[tex]\text{Given that,}\\\\~~~~~~~~\cos \theta = \dfrac 35\\\\\implies \cos^2 \theta = \dfrac 9{25}\\\\\implies 1-\sin^2 \theta = \dfrac{9}{25}\\\\\implies \sin^2 \theta = 1-\dfrac{9}{25}\\\\\implies \sin^2 \theta = \dfrac{16}{25}\\\\\implies \sin \theta = \pm\sqrt{\dfrac{16}{25}}\\\\\implies \sin \theta = \pm\dfrac 45\\\\\text{Given that,}~ 270^{\circ} \leq \theta \leq 360^{\circ}, \text{So}~ \theta ~ \text{lies in fourth quadrant.}\\\\[/tex]
[tex]\text{Which means that}~ \sin \theta ~ \text{will be negative.}\\\\\text{Hence,}~ \sin \theta = -\dfrac 45[/tex]
I hope someone sees this!!! Can someone check my work please??
Hello there!
I will only explain the ones that do not appear correct to me. If you require further explanation, please let me know.
1] vertical
2] corresponding
-> These two angles are in corresponding places on points of the lines, so they are corresponding angles.
3] alternate interior
4] alternate exterior
-> These angles are on the "outside" of the parallel lines, and on "opposite" sides of the transversal. With this in mind, they are alternate exterior angles
5] same side interior
6] same side exterior
-> These angles are on the "outside" of the parallel lines, and on the same side of the transversal. With this in mind, they are same-side exterior angles
Use properties of operations to write two expressions that are equivalent
to 2n + (8 + 32).
The equivalent expressions of 2n + (8 + 32)are 2n + 40 and 2(n + 20)
How to determine the equivalent expressions?The expression is given as:
2n + (8 + 32)
The first equivalent expression
Evaluate the sum of the numbers in the bracket
2n + (8 + 32) = 2n + 40
This means that 2n + 40 and 2n + (8 + 32) are equivalent.
The second equivalent expression
In (a), we have:
2n + (8 + 32) = 2n + 40
Factor out 2 from the expression
2n + (8 + 32) = 2(n + 20)
This means that 2(n + 20) and 2n + (8 + 32) are equivalent.
Hence, the equivalent expressions are 2n + 40 and 2(n + 20)
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A class sold tickets to their school play. Each of the 232323 students in the class sold 444 tickets. The cost of each ticket was \$7$7dollar sign, 7.
How much money did the class earn by selling tickets to the play?
\$
Answer:
the class earned $722059884
Step-by-step explanation:
because each person sold 444 tickets and there was 232323 students
=232323×444
=103151412
because 103151412 tickets were sold and a ticket cost $7
=103151412×7
=722059884
The ratio of the one leg of
the right triangle to the other
leg of the right triangle must
be 8:7. Determine the
greatest length of one leg of
the right triangle given the
other leg of the right triangle
is 10.5 feet.
Answer:
12 ft
Step-by-step explanation:
We assume right triangle ABC with the right angle being at B. We are given that the ratio of AB/CB = 8/7, and one leg is 10.5. Let's call the other leg is X. We don't know which leg is which so assume both. Then
(a) assume the X leg is the longer
8 / 7 = X / 10.5
(8 * 10.5) / 7= X
X = 12
OR (b) assume the X leg is the shorter
8/7 = 10.5 / X
(8X / 7) = 10.5
8X = 10.5 * 7
8X = 73.5
X = 9.1875
(a) is the greater so (a) wins
find the radius of a circle whose arc length is 55 m and its central angle measure if 5 radians
Answer:
Step-by-step explanation:
To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.
In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]
This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]
Leonardo, who is married but files separately, earns $80,000 of taxable income. He also has $15,000 in city of Tulsa bonds. His wife, Theresa, earns $50,000 of taxable income.
If Leonardo and his wife file married filing jointly in 2021, what would be their average tax rate?
