior angle property.
According to exterior angle property,
The sum of two interior angles is equal to exterior angle.
Since, 100° is the exterior angle of x and 38.
x + 38 = 100
x = 100 - 38
x = 62.
The required value of angle x is 62°.
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the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat
Answer:
450
Step-by-step explanation:
First we have to find the discount
20% of 1500 = 300
if you search up 20 x 1500/100, it would say 300
you can do that same equation in your maths book, and also by canceling out
10% vat tax
so 10% of 1500 = 150
since it is tax, we have to add it to our discount
300 + 150 = 450
450 is the answer
18. An automotive plant makes the Quartz and the Pacer. The plant has a maximum production capacity of 1200 cars per week, and they can make at most 600 Quartz cars and 800 Pacers each week. If the profit on a Quartz is $500 and the profit on a Pacer is $800, find how many of each type of car the plant should produce. Quartz PacersWhat is the maximum profit? $
First,
Let x be the Quartz and let y be the Pacer.
We can write:
x+y≤1200 ( maximum production capacity of 1200 cars per week)
We also know that:
0≤x≤600
0≤y≤800
And, the profit is given by the expression: 500x+800y
At a point, we got that : x=0 and y=800. So, if we replace this:
Profit=500x+800y ⇒ 500(0) + 800(800)= 640000
When x=600(max), y=0:
profit = 500(600) + 0 = 300000
Using (x,y) = (600,600):
Profit = 500(600)+800(600)= 780000
And, if we make x=400 and y=800:
Profit =500(400)+800(800) = 840000. This is the maximum profit, and it occurs when Quartz = 400 and Pacers = 800.
The price of an item has risen to $186 today. Yesterday it was $120 find the percentage increase
Answer:
55%
Step-by-step explanation:
180-120=66
66/120 = 0.55
55%
A line passes through the point (3, 6) and is parallel to 6x +2y = 4. What is the equation of
the line?
similar to your question hope it will helpful for you
use the two given vectors to answer the following questions
u=3i-2j and v=7i +5j
convert the vectors into component form
find the angle formed between the two vectors
Answer:
convert into components:
u=3i-2j
v=7i+5j
Step-by-step explanation:
so now we starting the question by multiplying to both vectors.
u*v = (3i * 7i) - (2j * 5j)
since i^2=1 and j^2=1
so,
u*v = 21 - 10
u*v = 11
i'm pretty sure!
Thank you!
consider the function y=-2-cos(x-pi). What effect does pi have on the basic graph?
Using translation concepts, it is found that pi is the phase shift of the graph, and since it is negative, the graph is shifted right pi units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the change is given as follows:
x -> x - pi
It means that the change is in the domain, in which pi is the phase shift of the graph, and since it is negative, the graph is shifted right pi units.
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Please help I’m really stuck on this
Answer:
120
Step-by-step explanation:
Above 44 years ----> 45 to 84.
44 - 64 range 70 are there
65 to 84 range 50 are there
Totally 70 + 50 = 120
120 residents
Which number is 150 more than 689?
Answer:
839
Step-by-step explanation:
689+150=839
Hope this helped!
A) what slope does this line have?
B) what is the slope of the line?
C) what is the y- intercept of the line?
D) what is the equation of the line?
Answer:
The slope is a positive linear slope
The slope is 2
The y-intercept is -4
The equation of this line would be: y = 2x - 4
Step-by-step explanation:
y = mx + b format
m = slope
b = y-intercept
and x and y are the x and y components
What equation models the points on the graph
Assuming that a 330-foot tall giant redwood grows vertically, if I walk a certain distance from the
tree and measure the angle of elevation to the top of the tree to be 69°, how far from the base of the
tree am I?
Round your answer to four decimal places.
I am about Number
feet away from the base of the tree.
9514 1404 393
Answer:
126.6751 feet
Step-by-step explanation:
The tangent relation can be helpful.
