Answer:
The answer is 28
Step-by-step explanation:
sin0=opp/hyp
let hyp be x
sin30=14/x
0.5x=14
divide both sides by 0.6
x=14/0.5
x=28
x+4x=20
show your work
there are 12 inches in a foot how many square inches are in 1 1/2 feet
Answer:
144.
The reason is because 1 ft = 12 in, (1 ft)2 = (12 in)2 = 144 in2.
Please find ‘?’ Please help me out
Answer:
? = 16
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp side / adj
tan ? = 13 / 46
Taking the inverse tan of each side
tan ^ -1 ( tan ? ) = tan ^-1 ( 13/46)
? = 15.78075
To the nearest degree
? = 16
2 The density of a substance can be determined
by finding the unit rate that compares mass to
volume. A nugget of gold has a mass of
463.2 grams and a volume of 24.0 milliliters.
What is the density of gold?
F 11,116.8 g/mL
G 439.2 g/mL
H 0.052 g/mL
J 19.3 g/mL
Answer:
88888
Step-by-step explanation:
6201005050
Solve for x!!
1) x + 2(1.5x - 6) = 16
A) 4.25
B) 6
C) 6.5
D) 7
x+6y=-2
slope intercepct
The slope intercept is mathematically given as
x-intercept(s): (-2,0)
\(y=-\frac{1}{3}\\\\$y$-intercept(s): $\left(0,-\frac{1}{3}\right)$\)
This is further explained below.
What is slope intercept?Generally,
x+6 y=-2
Find the x-intercepts.
To find the x-intercept(s), substitute 0 for y and solve for x.
x+6(0)=-2
Simplify x+6(0).
x=-2
x-intercept(s) in point form.
x-intercept(s): (-2,0)
Find the y-intercepts.
To find the y-intercept(s), substitute 0 for x and solve for y.
(0)+6 y=-2
Solve the equation.
List the intersections.
x-intercept(s): (-2,0)
\(y=-\frac{1}{3}\)
\(y=-\frac{1}{3}\\\\$y$-intercept(s): $\left(0,-\frac{1}{3}\right)$\)
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Clara put 860 miles on her car in May. In
June, she put 28 less than twice the number
of miles on her car than she did in May.
Answer:
Let x be the number of miles Clara put on her car in June.
We are given that Clara put 860 miles on her car in May, so we can write:
Number of miles Clara put on her car in June = 2(860) - 28 (since she put 28 less than twice the number of miles on her car than she did in May)
Simplifying this expression, we get:
Number of miles Clara put on her car in June = 1,692
Therefore, Clara put 1,692 miles on her car in June.
Answer: increase 96.74%
Step-by-step explanation:
860 x 2 - 28 = 1692
1692 = 860 = 1.9674
( 1.9674 - 1 ) x 100 % = 96.74 %
! carefully calculated !Let f:R + R be a function that satisfies 0 < f(x) 0. Show that the series f(n) Σ 2m3 – 1 , n=1 converges regardless of the rule for f.
By the Comparison Test, the series Σ f(n)(2m^3 - 1) also converges, regardless of the rule for f.
The given series is Σ f(n)(2m^3 - 1), n = 1 to infinity. To show that it converges, we can use the Comparison Test.
Consider the series Σ |f(n)(2m^3 - 1)|. Since 0 < f(x) for all x, we have |f(n)| = f(n). Thus, the series becomes Σ f(n)(2m^3).
Now, let's compare this series to Σ 2m^3. Since f(n) > 0 for all n, we know that f(n)(2m^3) ≤ 2m^3 for all n. Thus, Σ f(n)(2m^3) ≤ Σ 2m^3.
The series Σ 2m^3 is a convergent p-series with p = 3 (since 3 > 1). Therefore, by the Comparison Test, the series Σ f(n)(2m^3 - 1) also converges, regardless of the rule for f.
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Find the average rate of change for the function
Answer:
average rate of change on [-1,3] = 11
Step-by-step explanation:
avg rate of change = \(\frac{f(b)-f(a)}{b-a}\)
\(\frac{f(3)-f(-1)}{3-(-1)}\)
1. find your y-values.
we are given the x values from the interval [-1,3]. Plug each into the equation to get the y-value of the coordinates.
