Answer:
6 ft
Step-by-step explanation:
volume of cone πr^2 (h/3)
84π = πr^2 (7/3)
84π/(7/3) = r^2π
84/(7/3) = r^2
sqrt (84 /(7/3)) = r
6 = r
What are the solutions of sin(2theta)+sin(theta)=cos(theta) on the interval [0, 360]
The solutions are: θ = 90º, 270º, 30º, and 150º
Given,
sin2θ = cosθ
sin2 θ = 2sinθ cosθ
2sinθ cosθ = cosθ
2sinθ cosθ - cosθ = 0
factor
cosθ(2sinθ-1) = 0
cosθ = 0 or 2sinθ - 1 = 0
cosθ = 0 when θ=90º or θ=270º (look on the unit circle)
2sinθ - 1 = 0
2sinθ = 1
sinθ = 1/2
look at the unit circle and see that sinθ=1/2 when θ=30º
sin is positive in Quadrant2 as well as Quadrant 1
180º-30º=150º
θ=150º
answers: θ=90º, 270º, 30º, and 150º
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Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)
A) Does y vary directly with x?
B) What is the constant of variation?
Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
Variationy = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
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f(x) is a function. O A. True 0 False 6 12 9 f(x) 3 4 7
Answer:Answer: true
Step-by-step explanation: f(x) is a function because each x value (left oval) has one y value (right oval)!
The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) f(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. f(x) is an odd degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a positive leading coefficient.
Last option. The correct statement about the graph is g(x) is an odd degree polynomial with a positive leading coefficient.
How to solve the questionWe have the function as
[tex]f(x) = x^2 - 2x + 1[/tex]
The polynomial that we have here is of an even degree. The highest degree we have here is 2. The coefficient that has the highest degree is 1.
Hence all of the options that have f(x) are incorrect.
The answer to the question is option 4.
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Can someone please help me on this
Answer:
? = 38°
Step-by-step explanation:
We can use the property of sine to find the missing angle value.
sin (angle) = opposite / hypotenuse
sin (?) = 16 / 26 <----- Insert values
? = sin⁻¹(16 / 26) <----- Rearrange
? = 37.97... <----- Solve
? = 38° <----- Round
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte
The probability of winning a lottery by selecting the correct six integers, are
[tex]\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}[/tex]
What is binomial distribution?The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
Part (a); positive integers not exceeding 30.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.
[tex]\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}[/tex]
Part (b); positive integers not exceeding 36.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}[/tex]
Part (c); positive integers not exceeding 42.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}[/tex]
Part (d); positive integers not exceeding 48.
To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}[/tex]
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The complete question is-
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.
Which statement is true of the graph on the
right?
The average salary doubled between year 1
and 2.
The average salary tripled between year 1
and 3.
The average salary increased by the same
amount each year.
DONE
1. The TRUE statement about the graph, which is represented here by the data table, is D. The average salary increased by some irregular amount each year.
2. The average salary per year between 2001 and 2006 is $3,600?
What is an average?An average number is the mean of a total value.
The average is computed as the total value of observations divided by the number of observations.
Data for the graph and Calculations:Year Salary
2001 $1,500
2002 2,600
2003 3,200
2004 4,100
2005 5,000
2006 5,200
Total $21,600
Average = $3,600 ($21,600/6)
Thus, the graph or the data table shows that D. The average salary increased by some irregular amount each year.
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Question Completion:1. Option D: The average salary increased by some regular amount each year.
2, What is the average salary per year between 2001 and 2006?
Answer: C-The average salary increased by the same amount each year.
NEXT ANSWER-B
Step-by-step explanation:
Solve the polynomial congruence x^2-3x+2 is congruent to 0 mod 5. Solve for x=? or x=?,when k is any integer
The solutions of x² - 3x + 2 ≡ mod 5 does not exist.
How to solve Polynomial Congruence?
We are given the Polynomial;
x² - 3x + 2 ≡ mod 5
Finding the roots of the equation gives;
x² - 2x - x + 2 = 0(mod 5)
x(x - 2) - 1(x - 2) = 0(mod 5)
Thus, RHS = 0(mod 5) = 0
The roots of the equation are;
x = 1 and x = 2
Thus, the solutions of x² - 3x + 2 ≡ mod 5 does not exist.
