By the Law of Sines,
[tex]\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ =\frac{244\sin 37.8^{\circ}}{229} \\ \\ B \approx 37.42^{\circ}, 142.58^{\circ}[/tex]
Of these, only 37.42° is a possible value of B (sum of angles of a triangle is 180°).
So, we have that:
[tex] a=229, b=244, A=37.8^{\circ}, B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]
Angles of a triangle add to 180°, so:
[tex]C=180^{\circ}-A-B=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)
[/tex]
Using the Law of Sines again,
[tex]\frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a \sin C}{\sin A} \\ \\ =\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}}[/tex]
So, there is one possible triangle, where:
[tex]a=229 \\ \\ b=244 \\ \\ c=\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}} \\ \\ A=37.8^{\circ} \\ \\ B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right) \\ \\ C=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]
The temperature at 2 AM was -3°F is the temperature decreased 12°F and then increase 7°F what integer represents the new temperature?
The integer represents the new temperature is (-8) F.
what are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
Given:
At 2 a.m. temperature = -3F
Then temperature decreased 12°F = -12 F
and then increase 7°F = +7F
Now, the temperature is
= (-3) - 12 + 7
= -3 -5
=-8 F
Hence, the temperature is (-8) F
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if -10,p,q,20 are in A.P, find p and q
The value of arithmetic progression of p = 0 and q = 10
What is arithmetic progression ?When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word.
Given that : -10,p,q,20 are in A.P
if this -10,p,q,20 are in A.P then it must follow
2b = a+ c
2p = -10 + q ... (i)
2q= p+20 ....(ii)
Solving both equation we get
Multiplying (1) with 2,
4p - 2q = -20
Now adding both the equations
4p - 2q + 2q - p = 0
3p = 0
p = 0
Then, q = 0 + 10 = 10
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600 people went to the basketball game on Friday and 14% of them bought popcorn. How many people bought popcorn at the basketball game?
Answer:
84 people
Step-by-step explanation:
14 percent means that for each 100, there are 14 of something.
This is the most common method to calculate 14% of 600. 600 is the Whole, 14 is the Percent, and the Part is what we are calculating. Below is the math and answer to "What is 14% of 600?" using the percent formula.
Percent Formula:
(Whole × Percent)/100 = Part
(600 × 14)/100 = 84
14% of 600 = 84
Rapunzel was playing a game in which she gained and lost points.
First, she lost nine points three times. Next, she lost three points. Write
the total change to her score as an integer.
The total change to Rapunzel's score as an integer is (x - 30), where x is the initial score.
How can linear addition and subtraction be carried out?
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. It is one of the fundamental mathematical operations we employ on a daily basis.
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction.
Let the initial score of Rapunzel be = x
Given, she first lost nine points thrice and then three points, thus her score is: x - (9*3) - 3 = (x - 30) points.
Thus, the total change to her score is (x-30) points.
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6-8 7-12 1-4 0-1 find the value of these cards and put them in order from lowest to highest
The order from lowest to highest is -5, -3, -2, -1 .
What is ascending order ?
Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
6-8=-2
7-12=-5
1-4=-3
0-1=-1
Order : -5, -3, -2, -1
Avoid becoming confused by the values following the negative sign. The value of a number decreases with increasing size after a negative sign.
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4. 14% of 81 is what number?
Answer:
11.34
Step-by-step explanation:
14% of 81 =
14% × 81 =
14/100 × 81 =
(14 ÷ 100) × 81 =
14 × 81 ÷ 100 =
1,134 ÷ 100 =
11.34
a refrigerator was originally priced at $250. it was then put on sale for 20% of. what is the number of dollars in the final price of the refrigerator if an additional 15% is taken off from the sale price?
the angles of a triangle are in the ratio 3:5:4 calculate the size of each angle
The 3 angles in a triangle always add up to be 180.
Call the smallest angle as x
-> The 3 angles are x, 4/3x and 5/3x
-> 4x = 180
-> 45
So, the sizes of the 3 angles are 45, 60 and 75.
Help with this question asap please help
The meaning of vertical intercept in this context can be inferred from the options to mean that the helicopter took off from a height of 50 ft.
