Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
Applying the trigonometric ratios, the equations that can be used are:
sin 45 = BC/9
cos 45 = BC/9
How to Apply the Trigonometric Ratio?In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:
To find AC, use the cosine ratio, CAH.
To find BC, use the sine ratio, SOH.
sin 45 = opp/hyp = BC/9
sin 45 = BC/9
cos 45 = adj/hyp = BC/9
cos 45 = BC/9
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Answer: A, E
Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. (round your answer up to the nearest whole number.) the answer is not 384. i already submitted that answer and it was incorrect
The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.
Given margin of error of 0.05 and confidence interval of 95%.
We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.
Margin of error is the difference between real values and calculated values.
The formula of margin of error is as under:
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where
z is the critical value of z for given confidence level
n is sample size
σ is population standard deviation
We have not given population standard deviation so we will use the following formula:
Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]
We have to find z value for 95% confidence level.
z value=1.96
We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2
put [tex]\sqrt{p(1-p)}[/tex]=1/2
Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]
0.05=1.96*0.5/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=0.98/0.05
[tex]\sqrt{n}[/tex]=19.6
squaring both sides
n=384.16
After rounding off we will get
n=384.
Hence the sample size needed to obtain a margin of error of 0.05 is 384.
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Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) 4 ex cos 3x
If the function is
[tex]y = 4 e^x \cos(3x)[/tex]
then we have derivatives
[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]
[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]
Now consider the linear ODE
[tex]aD^2y + bDy + cy = 0[/tex]
Substituting [tex]y[/tex] and its derivatives reduces the equation to
[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]
Now,
[tex]-24a - 12b = 0 \implies b = -2a[/tex]
[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]
Then the minimal ODE with the given solution is
[tex]aD^2y -2a Dy + 10ay = 0[/tex]
or
[tex]\boxed{D^2y -2 Dy + 10y = 0}[/tex]
Which expression illustrates the associative property of addition? (3 19) – 12 = (3 12) – 19 3 (19 – 12) = 3 (19 12) (3 19) – 12 = 3 (19 – 12) 3 (19 –12) = 3 – (19 12)
Answer:
Associative Property
For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.
Answer:
3rd Option!
Step-by-step explanation:
EDGE 2022; good luck
Please help me solve this, random answers will be removed
[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]
Answer:
Step-by-step explanation:
Yasmin designed a square table using a scale drawing. The actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet. Choose the figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet.
The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.
How to calculate the length?From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.
The new length will be:
= 2 × 3 2/3
= 7 1/3
Therefore, the new length is 7 1/3 feet.
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The double number line shows that 333 back-to-school packages contain 363636 pencils. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, two unlabeled tick marks, 3, another unlabeled tick mark. The line labeled Pencils, reads from left to right: 0, two unlabeled tick marks, 36, another unlabeled tick mark. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, two unlabeled tick marks, 3, another unlabeled tick mark. The line labeled Pencils, reads from left to right: 0, two unlabeled tick marks, 36, another unlabeled tick mark. Select the double number line that shows the other values of packages and pencils. Choose 1 answer: Choose 1 answer: (Choice A) A A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48. (Choice B) B A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 10, 22, 36, 52.
HELP MEEEEEEEEEEEEEEEEEEEE
The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.
What is a number line?It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.
In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information
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mr hassell came home to find that each of the 6 kit kat bars he brought had 1 bar eaten. They each had 3/4 in it.How many bars of kitkat are there in total.
The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars
AlgebraNumber of bars = 6Number of bars eaten = 1Number of bar in each KitKat = 3/4Total bars of KitKat = 6 × 3/4
= (6×3)/4
= 18/4
= 9/2
= 4 1/2 bars
Number of bar remaining after eating 1 bar = 4 1/2 - 1
= 3 1/2 bars
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Genevieve wants to verify that negative x is the simplified expression of one-fifth (5 x minus 20) minus one-half (4 x minus 8). which procedure can genevieve follow to verify this? add one-fifth (5 x minus 20) minus one-half (4 x minus 8) and negative x. put an equal sign between one-fifth (5 x minus 20) minus one-half (4 x minus 8) and one-fifth (5 x minus 20) minus one-half (4 x minus 8) and then solve for x. substitute 5 into the first expression, substitute 4 into the second expression, and evaluate them. substitute 5 into each expression and evaluate them.
Answer: -x
Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)
Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 4
Reorder and gather like terms: (x - 2x) + (- 4 + 4)
Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)
Calculate the sum or difference : - x + (- 4 + 4)
The sum of two opposites equals 0: -x
Answer: -x
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Answer:
D) Substitute 5 into each expression and evaluate them.
Step-by-step explanation:
y
T
N
9
6
U
3
M
What is the value of y?