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Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
-Write the piecewise function for 0 to 2 miles.
f(x) = ?
The piecewise function is
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
How to determine the piecewise function?From the question, we have:
Fares = $2.00 ⇒ up to (and including) 1/2 miles
Fares = $0.70 increment ⇒ greater than 1/2 miles
Let x represent the number of miles, and f(x) the fares.
So, we have:
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
The above represents the piecewise function
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Read the excerpt from Chapter 3 of Wheels of Change . In 1881, as women in the United States continued to struggle with hoops and corsets and other fashion architecture, their counterparts in England formed the Rational Dress Society. This society called for more reasonable clothing solutions, including limiting the weight of a woman's undergarments to seven pounds. Why was the Rational Dress Society formed? to advocate for more functional cycling and athletic gear for women to push for more beautiful, intricate styles of clothing for women to encourage English women to dress differently than American women to promote safer, more comfortable styles of dress for women
Step-by-step explanation:
Chapter 3 of Wheels of Change .
But the bicycle craze had a more lasting impact on women’s clothing than just the use of bloomers. Thanks in large part to cycling, the innovation of rational dress reformers were starting to take effect by the end of the 1890s. Corsets were on their way out, dresses were getting shorter, and women no longer wore the heavy, bulky undergarments that gave them round, unnatural shapes. These changes went a long way toward unburdening women and setting the stage for them to be healthier and more active in the coming century.
Based on the excerpt, women in the 1890s became more independent and their lives improved as a result of
a rise in the popularity of bicycles.
a rise in the popularity of corsets.
cycling becoming less socially acceptable.
clothing becoming more restrictive.
Answer:
to promote safer, more comfortable styles of dress for women
Step-by-step explanation:
to promote safer, more comfortable styles of dress for women
Solve for xxx in the diagram below.
Answer:
x = 34
Step-by-step explanation:
The three angles form a straight line and are thus supplementary angles. The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:
180 = 2x + 112
68 = 2x
x = 34
Identify the factors of 6ab − 8a 21b − 28. (2a 4)(3b − 7) (2a − 4)(3b 7) (2a 7)(3b − 4) (2a − 7)(3b 4)
Answer: ) (2a+7)(3b- 4)
Step-by-step explanation:
Analyzing the Discrim
Which values of c will cause the quadratic equation-x²+3x+c=0 to have no real number solutions? Check all that
apply.
0-5
0 0 0
9
Intro
ant of a Quadratic Equation
Done
The values of x that will give the quadratic equation no real number solutions are -5 and 9
What are real roots of a quadratic equation?Real roots of a quadratic equation are values of x, whose numbers can be represented on a number line.
Analysis:
We have -[tex]x^{2}[/tex] +3x +c = 0
[tex]b^{2}[/tex] - 4ac is called the discriminant of a quadratic equation.
if [tex]b^{2}[/tex] - 4ac < 0, then the quadratic equation has no real root.
where a = -1, b = 3 c = c
[tex](3)^{2}[/tex] -4(-1)c < 0
9 + 4c < 0
4c < -9
c < -9/2
Which means values lower than -9/2 would give the solution no real root.
From, the options, only -5 would give no real solution, since it is lower than -9/2.
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Question is in the pic.
Answer is C as all other choices are even numbers therefore make the equation non-integer.
Answer:
C)7
Step-by-step explanation:
Due to the fact that all other options are even numbers so it Wii make the equation non-integer.
Can someone pls pls PLS, help me out? ASAP!! (Geometry)
“Complete the proof”
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)
4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)
5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)
1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20
Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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Which of the following statements about angles is NOT correct?
Complementary angles are two angles whose sum is 90 degrees.
The measure of an obtuse angle is always greater than the measure of an acute angle.
The measure of an acute angle and the measure of an obtuse angle added together will always
be supplementary.
Two right angles that share a leg are supplementary.
ANSWER: The third statement appears to be incorrect.