What is the vertical intercept?In a linear problem or a graph, the vertical intercept, which is also known as the y-intercept, refers to the value of y when the value of x is 0.
Assuming y in this problem refers to the height and x refers to the minutes, the vertical intercept would be the height at 0 minutes.
If the vertical intercept is 50 ft then it means that the helicopter took off from 50 feet because at takeoff, the value of x would be 0 minutes.
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Por favor ayúdenme no sé cómo hacer esto
1. The value of x in the triangle is B. 22.5°.
2. The value of x in the triangle is B. 22.5°.
3. The value of the limit illustrated is D. 32
How to calculate the value?1. It should be noted that the total angle in a triangle is 180°. The three angles given are illustrated as:
Angle 1 = 3x
Angle 2 = x + 30°
Angle 3 = 180° - 120° = 60°
The value of x will be:.
3x + x + 30 + 60 = 180
4x + 90 = 180
4x = 180° - 90°
4x = 90°
x = 90/4.
x = 22.5°
2. Note that the question was repeated. Therefore, the answer is illustrated above The value of x is 22.5°.
3. x³ + 7x² - 4
when x = 2
x³ + 7x² - 4
= 2³ + 7(2)² - 4
= 8 + 28 - 4
= 32
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Creating equivalent ratios
12:___=16:24
The equivalent ratio is 12: 18
The ratio is 12:_ = 16: 24
12/x = 16/ 24
x≠0, because the denominator can never be 0.
Solve the equation
12/x = 16/24
12/x = 2/3
x = 18
Therefore the equivalent ratio is 12:18.
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2 x 10 to the negative 6 power times what number is equal to 6 x 10 to the negative 4 power?
By using division, 2×[tex]10^{-6}[/tex] times 300 is equal to 6×[tex]10^{-4}[/tex]
Scientific notation is a form of writing a very larger number or very smaller number in a simpler form. The general form of the scientific notation is a number from 1 to 10 is multiplied by a power of 10.
Consider the unknown number as x
The first number = 2×[tex]10^{-6}[/tex]
The result of 2×[tex]10^{-6}[/tex] times x = 6×[tex]10^{-4}[/tex]
So the equation will be
2×[tex]10^{-6}[/tex] × x = 6×[tex]10^{-4}[/tex]
Move 2×[tex]10^{-6}[/tex] to the right hand side of the equation
x = 6×[tex]10^{-4}[/tex] ÷ 2×[tex]10^{-6}[/tex]
Here we have to use the division
x = 300
Hence, by using division, 2×[tex]10^{-6}[/tex] times 300 is equal to 6×[tex]10^{-4}[/tex]
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The line parallel to y=1/4x+1 that passes through the point (6,-2)
The equation for the line parallel to y=1/4x+1 that passes through the point (6,-2) is x-4y=14 as the slope for both lines are equal and using slope-point form of equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What is Slope-Point form?The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
The slope for the line will be 1/4 and the given points will be (6,-2) so the equation for the line is
y-y1=m(x-x1)
y+2=1/4(x-6)
4y+8=x-6
x-4y=14
Given that both lines have an equal slope and using the slope-point form of equation, the equation for the line parallel to y=1/4x+1 passing through the point (6,-2) is x-4y=14.
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A gym employee earns the same amount each month. After working for three months, he earned $4,500. Complete the table to determine how much money he will make over a five-month period. how much will he earn after working 1 month?
1. The money that the gym employee earns in 1 month is $1500.
2. The money that the gym employee earns in 5 months is $7500.
How to calculate the value?The gym employee earns the same amount each month and after working for three months, he earned $4,500.
In this case, the amount that he earns monthly will be:
= Total amount / Number of months
= $4500 / 3
= $1500
He earns $1500 monthly.
The money that the gym employee earns in 5 months will be:
= 5 × $1500
= $7500.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. N=3; 3 and 2i are zeros; f(-1)=20
An nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).
As given in the question,
Number of zeros of the polynomial function N = 3
Real and complex zeros = 3, 2i , -2i
Function value f(-1) = 20
f(x) = k (x-3)(x-2i)(x+2i)
⇒f(x) = k(x-3)(x²-4i²)
⇒f(x) =k(x-3)(x²+4)
⇒f(-1) = k(-1-3)((-1)² +4)
⇒ 20 =k(-4)(5)
⇒k =-1
Now , f(x) = (-1)((x-3)(x²+4)
= (-1)(x³ -3x²+4x -12)
Therefore, nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).