Tan = Opposite/Adjacent
tan(69°) = (330 ft)/(distance to base)
distance to base = (330 ft)/tan(69°) ≈ 126.6751 ft
_____
Comment on precision
It would make more sense to round to 4 significant figures. The value of a unit in the fourth decimal place is 0.0001 feet = 0.0012 inches, somewhat less than the thickness of a human hair. We know of no technology that will make a measurement of that distance to that accuracy.
4. Approximate the solution to this system of equations.
y = -2x+6
y = 4x - 1
The solution of the system of linear equations, is (1.167, 3.667).
Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,
y = -2x+6............(i)
y = 4x - 1.......(ii)
Equating the equations since the LHS is same,
-2x+6 = 4x-1
6x = 7
x = 1.167
Put x = 1.16 to find the value of y,
y = 4(1.16)-1
y = 4.66-1
y = 3.667
Therefore, the solution of the system of linear equations, is (1.167, 3.667).
You can also find the solution using the graphical method,
Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]
Hence, the solution of the system of linear equations, is (1.167, 3.667).
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Can someone help me with Writing equations of lines
Answer:
y=-1/5x-1
Step-by-step explanation:
given two points (10, -3) and (5, -2) y intercept at -1
There are different ways. One of them:
Slope: -2-(-3)/5-10=-1/5
y=mx+b
m-slope -1/5
b y-intercept (-1)
y=-1/5x-1
You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 11 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.
13 5 10 11 26 20 18 18 24 23 5
a. To compute the confidence interval use a
t
Correct distribution.
b. With 95% confidence the population mean number of visits per physical therapy patient is between
and
visits.
c. If many groups of 11 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About
percent of these confidence intervals will contain the true population mean number of visits per patient and about
percent will not contain the true population mean number of visits per patient.
For finding a 95% confidence interval:
a. To compute the confidence interval, use a t distribution with 10 degrees of freedom.b. With 95% confidence, the population mean number of visits per physical therapy patient is between 13.011 and 19.249 visits.c. About 95% of these confidence intervals will contain the true population mean number of visits per patient and about 5% will not contain the true population mean number of visits per patient.How to solve confidence interval?a) The sample mean is x = 16.13.
The sample standard deviation is s = 6.948.
The degrees of freedom are df = 10.
The critical value of t for a 95% confidence interval is t = 2.228.
The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.
The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).
b) The 95% confidence interval is (11.867, 20.393).
This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.
c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.
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1/2, 2/3, 1/4, 5/6 order from least to greatest
A 3. One-third of which number must be subtracted 7 24 from to give ? 11 55 Tumbers are such that the ratio between
Let number be x
ATQ
\(\\ \bull\longmapsto \dfrac{7}{11}-\dfrac{x}{3}=\dfrac{24}{55}\)
\(\\ \bull\longmapsto \dfrac{7}{11}-\dfrac{24}{55}=\dfrac{x}{3}\)
\(\\ \bull\longmapsto \dfrac{35-24}{55}=\dfrac{x}{3}\)
\(\\ \bull\longmapsto \dfrac{11}{55}=\dfrac{x}{3}\)
\(\\ \bull\longmapsto \dfrac{1}{5}=\dfrac{x}{3}\)
\(\\ \bull\longmapsto 5x=3\)
\(\\ \bull\longmapsto x=\dfrac{3}{5}\)
Step-by-step explanation:
hope it's helpful for you
pls mark above guy ans as brainliest
What is the median for the set of data shown below 45 23 16 78 24
The box plots represent the birth weights, in pounds, of
babies born full term at a hospital during one week.
Female Birth Weight
Complete the statements to compare the weights of
female babies with the weights of male babies.
The median female birth weight is
the
median male birth weight.
The range of female birth weight is
the
range of male birth weight.
Which birth weight measure is the same for both
genders?
5
6
7
8
9
10
11
Male Birth Weight
Answer:
Step-by-step explanation:
The median female *less than*
The range of female*less than*
Which birth weight:*minimum*
Answer:
The median female birth weight is
✔ less than
the median male birth weight.