When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent
What is the tax rate about?In the question above, Leonardo's taxable income = $80,000
Theresa's taxable income = $15,000
Total taxable income for both of them will be:
$ 80,000 + $ 50,000 = $ 130,000
When you make use of the Schedule Y-1,
The amount of the tax on total income shall be said as:
Tax liability = $9,086 + (($130,000 - $78,950) * 22%)
= $9,086 +($51,050 * 22%)
= $9,086 + $11,231
= $ 20,317
To get the Effective tax rate, it will be:
= tax liability / Total taxable income Effective tax rate
= [tex]\frac{20,317}{30000}[/tex] that is also written as $20,317/ $130,000
So, the average tax rate is = 15.63%
Therefore, the average tax rate will be = 15.63 percent
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Work out (5*10^3)*(9*10^7).
Give your answer in standard form.
Work out (7*10^5) / (2*10^2).
Give your answer in standard form.
Answer:
(5*10^3)*(9*10^7) = 4.5*10^11
(7*10^5) / (2*10^2) = 3.5*10^3
Step-by-step explanation:
calculate 5 multiply by 9
5*9=45
the multiple of the power in the same base of number is calculated by using addition(+)
(10^3)*(10^7) = 10^(3+7)
= 10^10
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
45*(10^10)
= (4.5*10^1) * (10^10)
= 4.5*10^(1+10)
= 4.5*10^11
calculate 7 divide by 2
7/2=3.5
the dividing of the power in the same base of number is calculated by using subtraction(-)
(10^5)/(10^2)
= 10^(5-2)
= 10^3
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
3.5*10^3
Answer:
→ (5×10³)×(9×10⁷) = 4.5 × 10¹¹→ (7×10⁵) / (2×10²) = 3.5 × 10³Step-by-step explanation:
(5×10³)×(9×10⁷)
= 5×10³×9×10⁷
= 5×9×10³×10⁷ (commutative property)
= (5×9)×(10³×10⁷) (associative property)
= 45 × 10³⁺⁷
= 45 × 10¹⁰. (Exponent property)
= 4.5 × 10¹¹
…………………………………………
(7×10⁵) / (2×10²)
= (7/2) × (10⁵/10²)
= 3.5 × 10⁵⁻²
= 3.5 × 10³
Find the area of the circle. A circle has a diameters of 17 centimeters. Pi value is 3.142
Answer:
Area of the circle = 227.0095 cm^2
Step-by-step explanation:
Given:
Diameter (D) = 17 cmπ = 3.142To Find:
Area of the circle
Soln:
We know that,
Area of the circle: πr²
where:
π = 3.142r = radiusBut we don't know the radius,as the diameter is given.We could use the formula of diameter & plug the value of it do find the radius.
We know that,[tex] \rm \: Diameter = 2(r)[/tex]
Where
r = radiusSubstitute the value of Diameter:
Diameter = 2r
17 = 2r
17/2 = r
8.5 = r
r = 8.5
Now we got the radius, so substitute radius onto the formulae:
Area of the circle = πr²Ar(circle) = π(8.5)²Ar(circle) = 72.25π(Answer in terms of π)Ar(circle) = 72.25 * 3.142Ar(circle) = 227.0095 cm^2[tex]\text{Area of circle} = \pi\cdot \text{Radius}^2\\\\\\~~~~~~~~~~~~~~~~~~=\pi~ \left( \dfrac{\text{Diameter}}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=3.142 \left(\dfrac{ 17}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=227.0095~ \text{cm}^2[/tex]
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
A 2-column table with 6 rows. Column 1 is labeled x with entries 25, 28, 30, 31, 33, 40. Column 2 is labeled y with entries 7.5, 6, 5.5, 5, 4.5, 4.5.
The regression line shows a:
negative trend line with a strong relationship.
negative trend line with a weak relationship.
positive trend line with a strong relationship.
positive trend line with a weak relationship.
Finding the correlation coefficient, it is found that the regression line shows a:
negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.
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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures the correlation between two variables, assuming values between -1 and 1.
If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.
Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.
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Help please and thank you
Answer: 9
Step-by-step explanation:
By the geometric mean theorem, [tex]\frac{x}[6} =\frac{6}{4} \longrightarrow x=\left(\frac{6}{4} \right)(6)=\boxed{9}[/tex]
What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the line
y=x?
O (10,-2)
O (-10, 2)
O (-2,-10)
O (2, 10)
Answer:
it is b
Step-by-step explanation:
The solution is Option A.