\(f(-1)=4(-1)^2+3(-1)-4\\f(-1)=4(1)-3-4\\f(-1)=-3\\\)
coordinate: (–1,3)
\(f(3)=4(3)^2+3(3)-4\\f(3)=4(9)+9-4\\f(3)=36+9-4\\f(3)=41\)
coordinate: (3, 41)
2. plug into the slope formula
\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{41-(-3)}{3-(-1)} \\m=\frac{41+3}{4} \\m=\frac{44}{4} \\m=11\)
9.Which of the following are used to represent unknown quantities in algebra? A) Upper case letters B) Lower case letters C) Only letters a and x D)None of the above
Have no idea how to do this lok
Answer:
that hard
Step-by-step explanation:
Students in a sixth grade class are raising money for an end-of-the-year
camping trip. So far, they have raised $240. This is ⅖ of the cost of the trip. How
much does the trip cost?
Answer:
$600
Step-by-step explanation:
We know
2/5 = $240
1/5 = $120
5/5 - 2/5 = 3/5
So, we need to find the 3/5 missing
1/5 = $120
3/5 = $360
So, we add both numbers to find the trip cost
240 + 360 = $600
So, the trip costs $600
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Aria paid $75,000 for her house. its property value increased by 2.2% per year. when aria sold her house after eleven years, how much was it worth, to the nearest hundred dollars? a. $133,700 b. $95,400 c. $95,300 d. $93,100
The worth of the Aria's house, when she sold her house after eleven years, is $95300 to the nearest a hundred dollars.
What is percentage increase?Percentage increase is the amount added to the initial value of a product in the percentage part.
The percentage increase over a year can be found out using the compound interest formula,
\(A=P(1+\dfrac{r}{100})^n\)
Here, (A) is the final amount (P) is the principal amount, (r) is the rate and n is the time period.
Aria paid $75,000 for her house. its property value increased by 2.2% per year. The time period is 11 years. Put these values in the above formula as,
\(A=75000(1+\dfrac{2.2}{100})^{11}\\A=95284.3\)
To the nearest, a hundred dollars,
\(A=95300\)
The worth of the Aria's house, when she sold her house after eleven years, is $95300 to the nearest a hundred dollars.
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Answer: incase you're still confused, the answer is $95,300. Hope this helps <3
in an orthic triangle, show that triangle aef, triangle bfd, and triangle cde are each similar to triangle ABC
In an orthic triangle, triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC.
An orthic triangle is formed by constructing perpendiculars from the vertices of a given triangle to the opposite sides. In this case, we have triangle ABC, and by constructing perpendiculars from the vertices A, B, and C to the opposite sides, we obtain triangle AEF, triangle BFD, and triangle CDE.
To show that triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.
Since triangle ABC and its orthic triangles share the same vertices, their corresponding angles are congruent. The perpendiculars drawn from the vertices of triangle ABC to the opposite sides create right angles, ensuring that the corresponding angles in the orthic triangles are also right angles.
Regarding the sides, the perpendiculars from the vertices of triangle ABC divide the sides into segments. By the properties of perpendicular lines, these segments form similar triangles with triangle ABC. Therefore, the corresponding sides of triangle AEF, triangle BFD, and triangle CDE are proportional to the sides of triangle ABC.
By establishing congruent angles and proportional sides, we can conclude that triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC.
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A rectangle has a perimeter of 64. the width is 3 less than the length. the equation for the scenario is 2x 2(x â€"" 3) = 64. what does the variable x represent in the equation? what will finding x â€"" 3 determine?
The variable x represent the length of rectangle.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter= 64 units
let the length be x.
So, width = x - 3
So, Perimeter of rectangle = 2 ( l + w)
64 = 2( x+ x -3)
32 = 2x -3
29= 2x
x= 29/2
Hence, the variable x represent the length of rectangle.