3√3 units
6√3 units
O
9√3 units
O 12√3 units
The value of y from the given figure is 6√3
Pythagoras theoremFrom the given figure, according to the theorem;
H² = 6² - 3²
H² = 36 - 9
H² = 27
H = 3√3
Determine the value of y using the same theorem;
y² = 9² + ( 3√3)²
y² = 81. + 27
y = √108
y = 6√3
Hence the value of y from the given figure is 6√3
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2. The Kenya Seed Company sold 6 460 t 760 kg of maize seeds to 95 farmers. The farmers bought equal masses of seeds. What mass of seeds did each farmer buy? fond his cous in equal
Using proportions, it is found that each farmer bought 68,008 kg.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:
6460 x 1000 + 760 = 6,460,760 kg
The amount per farmer is:
6,460,760/95 = 68,008 kg.
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Pls help solve for part b)iii.
Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;
a. The height of the tree is approximately 31.2 m.
b. i. The distance of Q from the base of the tree is 50•√5 m.
ii. The angle of elevation of the top of the tree from Q is approximately 15.6°
iii. The bearing of the tree from Q is 296.565°
How can the distances and bearing of the tree from Q be found?a. tan(32°) = Height/50
Height = 50 × tan(32°) = 31.243 m.
Height of the tree ≈ 31.2 m.b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;
d = √(100² + 50²) = 50•√5
The distance of Q from the base of the tree, d = 50•√5 m.ii. The angle of elevation is given by trigonometric ratios as follows;
[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]
Which gives;
[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]
The angle of elevation of the top of the tree from Q ≈ 15.6°iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;
Angle = arctan(50/100) ≈ 26.565°
The angle between the direction north of Q and a line from Q to the tree is therefore;
90° - 26.565° = 63.435°
The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;
Bearing = 360° - 63.435° = 296.565°
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What's 2 divided by X
Answer:
2/x
Step-by-step explanation:
A sweatshirt costs $48 at Hollister. The sales tax rate is 7%. How much will it cost to buy the sweatshirt?
Answer:
$ 51.36
Step-by-step explanation:
To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.
Sales tax = tax rate * cost price
= 7% * 48
= 0.07 * 48
= $ 3.36
Cost price = cost of product + sales tax
= 48 + 3.36
= $ 51.36
On a number line, point D is at -3, and point E Is at 6. The point F lies on DE. The ratio of Df to FE ls 2:3. Where does point F lie on the
number line?
Point F is at
. All rights reserved.
on the number line.
Helppp me please
The point F as described in the task content is at point; 0.6 on the number line.
Where does point F lie on the number line?Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.
Consequently, since the ratio of Df to FE ls 2:3
It follows that point F is at -3 + (2/5) × 9.
Point F is therefore at 0.6 on the number line.
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CALLING ALL EXPERTS PLS ILL GIVE BRAINLIEST
On Monday, Gian spent 5 minutes watching videos. On Tuesday, he spent 25 minutes watching videos. Place points on the graph to show Gian's activity for Monday and Tuesday.
Julie has 20 times as many bouncy ball as her brother her brother haves 4 balls how many does Julie have?
Answer:
80
Step-by-step explanation:
Answer:
80 balls
Step-by-step explanation:
Julie's brother's balls x 20 = Julie's balls
4 x 20 = 80
Brainliest, please :)
The wall around a playground is 410 m.if one wall along the length is 80 m what is the length of the wall along the breadth what is the area of playground.
The length of the wall = 125m
The area of the Playground = 10000[tex]m^{2}[/tex]
What is geometry?
A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.
Given data:
Perimeter of the playground=410m
length of the wall = 80m
The playground's width can be calculated as follows if its length is 80 meters:
(Formula of Perimeter of a rectangle)
P=2(L+B)
410=2(80 +B)
410= 160 + 2B
2B= 410-160
2B= 250
B= 125 m
This results in a 125 m length for the playground.
The area of playground.
Area = Length x Width
Area = 80 x 125
area = 10000[tex]m^{2}[/tex]
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Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
1.4 meters
2 meters
0.5 meters
1 meter
Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.
What is the seesaw's maximum length?This can be found as:
Sin 30° = 1 / Maximum length
Solving gives:
Sin 30° = 1 / Maximum length
Ml = 1 / Sin 30°
= 1 / 0.5
= 2 meters
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Can someone help me please
Answer:
10. 20.9°
11. 73.2°
Step-by-step explanation:
The inverse sine function is used to find the angle from its sine value.
10.In each case, the equation is of the form ...
a/sin(x) = b/c
Multiplying both sides by c/b·sin(x), we find the solution is ...
sin(x) = ac/b . . . . . find sin(x)
x = arcsin(ac/b) . . . . . find the corresponding angle
For the given values a=7.2, b=13, c=sin(40°), we have ...
x = arcsin(7.2sin(40°)/13) ≈ 20.9°
11.For the given values a=6.53, b=√40, c=sin(68°), we have ...
x = arcsin(6.53sin(68°)/√40) ≈ 73.2°
Please find answers of 14 a, b, c and d
Q14)
a) The smallest prime number is 2. The smallest composite number is 4.
b) Rs 720 - 20 [as loss]
=> Rs 790 = SP
c) Rs 500 - 30 [as profit]
=> Rs 470 = CP
d) a° + b° = 180°
Hope it helps you!