The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the coordinates of the point A be A ( x , y )
Now , the vertex A is reflected over the line y = x
When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )
So , the coordinates of the point A' ( -2 , 10 )
Now , the coordinates of the point A will be
A ( x , y ) = A ( 10 , -2 )
Therefore , the value of A is A ( 10 , -2 )
Hence , the coordinates of the point before reflection is A ( 10 , -2 )
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The revenue from selling x necklaces is r(x) =10x. The cost of buying x necklaces is c(x)=4x+15. The profit from selling x necklaces is p(x)=r(x)-c(x).
Answer:
the revenue is 280 by 190
Help please asap aaaaaaaaaaaaaaaaaa
Answer:
Step-by-step explanation:
Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.
__
Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...
a = 78,500b = 1.02 = 1 +0.02 = 1 +2%The value of x is zero in the year 2000, so the population that year is ...
p(0) = a = 78,500
The increase per year is the value of 'b' with 1 subtracted:
growth rate = 2% per year
EASY POINTS
NEED HELL ASAP WIT THIS
Answer:
5
Step-by-step explanation:
You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.
MATH
•••••••••
AGAIN DON'T DELETE THIS QUESTION!
••••••••••••
PLEASE ANSWER THIS CORRECTLY
(NEED SOLUTIONS)
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Step-by-step explanation:
See the attached pics it explains everything
Answer:
Corresponding Angles Theorem
When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).
Alternate Exterior Angles Theorem
When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Part AQ1. As s ║ c we can apply the Corresponding Angles Theorem:
⇒ 11x - 5 = 116
⇒ 11x - 5 + 5 = 116 + 5
⇒ 11x = 121
⇒ 11x ÷ 11 = 121 ÷ 11
⇒ x = 11
Q2. As s ║ c we can apply the Alternative Exterior Angles Theorem:
⇒ 12x - 4 = 148
⇒ 12x - 4 + 4 = 148 + 4
⇒ 12x = 152
⇒ 12x ÷ 12 = 152 ÷ 12
⇒ x = 38/3 = 12.7 (nearest tenth)
Part BQ1. As j ⊥ r then the sum of the angles is 90°
⇒ 4x + 6x + 10 = 90
⇒ 10x + 10 - 10 = 90 - 10
⇒ 10x = 80
⇒ 10x ÷ 10 = 80 ÷ 10
⇒ x = 8
Q2. As j ⊥ r we can apply the Vertical Angles Theorem:
⇒ 5x - 10 = x + 70
⇒ 5x - 10 + 10 = x + 70 + 10
⇒ 5x = x + 80
⇒ 5x - x = x + 80 - x
⇒ 4x = 80
⇒ 4x ÷ 4 = 80 ÷ 4
⇒ x = 20
The regular hexagon has a radius of 4 in.
A regular hexagon has a radius of 4 inches.
What is the approximate area of the hexagon?
24 in.2
42 in.2
48 in.2
84 in.2
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
What is the approximate area of the hexagon?Given that;
Radius of the regular hexagon = 4inArea A = ?Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.
Angle of one triangle in the regular hexagon = 360°/6 = 60°.
To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.
We find the perpendicular height using Pythagoras theorem
h = √( (4)² - (2)² )
h = √( 16 - 4 )
h = √( 12 )
h = √( 2² × 3 )
h = 2√3
Now, we determine the area of a single triangle.
Area = (1/2) × base × height
Area = 0.5 × 4 × 2√3
Area = (4√3)in²
Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6
Area of regular hexagon = 6 × (4√3)in²
Area of regular hexagon = 24(√3)in²
Area of regular hexagon = 41.57in² ≈ 42in²
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
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Answer: b
Step-by-step explanation:
Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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find x
give your answer to 3 significant fingers
Answer:
1.64
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
6.6^2 + x^2 = 6.8^2
43.56+x^2=46.24
Subtract 43.56 from each side
x^2 = 46.24-43.56
x^2 =2.68
Take the square root of each side
sqrt(x^2) = sqrt(2.68)
x =1.637080554
To 3 significant digits
x = 1.64
Answer:
Step-by-step explanation:
x = 1.637 mm
Pythagorean theorem:We can use Pythagorean theorem, to find the unknown side for a right angled triangle.
The side opposite to 90 is the longest side and it is the hypotenuse.
