Answer:
D) 65°
Step-by-step explanation:
Use Snell's Law
[tex]n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ[/tex]
Thus, the angle of incidence is D) 65°
What are the first three terms of a geometric sequence in which (picture below) and the common ratio is 5?
Answer:
5, 10, 15
Step-by-step explanation:
the increase in the sequence is 5 so since it starts from 0 which you can find out because 25 is the 5th sequence and that means that +2*5 =25 . x=0
0+ 5 = sequence 1
0+ 5+5 = seq 2
0+5+5+5= seq 3
Mika bought 9 rolls of film to take 180 pictures on a field trip. Some rolls had 36 exposures and the rest had 12 exposures. How many of each type did Mika buy
The number of each type Mika bought =x = 6.8 rolls; y= 2.2 rolls.
Calculation using ratioThe number of rolls of film Mika bought = 9 rolls
The number of rolls that had 36 exposures = x
The number of rolls that had 12 exposures = y
The total number of exposures = 36 + 12 = 48
To find the exposure by one roll = 48/9 = 5.3
If one roll = 5.3 exposure
x roll = 36 exposure
Make x roll the subject of formula,
x roll = 36/5.3 = 6.8 rolls
If one roll = 5.3 exposurey roll = 12 exposure
Make y roll the subject of formula,
y = 12/5.3 = 2.2 rolls
Therefore, the number of each type Mika bought = x = 6.8 rolls; y= 2.2 rolls.
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Assuming that no denominator equals zero, which is equivalent to? r^2-r-6/(r-2)(r-3)
The given expression is [tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]. the option C [tex]\dfrac{ (r+2)}{(r-2)}[/tex]is correct.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]
By solving the numerator
[tex]r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)[/tex]
Put the solution in the above equation
[tex]\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}[/tex]
[tex]\dfrac{ (r+2)}{(r-2)}[/tex]
Therefore, the option C is correct.
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On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 3, 3), (1, 4), (1, negative 4), (2, negative 4), (2, negative 2).
How many points need to be removed from this graph so that it will be a function?
1 point
2 points
3 points
0 points
Three points must be removed from this graph so that it will be a function
How to determine the number of points?The points are given as:
(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).
For a set of point to represent a function;
Each x coordinate must point to only one y coordinate
From the given points, we have the following highlights:
The x value -3 has two y values (2 and 3)The x value 1 has two y values (4 and -4)The x value 2 has two y values (-4 and -2)In the above highlights, one point each must be removed.
This means we have a total of 3 points
Hence, three points must be removed from this graph so that it will be a function
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Answer:
C. 3 points
Step-by-step explanation:
Compute the indicated power by using de Moivre's theorem.
[tex]\sqrt[4]{1-i\sqrt{3} }[/tex]
please hurry
I assume you know that there are n total n-th roots for any non-zero complex number.
(If you're looking for "the" principal root, you'll have to specify which branch you're calling the principal branch of the n-th root function.)
Start by writing [tex]1 - i\sqrt3[/tex] in exponential form. We have modulus/magnitude
[tex]|1 - i\sqrt3| = \sqrt{1^2 + (-\sqrt3)^2} = \sqrt4 = 2[/tex]
and [tex]1-i\sqrt3[/tex] lies in the fourth quadrant of the complex plane, so its argument is
[tex]\arg(1-i\sqrt3) = \tan^{-1}\left(-\sqrt3\right) = -\dfrac\pi3[/tex]
Then the exponential form is
[tex]1 - i \sqrt3 = 2 \exp\left(-i\dfrac\pi3\right)[/tex]
(where [tex]\exp(x) = e^x[/tex], if you're not familiar with the notation)
By de Moivre's theorem, we have the fourth roots
[tex]\sqrt[4]{1 - i\sqrt3} = \sqrt[4]{2} \exp\left(i \dfrac{-\frac\pi3+2k\pi}4\right)[/tex]
where [tex]k\in\{0,1,2,3\}[/tex], so that we have a choice of
[tex]\sqrt[4]{1 - i\sqrt3} = \begin{cases} \sqrt[4]{2} \exp\left(-i\dfrac\pi{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{5\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{11\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{17\pi}{12}\right) = \sqrt[4]{2} \exp\left(-i\dfrac{7\pi}{12}\right) \end{cases}[/tex]
(I rewrote the exponent to the last root just to be consistent about having each argument between -π and π radians)
If you want these in rectangular form (a + bi), sorry, that's where I draw the line; it can be done with simple trigonometry and algebra, but it's rather tedious, and the exponential forms are far more compact.