The range of female birth weight is
✔ less than
the range of male birth weight.
Which birth weight measure is the same for both genders?
✔ minimum
Rafael's chocolate bar is 37% cocoa. If the weight of the chocolate bar is 96 grams, how may grams of cocoa does it contain? Round your answer to the nearest tenth.
You can use the weight of the chocolate bar given and find its 37% to get the weight of cocoa used in it.
The weight of cocoa in the given chocolate bar is 35.52 grams.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
Since weight of cocoa = 37% percent of chocolate bar's weight which is 96 gram,
Thus,
\(weight\) \(of\) \(cocoa=\frac{37}{100}\) × \(96=35.52\)Thus,
The weight of cocoa in the given chocolate bar is 35.52 grams.
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x^4+2x^3-12x^2+14x-5 > 0
The value of x is (-∞, -5) ∪ (1, ∞).
Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),
Solving for x,
Factors =
\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)
Therefore,
\(\left(x-1\right)^3\left(x+5\right) > 0\)
\(x < -5\quad \mathrm{or}\quad \:x > 1\)
Hence the value of x is (-∞, -5) ∪ (1, ∞).
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HELP ME!! whats the answer? no goofing around pleaze
Answer: A
Step-by-step explanation:
\(\frac{6.3\cdot \:10^8}{9\cdot \:10^2}\)
\(=\frac{6.3\cdot \:10^6}{9}\) --> Exponent rule for division, 10^8/10^2 = 10^6
= 700,000 --> In scientific notation, 7.0×10^5
Which equation gives the sum of...
S=0.2/1-8
S=1/8-0.2
S=8/0.2-1
S=8/1-0.2
Answer:
Option D
S=8/1-.2
Step-by-step explanation:
Edg
The sum of the sequence will be S = 8 / (1 – 0.2). Then the correct option is D.
What is the sum of the geometric series?Let a be the first term and r be the common ratio. Then the sum of the geometric series will be
S = a / (1 – r) if r < 1
S = a / (r – 1) if r > 1
The sum of \(\rm \Sigma_{n = 1}^{\infty} 8(0.2)^{n - 1}\).
Then the first term of the geometric sequence will be 8.
And the common difference between the successive terms will be 0.2.
The common ratio less than one, then the formula for the sum will be given as
S = a / (1 – r) if r < 1
Then the sum of the sequence till infinity will be
S = 8 / (1 – 0.2)
S = 8 / 0.8
S = 10
Thus, the sum of the sequence will be S = 8 / (1 – 0.2).
Then the correct option is D.
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Bob did chores for his neighbor. The first day he earned $8. Then he earned $10 a day for
two weeks. If he took one day off each week, how much did he earn?
Answer: $128
Step-by-step explanation: So first Bob earned 8 dollars. Then he started earning 10 dollars a day every week for 2 weeks. that would have been 148 dollars (plus the 8 dollars he earned in the beginning), but he took a break once a week, subtracting 20 dollars from his pay, giving him 128 dollars in total.
Let me know if this was helpful! :D
If you draw one card at random, what is the probability that card is a (n) Heart?
Answer:
1/13
Step-by-step explanation:
There are 52 cards in a deck of cards and 13 of them are hears
P(heart) = hearts / total
= 13/52 = 1/13
1. Find extrema and intervals of increasing and decreasing the function
\(y = \frac{ {e }^ { - (x + 2)} }{x + 2} \)
2. Find inflection points and intervals of concavity and convexity of the function:
\(y = \frac{2x - 1}{(x - 1) ^{2} } \)
The function y = (e⁻⁽ˣ⁺²⁾) / x + 2 increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but concave downwards along (-∞, 1) ∪ (1 ,∞)
Extrema and Intervals of a FunctionAn extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
The function given;
y = (e⁻⁽ˣ⁺²⁾) / x + 2
The extrema and intervals of increase or decrease of this function are
(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)
2. The inflection points and intervals of concavity and convexity of the function
y = 2x - 1 / (x - 1)² are
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) Quantifier negation.
