Answers
For the given measures of angles of heptagon, the value of x is equal to 27° .
As given in the question,
Sum of all the interior angles of the heptagon is equal to 900.
Given measure of all the angles of the heptagon is given by :
135°+( 5x - 4 )° +( 7x - 64 )° + 120° +( 6x - 8 )° +( 4x + 15 )° + ( 3x + 31 )°= 900°
Arrange all the like terms of the given expression together we get,
⇒ ( 5x + 7x + 6x + 4x + 3x )° + ( 135 - 4 - 64 + 120 - 8 + 15 + 31 )° = 900°
⇒ 25x° + 225° = 900°
⇒ 25x° = 900° -225°
⇒ 25x° = 675°
⇒ x = 27°
Therefore, for the given measures of angles of heptagon, the value of x is equal to 27° .
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Related Questions
In fractions what is the probability that a teenager selected at random is female and their favourite hobby is watching films
Answers
The probability that a teenager selected at random is female and their favourite hobby is watching films is 1/4.
What is probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From the information given, there is a total of 32 teenagers. Of those, 8 are female with a favorite hobby of watching films.
Therefore, the probability will be:
= Female who watch films / Total teenagers
= 8/32
= 1/4.
The probability is 1/4.
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Complete question
A group of teenagers is asked about their favorite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total
Male 9 2 3 14
Female 7 3 8 18
Total 16 5 11 32
Q6a. In fractions, what is the probability that a teenager selected at random is female and their favourite hobby is watching films? You can simplify this fraction if you wish.
Please help I was sick and missed out on class.Thank you
Answers
Determine f(5) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4.
11
29
41
125
Answers
The value of the function when the value of x is 5 is 29.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
[tex]f(x)= \left \{ {{x^3 \;\;\;\;\;\; x < -3} \atop {2x^2-9\;\;\;-3\leq x < 4}} \atop {5x+4\;\;\;x > 4}}\right.[/tex]
As the value of the function is to be found when the value of x is 5.
So, we can write the function as,
f(5) = 5x + 4
f(5) = 5(5) + 4
f(5) = 29
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In a telephone poll, 36 people said they like shopping and 7 people said they do not like shopping. What is the ratio of the number of people who do not like shopping to the total number of people polled?
Answers
Answer:
7:43 or [tex]\frac{7}{43}[/tex]
Step-by-step explanation:
The total is 43 7 + 36
Answer:
7:43
Step-by-step explanation:
36+7 = 43
43 is the total amount of people that were polled
those who don't like shopping are 7, as stated in the question
the ratio is 7:43
NO LINKS!! Please help me with this symmetry part 3 Select all that apply
Answers
Answer:
[tex]y=-\dfrac{1}{8}x^3[/tex]
Step-by-step explanation:
If a function is symmetrical about the origin, when y is replaced with (-y) and x is replaced with (-x), the resulting function will be equal to the original function.
Original function:
[tex]y=-\dfrac{1}{8}x^3[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies -y=-\dfrac{1}{8}(-x)^3[/tex]
[tex]\implies -y=-\dfrac{1}{8}\cdot -x^3[/tex]
[tex]\implies -y=\dfrac{1}{8}x^3[/tex]
Multiply both sides by -1:
[tex]\implies y=-\dfrac{1}{8}x^3[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the origin.
Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally
Answers
Answer: $110 but that may be wrong
Step-by-step explanation:
What do i right please help due tomorrow
Answers
Thank you for your service. It is greatly appreciated. Because of you and your many sacrifices, we are free and safe. It may not feel like it, but trust me when I say that your and your comrades’ courage and determination have been and continue to be thoroughly recognized and remembered. You are a true hero, and I look up to you with the utmost sober reverence.
Sincerely,
[your name]
4x+7=1+2(2x+3) linear equations
Answers
Solving the Question
[tex]4x+7=1+2(2x+3)[/tex]
⇒ Our goal is to solve for x. We can do this by moving everything else to the other side of the equation.
⇒ Open up the parentheses:
[tex]4x+7=1+4x+6[/tex]
⇒ Simplify:
[tex]4x+7=4x+7[/tex]
Because both sides are equal, we end up with x = x.
In this case, we can say that all values of x are true.
AnswerAll values of x are true.
Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability
that the first card will be a spade, the second card will be a black card, and the third card will be a ten.
Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.
Given that,
A normal 52-card deck is used to randomly select three cards.
We have to find the probability that a spade, a black card, and a ten will be dealt as the first, second, and third cards, respectively.
Three cards are drawn with replacement from a standard deck so for the first one i.e heart , probability is (13/52)=0.25
for 2nd one i.e red it is (26/52)=0.5
for 3rd one i.e queen it is (4/52)=0.0769
thus, the answer is 0.25*0.5*0.0769=0.0096
Therefore, The fraction in lowest terms or a decimal rounded to the nearest tenth is 0.0096.
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(11x=28)
(7x-8)
Solve for x
Answers
it divides to a repeating decimal 2.54
so just write it as a fraction 28/11
8 divided by 7 is a repeating decimal 1.142857 so just write as a fraction 8/7
4. (03.04)
Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x³ +1. Include the average rate of change in your answer. (10 points)
Answers
Answer:
39
Step-by-step explanation:
The given function to us is ,
[tex]\longrightarrow f(x) = 3x^3 + 1\\ [/tex]
We need to find the average rate of change between [tex] x=1 [/tex] and [tex] x=3[/tex] .