Factorise completely
12y² + 4y
Step-by-step explanation:
[tex]12y^{2} + 4y \\4y( \frac{12y^{2} }{4y} + \frac{4y}{4y} ) \\ 4y(3y + 1)[/tex]
Step-by-step explanation:
12y²+4y
divide both sides by 4
therefore,
3y²+y
y(3y+1)
kantabai bought 1/2 kg tea and 5 kg sugar from a shop .she paid rupess 50 as return fare for rickshaw .total expense was rupess 700 .then she realised that by ordering online the goods can be bought with free home delivery at the same price .so next month she placed the order online for 2 kg tea and 7 kg sugar she paid rupess 880 for that .find the rate of sugar and tea per kg
Answer:
40 Rs per kg.
Step-by-step explanation:
solution
Let the rate of tea be x Rs per kg and that of sugar be y Rs per kg.
When Kantabai bought the items by going to the shop,
3/2x+5y+50=700
⇒3x+10y=1300....(I)
When Kantabai bought the items online then
2x+7y=880......(II)
Multiplying (I) with 2 and (II) with 3 we get
6x+20y=2600......(III)
6x+21y=2640.......(IV)
eq.(IV)−(III)
y=40
Putting the value of y =40 in (II)
2x+7(40)=880
⇒2x=880−280=600
⇒x=300
Thus, tea is at 300 Rs per kg and sugar is 40 Rs per kg.
A family reunion planning committee with 8 members plans to elect 3 officers - a president, treasurer, and historian. if each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled
Using the permutation formula, it is found that these offices can be filled in 336 ways.
There are different roles, hence the order in which the people are chosen is important, hence the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
3 people will be chosen from a set of 8, hence the number of ways is given by:
[tex]P_{8,3} = \frac{8!}{5!} = 336[/tex]
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If you use 1/8 lb of ham on each sandwich you make, how many
sandwiches
can you make from a 22 lb ham?
Represent -5 / 4 and 5 / 4 on number line
Answer:
Image included:
Step-by-step explanation:
A triangle with an area of 60 square inches has a height that is 16 less than 6 times its base.
Find the base and height, in inches, of the triangle
Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
Which set represents the same relation as the graph below?
A coordinate plane has 7 points. The points are (negative 5, 4), (negative 3, negative 2), (negative 1, negative 2), (2, 0), (3, 3), (4, 5), (6, negative 4).
The set that represents the same relation as the graph given is: B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
What is a Relation?
A relation is defined as a relationship between the input and output, which can be displayed on a graph on a coordinate plane.
From the graph as shown in the image attached below,
The set that has the same coordinate points as indicated on the graph is:
B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
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if cos a =0.8290 then a < is approximately
Answer:
34 degrees
Step-by-step explanation:
Just reverse the cos function ( you will need a calculator)
arc cos (.8290) = 34 degrees
this is sometimes written as cos^-1 (.8290) <====it is the same thing
Which operation should be completed first to find the value of the expression below? 12 + 30/ (6 - 3) + 1
12 + 30
30 ÷ 6
3 + 1
6 - 3
The operation that should be completed first to find the value of the expression is 6 - 3
How to determine the first operation?The expression is given as:
12 + 30/(6 - 3) + 1
When solving an expression;
All expressions in the bracket must be first evaluated
This means that the operation that should be completed first is 6 - 3
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*£ HELP PLS !! URGENT!! AFFECT MY GRADE!! *Problem 5.3
Here are three lines that intersect at
one point.
Laila wrote the equation
x + 18 = 90.
Describe the error that Laila might
have made.
Answer:
Laila assumed that the lines that formed the angles x and 18° added up to 90. This is in fact false because of the lack of the square marking to signify it as a right or 90 degree angle.
What is 8 times the sum of x and 15 as an algebraic expression (written answer)
Answer:
8x+120 is the answer
Step-by-step explanation:
8(x+15)
=8x + 8×15
=8x+120
What does the phrase "in spite of" refer to?
The phrase "in spite of" refers to a scenario where regardless of what happened, there is always a yearning desire and ability to remain positive.
What is the meaning of the phrase "in spite of"?The meaning of the phrase "in spite of" mean notwithstanding or whatever the circumstances, there is no room for complaining and thinking negatively.
This phrase is used to rejuvenate the positive and optimism of a man's thoughts and desires during dark moments. Hence, "in spite of" what happened, there is always an ability to remain positive.
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Based on the data collected from 23 flights, what is the probability of at least one O-ring failing, regardless of temperature?
(Note: This probability is called an experimental probability because it’s based on only 23 flights, which is a fairly small number of events. To get a better approximation of the actual probability, we would need data from many more flights. Note also that even though there was O-ring failure on seven flights, all of those shuttles returned safely.)