From the given graph, use two points to write an equation in point-slope form and then
change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving for y. Show your
work!
y=mx+b
Step 1
Using the points (2,0) and (-2, -3), we get the slope is
[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]
Step 2
Using the point (2,0), the equation is
[tex]y=\frac{3}{4}(x-2)[/tex]
Step 3
Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].
A scientist studying insects starts with a population of 10. The population triples every hour. How many insects will there be after 20 minutes?
The population after 20 minutes is 14.
We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-
After 1 hour, the population is 3*10
After 2 hours, -> 3*3*10
After 3 hours, -> 3*3*3*10
Make a function from above observation in the increasing
number of the insects per hour
This can be generalized as a function of t, the time in hours:
f(t) = (3^t) * 10
putting the values in the function and get the desired answer,
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for
(1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.422 ≈ 14
The population after 20 minutes is 14.
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Answer:The population after 20 minutes is 14.
We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-
After 1 hour, the population is 3*10
After 2 hours, -> 3*3*10
After 3 hours, -> 3*3*3*10
Make a function from above observation in the increasing
number of the insects per hour
This can be generalized as a function of t, the time in hours:
f(t) = (3^t) * 10
putting the values in the function and get the desired answer,
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for
(1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.422 ≈ 14
The population after 20 minutes is 14.
Step-by-step explanation:
Which of the following best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers?
A) the sum is a constant
B) the sum is a polynomial
C) the sum is an exponential expression
D) nothing can be determined about the sum without more information
The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
Sum of Polynomial expressionPolynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.
ax^2+bx+c and;
mx^2+nx+p
Take the sum of the polynomials
P(x) =. ax^2+bx+c
f(x) = mx^2+nx+p
Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.
Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
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Which table shows a function that is increasing only over the interval(-2,1),and nowhere else?
table 1, and table 2 are the answers.
we know that any function is increasing when for an increase in x-values, y-value should also increase
we will verify each table
table-1:
we can see that
x increase as -3, -2, -1 , 0, 1,2
y is also increasing -6,-3,-1,1,3,6
so, this is increasing
table-2:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but it is asking between -2 to 1
y-values are -4,-1,1,4.....which is increasing
so, this is increasing
table-3:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from -3 to -5 .....which is decreasing
so, this is not increasing
table-4:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from 7 to 1 .....which is decreasing
so, this is not increasing
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PLEASE HELP MEEEEe
jhchnthnht
The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x
Which method can be used to find the equation of the perpendicular bisector?The slope, m, of the line BC is calculated as follows;
m = (2 - 1)/(4 - (-2)) = 1/6The slope of the perpendicular line to BC is -1/(1/6) = -6
The midpoint of the line BC is found as follows;
[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]
The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.
The equation of the perpendicular bisector in point and slope form is therefore;
(y - 1.5) = -6•(x - 1)
y - 1.6 = -6•x + 6
y = -6•x + 6 + 1.6 = 7.6 - 6•x
Which gives;
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Mrs karki purchased a sari for rs 8000 and sold it for Rs 11300 with 13% VAT , find her profit and loss percent.
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
VAT = 13% = 0.13 * 8000 = 1040
Selling price - VAT = 11300 - 1040 = 10260
Profit = [(10260 - 8000)/8000] * 100% = 28.25%
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
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7,
24*
nswer:
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
Answer:
1/12
Step-by-step explanation:
the chances of rolling a 3 is 1/6
there are 3 numbers more than 3 on a number die, 4,5, and 6
which is 3/6 or 1/2 if you decide to simplify
to find the probability you want you have to multiply the fractions by each other
1/6x1/2=1/12
There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. The events are dependent events.
Given that there are five vowels, which come from the letters A, E, I, O, and U, the likelihood of drawing a vowel is:
5/26
since there are a total of 26 alternatives available. After choosing that, we are left with 25 alternatives, 4 of which are vowels, thus the probability is:
4/25
The final likelihood is thus:
5/26 * (4/25) = 0.031
In other words, the likelihood is 3.1% when choosing a vowel and then another (without replacement).
The first event has an impact on the second event since there are fewer vowels and overall possibilities, hence the events are dependent.
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What is the equation I'm supposed to write?
The equation in slope intercept form is y = -4x/3 + 10
How to determine the equation?The representations are given as:
x represents peachesy represents applesSo, we have:
2 * x + 1.5 * y = 15
Evaluate the product
2x + 1.5y = 15
Subtract 2x from both sides
1.5y = -2x + 15
Divide through by 1.5
y = -4x/3 + 10
Hence, the equation in slope intercept form is y = -4x/3 + 10
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