Form the negation of the following statements. Then apply De Morgan’s law and/or conditional law, when
applicable. Negation should appear only within predicates, i.e., no negation should be outside a quantifier
or an expression involving logical connectives. Show all steps.
a) ∀x (P(x) ∧ R(x))
b) ∀y∃z(¬P(y) → Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
The negations of the given statements with the application of De Morgan's law and/or conditional law.
a) ∃x (¬P(x) ∨ ¬R(x))
De Morgan's law:
∃y ∀z(¬P(y) ∧ ¬Q(z))
b) ∃y ∀z(¬P(y) ∧ ¬Q(z))
The double negation:
∃y ¬∃z(P(y) ∨ Q(z))
c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
The conditional law:
¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:
a) ∀x (P(x) ∧ R(x))
The negation of this statement is:
∃x ¬(P(x) ∧ R(x))
Now let's apply De Morgan's law:
∃x (¬P(x) ∨ ¬R(x))
b) ∀y∃z(¬P(y) → Q(z))
The negation of this statement is:
∃y ¬∃z(¬P(y) → Q(z))
Using the conditional law, we can rewrite the negation as:
∃y ¬∃z(¬¬P(y) ∨ Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
The negation of this statement is:
¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
Using the conditional law, we can rewrite the negation as:
¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))
Applying De Morgan's law:
¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))
Simplifying the double negation:
¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))
Using De Morgan's law again:
¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))
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What is the area of the rectangle?
6 units
9 units
square units
Step-by-step explanation: 6x9=54
Answer:
6*9=54
Step-by-step explanation:
when you find the area of a rectangle you should multiply two different sides of the rectangle
9. Find the volume of a cone with a radius of 10 mm and a height of 6 mm.
O 628 mm³
O 600 mm³
O 1,884 mm 3
O 1,254 mm
Answer:
Step-by-step explanation:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume of the cone, r is the radius of the base, and h is the height of the cone.
Substituting the given values, we have:
V = (1/3)π(10 mm)^2(6 mm)
V = (1/3)π(100 mm^2)(6 mm)
V = (1/3)π(600 mm^3)
V = 200π mm^3
Using a calculator to approximate π to 3.14, we get:
V ≈ 628.32 mm^3
Therefore, the answer is O 628 mm³.
the see turtle population is modeled by equation p=400 x 5/4 power y
The value of p is 781.25.
What is a population growth?
Population Growth is defined as the increase in the number of individuals in a population is called population growth.
What is a common growth factor?
The growth factor is the ratio between the old price and the new price, once sales tax is included.
We want to know the population when y = 0, or when the number of years is zero.
Substitute the same in the equation
p = (400).\((\frac{5}{4} )^{y}\)
When y = 1 or at the 1st year, the population will be p = (400)(\(\frac{5}{4}\) ) = 500
This means that the population is increasing by a common growth factor of \((\frac{5}{4})\) .
When y = 3, or at year 3 we get the population as p = 400 \((\frac{5}{4} )^{3}\)
= 781.25
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High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country.
Their choices were as follows:
Grades 9–10—Rap: 40; Rock: 30; Country: 55
Grades 11–12—Rap: 60; Rock: 25; Country: 35
Which of the following is a correct two-way frequency table for the data?
The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:
Rap Rock Country Total
Grades 9 - 10 40 30 55 125
Grades 11 - 12 60 25 35 120
Total 100 55 90 245
Option A is therefore correct.
How to construct a two-way frequency table ?In a two-way frequency table, there will be totals for both the rows and the columns.
The totals for the rows in this instance are:
Grade 9 - 10 totals :
= 40 + 30 + 55
= 125
Grade 11 - 12 :
= 60 + 25 + 35
= 120
The totals for the columns are:
Rap totals :
= 40 + 60
= 100
Rock :
= 30 + 25
= 55
Country :
= 55 + 35
= 90
Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.
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