[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]
Let the smaller angle be x
Then, Larger angle would be x + 4°
Case -1:❍ They are complementary angles.
This means, they add upto 90°So,
➙ x + x + 4° = 90°
➙ 2x + 4° = 90°
➙ 2x = 86°
➙ x = 86°/2 = 43°
Then, x + 4° = 47°
So, Our required answer:
Smaller angle = 43°Larger angle = 47°Case -2:❍ They are supplementary angles.
This means, they add upto 180°So,
➙ x + x + 4° = 180°
➙ 2x + 4° = 180°
➙ 2x = 176°
➙ x = 176°/2 = 88°
Then, x + 4° = 92°
So, Our required answer:
Smaller angle = 88°Larger angle = 92°✌️ Hence, solved !!
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Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.
Complete Question
Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at [tex]\alpha =0.001[/tex] is?
Answer:
There is no sufficient evidence to support the professor believe
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 18[/tex]
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 19[/tex]
The standard deviation is [tex]\sigma = 1.7[/tex]
The level of significance is [tex]\alpha = 0.001[/tex]
The null hypothesis is [tex]H_o: \mu = 18[/tex]
The alternative hypothesis is [tex]H_a : \mu > 18[/tex]
The critical value of the level of significance from the normal distribution table is
[tex]Z_{\alpha } = 3.290527[/tex]
The test hypothesis is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 18}{ \frac{1.7}{ \sqrt{15} } }[/tex]
[tex]t = 2.28[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we can see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to support the professor believe
The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate, she approximates π using 3 in both the surface area and volume formulas for a sphere.
Using this method, what value does she get for the approximate surface area of the sculpture?
Answer:
192 [tex]ft^2[/tex]
Step-by-step explanation:
Given that
Volume of spherical sculpture = 256 ft³
[tex]\pi[/tex] is used as 3.
To find:
Surface area of sculpture = ?
Solution:
First of all, let us learn about the formula for Volume and Surface Area of Sphere:
1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]
2. [tex]Surface\ Area = 4\pi r^2[/tex]
Given volume is 256 ft³.
[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]
Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:
[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]
So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].
Answer:
192
Step-by-step explanation:
Is -8 an irrational number?
yes or no
no bc it is not no no no no no no no
Daniella accidentally left the drain partially open as she began filling the bathtub. The amount of water, in gallons, pouring into the tub after x minutes is given by the function f. f( x )=12x The amount of water, in gallons, draining from the tub after x minutes is given by the function g. g( x )=6x What is the equation of a function k that gives the amount of water in the tub in this situation after x minutes?
Answer:
k(x) = 6x
Step-by-step explanation:
A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.
Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:
k(x) = f(x) - g(x)
k(x) = 12x - 6x
k(x) = 6x
Biểu diễn 1 ràng buộc trên mặt phẳng tọa độ Oxy là
Step-by-step explanation:
yah kaun se language mein likha hai aapane
In one city, 35% of all aluminum cans distributed will be recycled each year. A juice company distributes 110,000 cans. The number still in use after time t, in years, is given by
Answer: [tex]n(t) = 110000(0.35)^t[/tex]
Step-by-step explanation:
Given: Rate of of all aluminum cans distributed will be recycled each year. = 35%
= 0.35
Total cans distributed = 110,000
Now , the number of cans recycled in 1 year = 110,000 ×0.35
The number of cans recycled in 2 years = 110,000 ×0.35 ×0.35 = 110,000 ×(0.35)²
..so on
The number of cans recycled in t years = [tex]110000(0.35)^t[/tex]
Let n(t) be the number still in use after time t, in years:
Then, [tex]n(t) = 110000(0.35)^t[/tex]
The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 35 36 39 43 37 35 34 30 36 34 30 39 37 40 38 33 31 28 39 35 35 36 41 24 36 How many classes would you recommend? What class interval would you suggest? (Round up your answer to the next whole number.) Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution. It is not symmetric. It is fairly symmetric, with most of the values between 24 and 43. It is not very symmetric, but most of the values lie between 24 and 43.
Answer:
It is not symmetric, but skewed left. Data appears more to be on the left side.
Step-by-step explanation:
The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.
19/4= 4.75 It will be rounded to 5.
The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as
Class Intervals Data Frequency
20-24 24 1
25- 29 28, 1
30-34 34,30,34,30,33,31, 6
35-39 35,36,39,37,35,36,39,37, 14
38,39,35,35,36,36
40-44 43,40,41 3
The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.
As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.
The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.
algebra and trigonometry difference
Answer:
Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.
Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.
Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.
Step-by-step explanation:
Answer:
Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.
hope this answer helps u
pls mark as brainliest .-.
Find the missing side of the triangle.
Answer:
x = 2(sqrt26) or x = 10.1980390272...