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Need help! please explain how you got the answer as well please and thank u <3
44 points till b givin
Answer:
C. between 14.1 and 14.2
Step-by-step explanation:
√100 × 2
√(10 × 10) × 2
10√2 = 14.14
I hope this helps!
Answer:
C. Between 14.1 and 14.2
10√2 ≈ 14.142135624
Step-by-step explanation:
a. write a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up. b. write a rule for congruence mapping that reflects a figure across the y-axis.c. why are these mappings called congruence mappings?
Given:
Two different congruency mapping
To find:
a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up
b) a rule for congruence mapping that reflects a figure across the y-axis
[tex]\begin{gathered} a)\text{ Translation rule to the right:} \\ f(x\text{ -d\rparen: \lparen x, y\rparen }\rightarrow\text{ \lparen x+d, y\rparen} \\ Translation\text{ rule up:} \\ f(x)\text{ + b: \lparen x, y\rparen }\rightarrow\text{ \lparen x, y + b\rparen} \\ \\ 5\text{ units to the right and 3 units up:} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ reflection across the y-axis} \\ The\text{ x coordinate will be negated while the x coordinate will remain constant} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ The mappings are called congruence mapping because the shapes and size remain the same } \\ \text{but the }position\text{ changes.} \\ As\text{ a result the corresponding angles and sides will be equal} \end{gathered}[/tex]4. Which of the following is the graph of y> -+3
Identify the following fraction as a proper fraction or an improper fraction
16
11
The given number [tex]\frac{16}{11}[/tex] is an improper fraction.
What are improper and proper fractions?Proper fraction = A fraction with a smaller numerator than denominator is said to be a correct fraction. A fraction whose numerator is the same as or bigger than its denominator is said to be inappropriate. Proper fractions include 3/4, 2/11, and 7/19.
Improper fraction = A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.
When we divide 16 by 11 we get a quotient of 1 and a remainder of 5.
This fraction after solving can be represented as [tex]11\frac{1}{6}[/tex] which is a mixed fraction.
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Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Group of answer choices
Nico
Aditi
Erick
Raj
Sandra
By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.
How to solve the given equation?In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:
2/5(5 + x) = 8
Multiplying both sides by 5/2, we have:
5/2 × 2/5(5 + x) = 8 × 5/2
5 + x = 40/2
5 + x = 20
Subtracting 5 from both sides, we have:
5 + x - 5 = 20 - 5
x = 15
Method 2.In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:
2/5(5 + x) = 8
Multiplying both sides by 1/2, we have:
1/2 × 2/5(5 + x) = 8 × 1/2
1/5(5 + x) = 4
Multiplying both sides by 5, we have:
5 × 1/5(5 + x) = 4 × 5
5 + x = 20
Subtracting 5 from both sides, we have:
5 + x - 5 = 20 - 5
x = 15
Method 3.In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:
2/5(5 + x) = 8
2/5 × 5 + 2/5 × x = 8
2 + 2x/5 = 8
Subtracting 2 from both sides, we have:
2 - 2 + 2x/5 = 8 - 2
2x/5 = 6
Multiplying both sides by 5/2, we have:
5/2 × 2x/5 = 5/2 × 6
x = 30/2
x = 15.
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take another guess: a student takes a multiple-choice test that has 10 questions. each question has four choices. the student guesses randomly at each answer. round the answers to three decimal places.
Value of P(5) is 0.058 by probability.
What is a math illustration of probability?
The likelihood or chance of an event happening is known as probability. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.Given that ,
p = 1 / 4 = 0.25
1 - p = 1 - 0.25 = 0.75
n = 10
Using binomial probability formula ,
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x
(a) x = 5
P(X = 5) = ((10! / 5! (10 - 5)!) * 0.255 * (0.75)10 - 5
= ((10! / 5! (5)!) * 0.255 * (0.75)5
= 0.058
P(5) = 0.058
(b)
P(X > 3) = 1 - P(X \leq 3)
= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= 1 - 0.776
= 0.224
P(ore than 3) = 0.224
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The complete question is-
Take another guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
PLEASE HELP ME ITS REALLY IMPORTANT 30 PTS
The 15 most populous states in the United States have an average population of 14.15 million, with a standard deviation of 8.75 million. Virginia and Washington have populations of 8.38 million and 7.17 million, respectively. Texas and Pennsylvania have z-scores of 1.52 and −0.15, respectively.