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A printer wants to put 54 square inches of text into a rectangle on an 8 x 11 sheet of paper. She wants the text to be surrounded by a border of constant width. Write an equation that can be used to find the width of the border (x)
\(4x^2 - 38x + 34 = 0\) ; This is a quadratic equation that can be solved using the quadratic formula. Once we solve for x, we can find the width of the border.
Let's assume that the width of the border around the text is x inches. Then the dimensions of the rectangle including the border will be:
Length = 11 inches
Width = 8 inches
The dimensions of the rectangle containing only the text will be:
Length = 11 - 2x inches (because there are two borders, one on each side)
Width = 8 - 2x inches (because there are two borders, one at the top and one at the bottom)
The area of the rectangle containing only the text will be:
Area = (11 - 2x) × (8 - 2x)
We know that the area of the rectangle containing only the text is 54 square inches. So we can set up the equation:
(11 - 2x) × (8 - 2x) = 54
Expanding the left-hand side of the equation, we get:
\(88 - 38x + 4x^2 = 54\)
Rearranging and simplifying, we get:
\(4x^2 - 38x + 34 = 0\)
This is a quadratic equation that can be solved using the quadratic formula. Once we solve for x, we can find the width of the border.
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Which of the following are solutions to the equation below?
Check all that apply.
3x^2 + 10x-30 = x
Answer:
x1= -5
x2= 2
Step-by-step explanation:
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
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\(\text{Solve for 'x'.}\\\\3x + 15 = 33\\\\\\text{Thank you.}\)
Hi there!
»»————- ★ ————-««
I believe your answer is:
\(x=6\)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
\(\boxed{\text{Solving for 'x'...}}\\\\3x + 15 = 33\\--------------\\\rightarrow 3x + 15 - 15 = 33 - 15\\\\\rightarrow 3x = 18\\\\\rightarrow \frac{3x=18}{3}\\\\\rightarrow \boxed{x = 6}\)
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=6
Step-by-step explanation:
3x+15=33
or as, 3x=33-15
or as, 3x=18
x=18/3=6
so we got 6 is the answer
determine the values of the following quantities. (round your answers to three decimal places.) (a) t0.10, 10 (b) t0.05, 10 (c) t0.05, 21 (d) t0.05, 60 (e) t0.005, 60
These values are based on the t-distribution table and represent critical values for the given probabilities and degrees of freedom.
To answer this question, we need to use a t-table. The values we are looking for are the t-values associated with specific probabilities and degrees of freedom.
(a) t0.10, 10 = 1.372 (from the t-table, using 10 degrees of freedom and the probability of 0.10)
(b) t0.05, 10 = 1.812 (from the t-table, using 10 degrees of freedom and the probability of 0.05)
(c) t0.05, 21 = 1.721 (from the t-table, using 21 degrees of freedom and the probability of 0.05)
(d) t0.05, 60 = 1.671 (from the t-table, using 60 degrees of freedom and the probability of 0.05)
(e) t0.005, 60 = 2.660 (from the t-table, using 60 degrees of freedom and the probability of 0.005)
Note that we round all answers to three decimal places, as specified in the question. The values we have found are the t-values for the specified probabilities and degrees of freedom. These values can be used in calculations involving t-distributions.
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Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10.
a. x squared divided by 5 plus y squared divided by 8 = 1
b. x squared divided by 25 plus y squared divided by 64 = 1
c. x squared divided by 8 plus y squared divided by 5 = 1
d. x squared divided by 64 plus y squared divided by 25 = 1
Answer:
c
Step-by-step explanation:
There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
The probability that the person uses exactly one of the facilities is 0.64
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Find analysis in the attached file.
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At a restaurant, you order an appetizer for $5.25, a meal for $12.75, and a drink for $2.99. If the sales tax is 9%, what is the total of your bill including sales tax?
Answer:
$22.88
Step-by-step explanation:
The total bill is the subtotal plus tax. The tax is computed by multiplying the tax rate by the subtotal, which is the total of all items being billed.
subtotal = $5.25 +12.75 +2.99 = 20.99
tax = $20.99 × 0.09 = $1.89
The total bill is ...
subtotal + tax = $20.99 +1.89 = $22.88
if the area of a square field is 360 sq. meters. determine the perimeter of the field.