Using it's concept, it is found that there is a 0.3043 = 30.43% probability of at least one O-ring failing.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, of the 23 flights, 7 had at least one failure, hence the probability is given by:
p = 7/23 = 0.3043.
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It's the last second of a playoff basketball game and Bridget has three free throws she must make to seal the win she typically makes about 75% of her free throws what is the probability that Bridget makes all three free throws to win the game
The probability that Bridget makes all three free throws to win the game is; 42.2%
How to find the probability?
We are told that the probability of Bridget making her free throw correctly is 75%.
Now, if she has to get all three free throws correctly, then the probability for that is;
P(3 free throws correct) = 0.75 * 0.75 * 0.75
P(3 free throws correct) = 0.421875 ≈ 42.2%
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1. What is the difference between the altitude rule and the leg rule?
Answer:
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle
The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
Below are statements that can be used to prove that the triangles are similar.
1.
AB=BC
ZY
YX
Z
2. ZB and LY are right
angles.
3.7
345x
-5-3-2-1₁.
0
4.?
B
Which two statements are missing in steps 3 and 4?
OLX =
AABC-AZYX by the SAS similarity theorem.
O
5
4+
3+
2+
271
in bo & mp
-3-
U
3) [tex]\angle B \cong \angle Y[/tex]
4) [tex]\triangle ABC \sim \triangle ZYX[/tex] by the SAS similarity theorem
ΔABC is similar ΔZYX by the SAS similarity theorem. Therefore, option B is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
1. AB/ZY = BC/YX = 2
2. ∠B and ∠Y are right angles
3. ∠B=∠Y
4. ΔABC is similar ΔZYX by the SAS similarity theorem.
Therefore, option B is the correct answer.
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In the diagram below, OO is circumscribed about quadrilateral ABCD. What is
the value of x?
B
A
93
O
x+30°
D
OA. 57
OB. 117
OC. 123
OD. 63
Answer:
Ans = A: 57
Step-by-step explanation:
Because
sum of the angke of opposite side of quardilateral triangle is 180°
x°+30°+93°=180°
x°+123°=180°
x°=180°-123°
x°=57°
Hence proved.
The value of x is option A. 57.
What is Cyclic Quadrilateral?A cyclic quadrilateral is a polygon with four sides where all of it's four vertices lie on a circle.
The circle thus formed is called circumcircle or circumscribed circle.
We have a property for the cyclic quadrilateral that the opposite angles formed on the quadrilateral is supplementary.
That is, sum of the opposite angles is 180°.
Here B and D are opposite angles.
So,
∠B + ∠D = 180
9x + x + 30 = 180
Solving,
x = 57
Hence the value of x is 57.
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in a rectangle rent, or = 2x + 4 and ot = 3x + 1 , then the length rn is
Answer:
3
Step-by-step explanation:
Put both expressions equal to each other.
2x+4=3x+1
Solve:
2x+4=3x+1
4-1=3x-2x
3=1x
x=3
Two times a number x increased by 8 is 20. Which one of the following
Equations represents this statement?
Considering the definition of equation, the equation that represents the statement "Two times a number x increased by 8 is 20" is: 2x + 8= 20
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The unknown values represents the number (or numbers), if any, that make the equality true. This unknown number is the solution of the equation.
This caseConsidering that:
"Twice' simply means "multiply by 2"."increased by 8" means "added or plus 8".the equation that represents the statement "Two times a number x increased by 8 is 20" is:
2x + 8= 20
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The equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.
The given statement is two times a number x increased by 8 is 20.
We need to write the equation to represent this statement.
What is an equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, two times a number x=2x
Increased by 8 is 20=2x+8=20
Hence, the equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.
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Caitlin has finished her schooling and training to be a dental hygienist. She has two job offers that she is considering.
Caitlin’s Job Offer Comparison
Job 1: Albuquerque, NM
Job 2: Ann-Arbor, MI
Salary
$54,000
$61,000
Benefits
$2,500 bonuses,
health insurance,
401K
Health insurance,
401K
Average Monthly Rent & Utilities
$925
$1,300
Which job would offer the best annual income considering the cost of living in each locale?
Job 2 is a better choice because the annual income after rent and utilities is $59,700 but that of job 1 is $55,575.
Job 2 is a better choice because the annual income after rent and utilities is $45,400 but the income for job 1 is $41,900.
Job 1 is a better choice because it costs $4,500 less per year to live there.
The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.
D) Caitlin should take the position in her preferred location because the annual salary is $45,400 after rent and utilities.