Base² + altitude² = hypotenuse²
x² + 6.6² = 6.8²
x² + 43.56 = 46.24
x² = 46.24 - 43.56
x² = 2.68
x = √2.68
[tex]\sf \boxed{\bf x = 1.637 \ mm }[/tex]
12. If angles of measures (x - 2)° and (2x + 5)° are a pair of complementary angles, find the measures of
those angles.
A) 57" and 123
O B) 27" and 63
OC) 50 and 40°
OD) 30 and 60
Answer: B
Step-by-step explanation:
The angles add to 90 degrees if they are complementary, so:
[tex]x-2+2x+5=90\\3x+3=90\\3x=87\\x=29[/tex]
So, the angles measure 29-2=27 degrees and 2(29)+5=63 degrees.
a body starts from rest and moves with uniform acceleration of 4m/s² until it travels a distance of 800m,find the velocity
Answer:
80 m/s
Explanation:
Given:
i) initial velocity (as starts from rest) = 0 m/s
ii) acceleration: 4 m/s²
iii) distance travelled: 800 m
Formula required:
(final velocity)² - (initial velocity)² = 2 × acceleration × distance
Now solve:
v² - 0² = 2 × 4 × 800
v² = 6400
v = √6400
v = 80 m/s
Must show work-Solve the conjunction and describe the solution set. −5 < 2x + 3 < 9
The solution set of the inequality −5 < 2x + 3 < 9 is (-4,3)
How to solve the inequality?The compound inequality is given as:
−5 < 2x + 3 < 9
Expand the inequality
−5 < 2x + 3 or 2x + 3 < 9
Rewrite as:
2x + 3 > -5 or 2x + 3 < 9
Subtract 3 from both sides
2x > -8 or 2x < 6
Divide both sides by 2
x > -4 or x < 3
Rewrite as:
(-4,3)
Hence, the solution set of the inequality is (-4,3)
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Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.
The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].
What is the slope of a straight line?A slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.
The slope of a line that passes through points ( p,q) and (x,y)
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
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I need help asap!!!!!!!!!
A total of 10,800 pharmacy technicians were hired last year in particular country. This is 3% of all pharmacy technicians employed in the country. How many pharmacy technicians are employed in the country?
well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]
HELPPP HELP MEH plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has__ sides.
The minimum number of sides that the polygon at the base of the prism must has 4 sides.
What is a Polygon?This refers to the plane figure in geometry that has three or more sides and angles in a finite straight line.
As we know the minimum number of sides a polygon does the base of the polygon have 4 side.
Now, as the plane intersect a prism parallel to base of the prism so the polygon of 5 sides will form then at least the base of the polygon will have 4 sides.
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Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
Step-by-step expiation : 5575.3
The weight of a bag of Brand A cookies is labeled as 3 ounces on the bag. However, the actual weights of the bags vary by a small amount. According to the packaging specifications, the weights are approximately normally distributed with a mean of 3.05 ounces and a standard deviation of 0.06 ounce. Select the number to complete the sentence. According to the specifications, approximately percent of the bags weigh 3.00 ounces or more
Using the normal distribution, it is found that approximately 79.67% of the bags weigh 3.00 ounces or more.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3.05, \sigma = 0.06[/tex]
The proportion of the bags that weigh 3.00 ounces or more is one subtracted by the p-value of Z when X = 3, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 3.05}{0.06}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
1 - 0.2033 = 0.7967 = 79.67%.
79.67% of the bags weigh 3.00 ounces or more.
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PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Circumference: 25.12m
Area: 50.24 [tex]m^{2}[/tex]
Step-by-step explanation:
Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius
C=3.14*2*4=3.14*8=25.12
Formula for area of a circle: A=[tex]\pi r^{2}[/tex]
A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24
sally has 10 pounds she wants to buy 28 cans of soda which cost 26p each. how much money does she spend and does she have enough
Answer:
she will need 728 pounds to buy 28 cans but she only has 10 pounds so she doesn't even have enough for 1 can of soda
I need the answer please
The graphed cosine function can either be:
cos(x + pi) or cos(x - pi).
Which is the equation of the graphed function?
We know that this function is a cosine function with a phase shift, so the general form is:
f(x) = cos(x + P).
Where P is the phase shift.
In the graph we can see that when x = 0, f(0) = -1
And we know that cos(pi) = -1 = cos(-pi)
Then we must have that:
f(0) = cos(P) = -1
By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:
f(x) = cos(x + pi).
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