Answer:
240 meters
Step-by-step explanation:
Since you dont know the length of any sides you would find the lengths of each side
√(360) = 18.973665961
Since each side equals 18.973665961 you would add that to its self 3 times
18.973665961+18.973665961+18.973665961+18.973665961
that equals which equals 75.894663844
What two numbers multiply to 7 and add up to -6?
Answer:
-7 and 1 multiply to 7 and add up to -6
Step-by-step explanation:
-7 and 1 multiply to 7 and add up to -6
PLEASE HELP! IT'S DUE TODAY!
Answer:
25 ft
Step-by-step explanation:
5x = 10² ⇒ x = 20
h = 20 + 5 = 25 ft tall
using y=-6x what is the value of x if y=42
Answer:
Step-by-step explanation:
Y = - 6x
Putting value of 42
42 = - 6x
42/-6 = x
-7 = x
Answer:
x=-7
Step-by-step explanation:
y=-6x
y=42
use substitution
42=-6x
divide both sides by -6
x=-7
told..................
Answer:
B
Step-by-step explanation:
You can solve the system of equations by elimination, since 3y and -3y will cancel out.
After combining the two equations, you will get 19x = -152.
Divide each side by 19:
x = -8, so the answer is B
You may need to use the appropriate appendix table or technology to answer this question. mathematics portion of the test. \( + \) Assume these test scores are normally distributed. 25 or higher
The given question is incomplete and lacks specific information or context. It mentions a mathematics portion of a test and a score requirement of 25 or higher, assuming the test scores are normally distributed. However, there is no clear question or task stated. To provide a comprehensive answer, it is necessary to have a specific question or prompt related to the given information.
Without a specific question or task, it is difficult to provide a detailed explanation or analysis. However, based on the limited information provided, it seems that the question might be asking for the probability or percentage of students scoring 25 or higher on the mathematics portion of the test, assuming a normal distribution of test scores. To calculate this probability, additional information is needed, such as the mean and standard deviation of the test scores or a z-score table.
Using the mean and standard deviation, one could calculate the z-score for a score of 25 and then determine the corresponding probability from the z-score table. The z-score represents the number of standard deviations a particular score is from the mean. By looking up the z-score in the table, one can find the corresponding probability or percentage.
However, since the question lacks specific information or context, it is not possible to provide a more detailed or accurate answer.
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Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).
x -6 -4 -11 5
g(x) -11 -7 -1 3 11
h(x) 16 10 1 -5 -17
The x - intercept of g(h(x)) is, 1/9.
What are linear functions?
Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.
Let g(x) and h(x) are linear functions.
We have to find the x - intercept of g(h(x)).
Let g(x) and h(x) are linear functions so
g(x) = ax + d and g(x) = cx + e
g(-6) = a(-6) + d
-11 = -6a + d ..(1)
g(-4) = a(-4) + d
-7 = -4a + d ..(2)
Subtract equation (1) and (2)
-11 - (-7) = -6a + d - (-4a + d)
-1 + 7 = -6a + d + 4a - d
6 = -2a
a = -3
Plug a = -3 in equation (1)
11 = -6(-3) + d
11 = 18 + d
d = 11 - 18
d = -7
⇒ g(x) = -3x - 7
Now h(x) = cx + e
h(-6) = c(-6) + e
16 = -6c + e ..(3)
h(-4) = c(-4) + e
10 = -4c + e ..(4)
Subtract question (3) and (4)
16 - 10 = -6c + e - (-4c + e)
6 = -6c + e + 4c - e
6 = -2c
c = -3
Plug c = -3 in equation (3)
16 = -6(-3) + e
16 = 18 + e
e = 16 - 18
e = -2
⇒ h(x) = -3x - 2
Now,
g(h(x)) = -3(h(x) - 7
= -3(-3x - 2) - 7
= 9x + 6 - 7
= 9x - 1
9x = 1
x = 1/9
Therefore, the x - intercept of g(h(x)) is 1/9.
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