Step-by-step explanation:
Right triangles can be solved using Pythagorean theorem, where the legs are squared and added together to get the hypotenuse's length squared.
If we set up the equation:
11^2 + x^2 = 15^2
which is
121 + x^2 = 225
subtract 121 from both sides
x^2 = 104
sqrt both sides
x = 2(sqrt26), or x = 10.1980390272...
Answer:
Using Pythagoras theorem
c²=a²+b²
(15)²=x² +(11)²
225=x²+ 121
-x²=121-225
-x²=-104
multiply both sides by (-1)
x²=104
x=✓104
x=10ft
. En el triángulo ABC, la medida del ángulo exterior en el vértice B es el triple de la medida del ángulo C y la mediatriz de BC corta a AC en el punto F. sabiendo que FC=12. Calcular AB.
Responder:
| AB | = 12m
Explicación paso a paso:
Verifique el diagrama en el archivo adjunto.
En el diagrama, se puede ver que el lado FC es igual al lado FB de acuerdo con el triángulo isósceles FBC.
Además, el lado FB es igual a AB ya que son paralelos entre sí.
De la declaración anterior, | FC | = | FB | y | FB | = | AB |
Esto significa | FC | = | FB | = | AB |
Por lo tanto desde | FC | = 12 m, | AB | = 12 m ya que ambos lados son iguales.
De ahí el lado | AB | se mide 12m
what is the answer to 5- -8
Answer:
13
5 - -8
When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.
A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total
Answer:
256 outcomes.
Step-by-step explanation:
Each time you flip the coin you have two possible outcomes, it can either come up with heads or tails.
You're going to flip the coin eight times so the first time you can have 2 possible outcomes, the second time you have 2 possible outcomes, the third time you have 2 possible outcomes, etc.
Since you are going to do this eight times you are going to multiply each of the outcomes, so you will have:
Possible outcomes = 2×2×2×2×2×2×2×2= 256
Thus, there are 256 different outcomes in total.
Need help please will mark brainliest
Step-by-step explanation:
Maximum = 62
Median = (34+37+39+32+48+45+53+62+58+61+60+41)/12= 47.5≈48
quartile
In increasing order
32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62
Upper quartile= (58+60)/2 = 59
Lower quartile= (37+39)/2 = 38
Minimum= 32
k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound? (1 point)
Ben and Susan are truck drivers who start at the same location. Ben drives 300 miles due west and Susan drives 160 miles due south. To the nearest mile, how far apart would they be?
Answer:
Ben and Susan will be 340 miles apart
Step by Step Solution
Step 1: We plot the problem on a graph to visualize the problem
Step 2: We notice that the problem creates a right triangle with the distance Ben and Susan travel as the legs of the right triangle
Step 3: We can use the Pythagorean Theorem: a²+b²=c² to solve the distance between Ben and Susan
Step 4: We enter the numbers into the formula
a² + b² = c²
300² + 160² = c²
90000 + 25600 = c²
115600 = c² *square root both sides
c = 340
Therefore Ben and Susan are 340 miles apart
Ben and Susan are apart by 340 miles.
After drawing diagram according to question, it is observed that a right angle triangle is formed.
The distance between Ben and Susan is represented by Hypotenuse of right angle triangle shown in attached diagram.
Applying Pythagoras theorem in right triangle shown in attached diagram.
Distance between Ben and Susan =
[tex]\sqrt{(300)^{2}+(160)^{2} } =\sqrt{90000+25600}=\sqrt{115600} =340 miles.[/tex]
Therefore, Ben and Susan are apart by 340 miles.
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Work out the values of a, b and k ? 30 points
Answer:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
Step-by-step explanation:
Note that the graph passes through the points: (0, 4), (1, 25), and (1.5, k).
The standard exponential function has the form:
[tex]\displaystyle y = ab^x[/tex]
The point (0, 4) tells us that y = 4 when x = 0. Therefore:
[tex](4) = a(b)^0[/tex]
Since anything raised to zero is one:
[tex]a=4[/tex]
Hence, our function is now:
[tex]y = 4(b)^x[/tex]
The point (1, 25) tells us that y = 25 when x = 1. By substituting:
[tex](25) = 4(b)^{(1)}[/tex]
Solve for b:
[tex]\displaystyle b = \frac{25}{4}[/tex]
Thus, our completed function is:
[tex]\displaystyle y = 4\left(\frac{25}{4}\right)^x[/tex]
To find k, simply substitute 1.5 for x. This yields:
[tex]\displaystyle y = k = 4\left(\frac{25}{4}\right)^{(1.5)}[/tex]
And evaluate. Hence:
[tex]\displaystyle \begin{aligned} k &= 4\left(\frac{25}{4}\right)^{3/2} \\ \\ &= 4\left(\left(\frac{25}{4}\right)^{1/2}\right)^3 \\ \\ &= 4\left(\frac{5}{2}\right)^3 \\ \\ &= 4\left(\frac{125}{8}\right) \\ \\ &= \frac{125}{2}\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
State the correct polar coordinate for the graph shown:
Answer:
Solution : ( - 5, 5π / 4 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.
( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.
( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.
And when r is negative ( r < 0 ),
( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.
Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.
!2,19,26 what comes nxt
Answer:
12 , 19 , 26 , 33
Explaination:Here, n+7
12+7=19
19+7=26
So,
26+7=33
Hope you understand ❣
Step-by-step explanation:
12 , 19 , 26 , ?
Given
___________
a1= 12
a2= 19
a3 = 26
d= ?
a4 = ?
––——————
we can solve this by using formula from Ap .
But for this we have to find d
As we know that
common difference(d) = a2-a1 = 19 -12
= 7
so difference after every no is 7 so
a4 = a3 + d
= 26 +7
= 33
So 33 is ur answer mate
Hope it helps
sipho's dad used 4/11 of the packet of oranges to make juice.The next day he used another 4/11 of the packet of oranges.How many eleventh were left of the pocket of oranges?
9514 1404 393
Answer:
3/11 were left
Step-by-step explanation:
A packet of oranges is 11/11. Subtracting 4/11 +4/11 = 8/11 from that leaves ...
11/11 -8/11 = (11 -8)/11 = 3/11
3 elevenths were left.
Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 71 . How old are they now?
Answer:
Lacy is 13 and Jack is 52
Step-by-step explanation:
In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.
Find X using the Angle Sum Theorem
Answer:
x = 20°
Step-by-step explanation:
So when I learned it we called it the exterior angle theorem not the angle sum theorem but here goes.
Since exterior angle = 110 Degrees,
--> The Inner 2 angles's sum = 110 Degrees
so, 70 + 2x = 110
=> 2x = 40
x = 20
x = 20°
Hope this helps!
f x equals 1 / x - 3 + 7 find the inverse of f x and its domain
Answer:
A
Step-by-step explanation:
f(x) = 1/(x-3)+7
f(x)-7=1/(x-3)
x=1/(f(x)-7)+3
f^-1(x)=1/(x-7)+3, where x≠7
The correct answer is option (a) [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].
DomainThe domain of a function is the complete set of possible values of the independent variable
How to find domain?Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]
Let
[tex]y= \frac{1}{x-3} +7[/tex]
⇒y-7= 1/x-3
⇒x-3 =1/y- 7
⇒ [tex]x= \frac{1}{y-7} +3[/tex]
hence option a is correct
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Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
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Look at the image to see the question
Answer:
Does the answer help you
The sum of the reciprocals of two consecutive even integers is 3/4
Find the two integers.
[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let one of those even numbers be x, Then other even number would be x + 2.
According to question,
⇛ Their reciprocal add upto 3/4
So, we can write it as,
⇛ 1/x + 1/x + 2 = 3/4
⇛ x + 2 + x / x(x + 2) = 3/4
⇛ 2x + 2 / x² + 2x = 3/4
Cross multiplying,
⇛ 3(x² + 2x) = 4(2x + 2)
⇛ 3x² + 6x = 8x + 8
⇛ 3x² - 2x - 8 = 0
⇛ 3x² - 6x + 4x - 8 = 0
⇛ 3x(x - 2) + 4(x - 2) = 0
⇛ (3x + 4)(x - 2) = 0
Then, x = -4/3 or 2
☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2
Then, x + 2 = 4
✤ So, The even numbers are 2 and 4.
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Which of the binomials below is a factor of this expression?
16x2 + 40xy + 25y2
16x²+40xy + 25y²
(4x+5y) (4x+5y)
(4x+5y)²
I hope I helped you^_^
PRACTICE ANOTHER A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? m (b) How much wire should be used for the square in order to minimize the total area? m
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 18 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (18 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (18 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(18 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(18 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(18 - x)/3 = 0
2x/4 - (√3/6)(18 - x) = 0
2x / 4 = (√3/6)(18 - x)
√3x = 18 - x
√3x + x = 18
x (√3 + 1) = 18
x = 18 / (1.732 + 1)
x = 18/2.732
x = 6.58
x = 7
Thus,
The length of the square must be 7 m in order to maximize the total area.
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Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 2nd longest side on quadrilateral EFGH?
Answer:
24
Step-by-step explanation:
For ABCD the three longest are:
60,40,30
60 to 40 is 20
40 to 30 is 10
so each time it's decreasing by 1/2
For EFGH the two shortest are:
6 and 12
12 to 6 is 1/2
Assuming there is a pattern
it logically would be 24
as 12(2)=24
Reflect the given triangle over
the y-axis.
[3 6 3 ]
[-3 3 3]
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex] ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]