Part A: List these four states in order from smallest to largest populations. (4 points)
Part B: Explain your reasoning mathematically and be sure to include all necessary calculations.
Answer:
A.-0.15
1.52
7.17
8.38
8.75
14.15
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
d
Step-by-step explanation:
because you're already given the hypotenuse "c" and a side length "a"
so
8^2+ y^2=12^2
several psychology students are unprepared for a surprise true/false test with questions, and all of their answers are guesses. a. find the mean and standard deviation for the number of correct answers for such students. b. would it be unusual for a student to pass by guessing (which requires getting at least correct answers)? why or why not?
The mean and standard deviation for the number of correct answers for such students is; μ = 6.5 and σ = 1.802776
How to find the mean and standard deviation?Given there is a surprise true/false test with 13 questions.
Thus, the probability of correctly guessing the answer is; p=0.5
Let "X' be the answers correctly guess by a student.
The formula for the binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
A) The mean of the binomial distribution is given by the formula;
μ = np
μ = 13 * 0.5
μ = 6.5
The formula for standard deviation is:
σ = √(np(1 - p))
σ = √(13 * 0.5(1 - 0.5))
σ = 1.802776
B) The probability that the student getting at least 11 correctanswers is given by:
P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13)
Using online binomial probability calculator, we have;
P(X ≥ 11) = 0.01123
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Complete question is;
Several psychology students are unprepared for a surprisetrue/false test with 13 questions, and all of their answers are guesses.
a. Find the mean and standard deviation for the number of correct answers for such students.
b. Would it be unusual for a student to pass by guessing (which requires getting at least 11 correct answers)? Why or whynot?
the question is the png
Answer:
this appears to already be in standard form?
Step-by-step explanation:
standard form has x and y on one side of the =
Which relation is a function?
Answer:
option C
Step-by-step explanation:
due to the vertical line test it only passes through the x point once
Riley is also making boxes to hold baseballs. She wants the dimensions of her boxes
to be 4 x 6 x 3 units. How many balls can one of Riley's boxes hold?
The volume of the box is 105 cubic units.
What is volume of cuboid ?The amount of space inside a cuboid is calculated using the term "cuboid volume." Having length, breadth, and height, the cuboid is a three-dimensional shape. A shape with a certain length, breadth, and height will be obtained if we start with a rectangular sheet and keep stacking them. Length x Width x Height is the formula for calculating the cuboid's volume.
Given that : The dimensions of her boxes to be 4 x 6 x 3 units.
The volume of cuboid=7×5×3=105 cubic units.
so ,The volume of the box is 105 cubic units.
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please help me FASTTT
Answer:
k=40
Step-by-step explanation:
Answer : Each week the amount goes up by $40
if two distinct numbers are selected at random from the first seven prime numbers, what is the probability that their sum is an even number? express your answer as a common fraction.
The probability that a sum is an even number will be 5/7.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is typically defined as the proportion of favorable outcomes to all outcomes in the sample space. The probability of an event P(E) = (Number of favorable outcomes) is how it is stated (Sample space).So, the first 7 prime numbers:
2,3,5,7,11,13,17Then,
Even numbers are always produced when two odd numbers are added together.Odd numbers are always created when Even numbers are added to Odd numbers.In the list of 7, there is only one even number. If that is one of the options, then the outcome will only be odd.As the same number cannot be chosen twice, there is a 6/7 chance that it won't be chosen the first time and a 5/6 chance that it won't be chosen the second time.By multiplying these two probabilities, we can determine the likelihood of an even sum.
5/6 × 6/730/425/7Therefore, the probability that a sum is an even number will be 5/7.
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question 1 and 2 (10 popints)
Exponential function:
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given,
The exponential function = 14²The value of this exponential function :
14 × 14 = 196
The exponential function = 4⁵The value of this exponential function :
4 × 4 × 4 × 4 × 4 = 1024
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