What is meant by annual income?To calculate your annual salary, multiply your gross income (before taxes) by the number of pay periods in a year. If an employee earns $1,500 each week, his or her annual income is $1,500 x 52 = $78,000.
Job 1 and Job 2 both generate the same or similar amount of income of $45,400 per year after additional expenses.
This means that Caitilin should choose her career based on the preferences of her neighboring neighborhood so that she can travel easily.
This is because moving to a more distant job location would result in no increase in her income, making it nonsensical to do so.
So, the correct answer is option D.
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Answer: D. edge 2023
The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.
Write an explicit formula for ay, the nth term of the sequence 39, 33, 27, ....
Answer:
ay = 39 -6(n -1)
Step-by-step explanation:
The explicit formula for an arithmetic sequence can be written by using the first-term value and the common difference in the generic formula.
__
The generic formula for the n-th term of an arithmetic sequence is ...
[tex]a_n=a_1+d(n-1)[/tex]
where a₁ is the first term of the sequence (39), and d is the difference between sequential terms (33-39 = -6).
Using the values for this sequence in the generic formula, we have ...
ay = 39 -6(n -1)
I need help with premetier and area for 7 8 9
The answers to the three shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
What is the perimeter of a shape?Perimeter is the outside boundary of a plane shape.
Analysis:
for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm
Height of triangle = [tex]\sqrt{((5.4)^{2} - (2.7)^{2} }[/tex] = 4.68
Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64[tex]mm^{2}[/tex]
For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches
Height of triangle = [tex]\sqrt{(5.9)^{2} - (1.7)^{2} }[/tex] = 5.65inches
Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61[tex]inches^{2}[/tex]
For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards
Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81[tex]yards^{2}[/tex]
In conclusion, the perimeter and area of the given shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
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DUE TODAY: PLEASE HELP
Use transformations to prove that the two figures are similar. Shape A is the original image
(Show work please, how it is similar or not)
Answer:
See below ~
Step-by-step explanation:
We need to prove that the figures are similar by applying the various kinds of transformations.
===============================================================
Question A :
⇒ Compare the side lengths of A and B
⇒ 2 : 5 (for all sides)
⇒ 1 : 2.5
⇒ Hence, Shape A has been dilated with a scale factor of 2.5 to form Shape B
=============================================================
Question B :
⇒ Compare the side lengths of A and B
⇒ A : B = 2 : 6
⇒ A : B = 1 : 3
⇒ Shape A has been dilated with a scale factor of 1/3 to form Shape B
-3x^6(-4x+9)
Simplify please lol
Answer:
-12X^7-27X^6
Step-by-step explanation:
-3x^6(-4X+9)=(-3X^6*)(4X^1)+-27X^6=-12X^7+-27X^6
Use the scenario to answer the question.
Bryan is asked to find the interquartile range for the data set {5,6,6,8,10,11,14,16,17}.
His work follows.
Step A: Find the median of the data set. The median, or Q2, is 10.
Step B: Find the value of Q1, or the median of the lower half of the data set, {5,6,6,8}.
Q1=6+62=6
Step C: Find the value of Q3, or the median of the upper half of the data set, {11,14,16,17}.
Q3=14+162=15
Step D: Find the difference between Q3 and Q1.
IQR=15−6=9
At which step did Bryan make a mistake, if he made one?
At Step B, he incorrectly found the value of Q1. He should have found the sum of the values and then divided by 4 to get Q1=6.25.At Step B, he incorrectly found the value of textsf cap q 1. He should have found the sum of the values and then divided by 4 to get
At Step A, he incorrectly found the value of the median. He should not have included both 6 values, so the median is 10+112=10.5.At Step A, he incorrectly found the value of the median. He should not have included both 6 values, so the median is
At Step C, he incorrectly found the value of Q3. He should have included 10 to get Q3=14.At Step C, he incorrectly found the value of textsf cap q 3. He should have included 10 to get
At Step D, he incorrectly found the IQR. He should have found the difference between each quartile to get 10−6=4 and 15−10=5.At Step D, he incorrectly found the IQR. He should have found the difference between each quartile to get 10 minus 6 is equal to 4 and
He did not make a mistake.
Given the steps used to calculate the interquartile range, Bryan did not make any mistake.
What is the interquartile range?
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1) : 3/4 x 10 = 7.5 term : (14 + 16) / 2 = 15First quartile = 1/4 x (n + 1) 1/4 x 10 = 2.5th term : (6 + 6) / 2 = 6Interquartile range = 15 - 6 = 9To learn more about interquartile range, please check: https://brainly.com/question/3966385
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