The lengths of three sides of a triangle are 2x + 1/5 feet , 4x + 1/2 feet , and x+ 1 5 . what is the perimeter of the triangle? the drondown menuto complete the answer
Answer:
7x + 9/10 ft
Step-by-step explanation:
To find the perimeter of a triangle, add the lengths of the three sides
P = 2x + 1/5 + 4x + 1/2 + x+ 1/ 5
Combine like terms
P = 7x + 2/5 +1/2
Get a common denominator
P = 7x + 2/5(2/2) + 1/2 * (5/5)
= 7x + 4/10 + 5/10
= 7x + 9/10
please put it in expanded form and solve it
Answer:
1/xyz^3
Step-by-step explanation:
exponents are subtracted when divided
x^0 is 1
negative exponents are positive in the denominator
(4x^0y^-2z^-3) / (4xy-1)
(4xy^-2z^-3) / (4xy^-1)
x-1y^-1z^-3
1/xyz^3
Solve the following system of equations:
3x-5y=-11
7x+2y=-12.
Express your answer as an ordered pair. (x, y)
Answer: (-2, 1)
Step-by-step explanation:
We will graph the given equations. The point of intersection is the solution to the system of equations. See attached.
They intersect at the point (-2, 1) giving us an answer of x = -2 and y = 1, but this question asks for the answer as an ordered pair so we leave it as is.
Does anyone know how to do this
Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.
What is the area of a rectangle?The area of a rectangle of length l and width w is given as follows:
A = lw.
In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:
A = 80.w = l + 2.Then:
l(l + 2) = 80
l² + 2l - 80 = 0
(l + 10)(l - 8) = 0.
We need the positive measure, hence:
l - 8= 0 -> l = 8 units.
w = l + 2 = 10 units.
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When y = -8, x = 8, what is x when y = -6?
Answer:
x = 6
Step-by-step explanation:
y = -8
x = 8
-x = -8 = y
-x = y
now, when y is -6
-x = y = -6
-x = -6
x = 6
The sum of 225 consecutive positive integers only has digits 1 or 0. What is the smallest possible value of the sum?
Answer:
1 +10=11 (since 0 is neither negative or positive the first and second positive integerswith 1 or 0
these box plots show the basketball scores for two teams.
The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.
What is a box plot ?A box plot is used to study the distribution and level of a set of scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
A box plot is symmetric when the median is at the center of the box and negatively skewed if the median is closer to the upper quartile.
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Solve for X. Please solve this.
Answer:
32
Step-by-step explanation:
Opposite angles are congruent, so Angle BAC is 58 degrees.
Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.
Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.
Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.
Helllllllppppppppppp what Is 20 divided by 8
Answer:
2.5
Step-by-step explanation:
IVE BEEN WATCHING YOUR ACCOUNT STOP STEALING POINTS OR YOUR ACCOUNT WILL BE TERMINATED.
Explain how to solve 4^(x + 3) = 7 (x+3 being an exponent) using the change of base formula. Include the solution for x in your answer—round your answer to the nearest thousandth.
Using natural logarithms properties, we will see that:
x = -1.596
How to solve the equation?
Here we can use the property:
[tex]ln(a^b) = b*ln(a)[/tex]
Now we have the equation:
[tex]4^{x + 3 }= 7[/tex]
If we apply the natural logarithm in both sides, we get:
[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]
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The area of the triangle shown is represented by A=s(s−12)(s−9)(s−7)−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle? Round your answer to the nearest hundredth. (25 points to answer!! please))
The height h of the triangle is 5.42 ft
How to find height of a triangle?The height of the triangle can be found using the formula below:
Area = 1 / 2 bh
where
b = baseh = heightTherefore,
A = √s(s - a)(s - b)(s - c)
Hence,
s = 14 + 7 + 11 / 2 = 32 / 2 = 16
A = √16(16 - 11)(16 - 7)(16 - 14)
A = √1440
A = 37.947331922
A = 37.95 ft²
37.95 = 1 / 2 × 14 × h
h = 37.95 / 7
h = 5.42104741743
h = 5.42 ft
Therefore, the height h of the triangle is 5.42 ft
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Total area=
Help asap please thank u so much
The total area of the figure shown is 320 square units.
How to get the total surface area?
We can see that we have 4 triangular faces and one square face.
The area of a square of side length S is:
A = S²
Here we can see that the side length of the square is 10 units, then the area of the base is:
a = (10)² = 100
For a triangle of base B and height H, the area is:
[tex]A = B*H/2[/tex]
Here we can see that the base measures 10 units and the height 11 units, so the area of each triangular face is:
A' = (10)*(11)/2 = 55
Then the total area is:
area = 100 + 4*55 = 320
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