We can calculate the average rate of change as ,
[tex]\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} [/tex]
So that ,
[tex]\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ [/tex]
[tex]\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ [/tex]
[tex]\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\[/tex]
[tex]\longrightarrow A(x) = \dfrac{78}{2}\\ [/tex]
[tex]\longrightarrow\underline{\boxed{ A(x) = 39}} [/tex]
The balance on a credit card, that charges a
28.5% APR interest rate, over a 1 month
period has a daily balance of $145. What is
the finance charge, on the average daily
balance, for this 1 month period?
28.5% = 0.285
Hint: Divide the decimal by 12 to get the monthly interest
rate. Do not round that answer. Take that answer and
multiply it to the average daily balance.
Finance charge = $[?]
Round to the nearest hundredth
Answers
The finance charge on the average daily balance for , this 1 month period is $3.45 .
In the question ,
it is given that ,
the daily balance over the period of 1 month = $145
The APR rate of interest = 28.5%
the monthly APR rate of interest = (28.5%)/12 = 2.375%
the finance charge for the 1 month period can be calculated using the formula .
finance charge = (daily average balance)×(monthly rate of interest)
Substituting the values , we get
finance charge = 145 × 2.375%
= 145 × 0.02375
= 3.44375
≈ 3.45
Therefore , The finance charge on the average daily balance for , this 1 month period is $3.45 .
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help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
-1/6 x 12/5
you will get -2/5
JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of
2:1.
What are the two possible locations of L?
(-9, 0.5)
(-2, -1)
(-7, 0.25)
(0, -1)
(-6, 0)
(1, -1.5)
(-4,-0.5)
Answers
The two possible locations of L are (-2,-1) and (14/3, -5/3).
According to the question,
We have the following information:
JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.
We know that the following formulas are used to find the coordinates of a point:
x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]
y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]
In this case, we have the following values:
x1 = -10 and y1 = 1
x2 = 2 and y2 = -1
m = 2 and n = 1
So, we have:
x = {2*2+1*(-10)}/(2+1)
x = (4-10)/3
x = -6/3
x = -2
For the negative sign:
x = {2*2-1*(-10)}/3
x = (4+10)/3
x = 14/3
x = 4.67
The values of y:
y = {2*(-2)+1*1}/3
y = (-4+1)/3
y = -3/3
y = -1
For the negative sign:
y = {2*(-2)-1*1}/3
y = (-4-1)/3
y = -5/3
y = -1.67
Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).
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The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 135 minutes with a standard deviation of 44 minutes. At
= 0.01 level, is the student academic group's claim correct?
1. What is the p-value
Answers
The p-value of this sample proportion is equal to 0.0360.
At the 0.01 (1%) significance level, there isn't enough evidence to conclude that freshmen students study less than 2.5 hours per day, on an average.
How to calculate value of the test statistic?For this statistical study, we would use a t-test statistic and the null and alternative hypotheses would be given by:
H₀: p ≥ 150 minutes
H₁: p < 150 minutes
Mathematically, the t-test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;\mu}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x represents the sample mean.μ represents the mean.σ represents the standard deviation.n represent the number of students.Substituting the given parameters into the formula, we have;
t-test, t = (135 - 150)/(44/√30)
t-test, t = (-15)/8.0333
t-test, t = -1.8672
From the t distribution table, the p-value is given by:
p-value = P(t < -1.8672)
p-value = 0.0360
Since the p-value (0.0360) is greater than the significance level (0.01), we fail to reject the null hypothesis because there is insufficient evidence to claim that the mean time of the freshman students is less than 2.5 hours per day.
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Use a compass and straight edge to create a line parallel to line AB through a point E that is not on line AB. First, draw a line from point E that crosses line AB, and label the intersection point C. Which step comes next?
- Set the compass point on A and draw an arc of any size across line .
- Move the compass point to the upper arc and mark off an arc, creating point D.
- Set the compass width to the width of the arc that crosses line .
- Place the point of the compass on C and draw an arc that crosses both lines.
Answers
Answer:
Step-by-step explanation:
The given steps describe constructing a parallel line using a compass and straightedge given line and a point E that is not on line .
Step 1: Draw a line through point E that intersects line , and label the point of intersection, C.
Step 2: Place the point of the compass on C and draw an arc that crosses both lines.
Step 3: Without adjusting the compass width, move the compass to point E and draw an arc that has a similar orientation to the first arc drawn.
Step 4: Set the compass width to where the lower arc crosses the two lines.
Step 5: Move the compass point to the upper arc on the intersection of the arc and line .
Step 6: Draw an arc so it intersects the bottom of the arc. Label the intersection D.
Step 7: Use a straightedge to connect points E and D to form the parallel line .
so the answer is Place the point of the compass on C and draw an arc that crosses both lines
Determine the number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27}
Answers
The number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27] is 13.
What is a subset?A subset implies a part of the mathematical concept that's referred to as the set. The set is the collection of the elements that are grouped in the curly braces.
In this case, since x is an even number and less than 27, this will be:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, and 26.
Therefore, the numbers are 13.
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The mass, m , of a lorry is 6.58 tonnes truncated to 2 decimal places. Write the error interval for m in the form a ≤ m < b .
Answers
The error interval for m is 6.58 ≤ m < 6.59
What is truncation?Truncation is a process of dropping all decimal places after a certain point without rounding the number.
Given that, the mass, m, of the lorry is 6.58 tonnes truncated to 2 decimal places.
Since the number is truncated to two decimal places, the error interval is,
6.58 ≤ m < 6.59
Hence, the error interval for m is 6.58 ≤ m < 6.59.
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Use the discriminant to determine the number of solutions to the quadratic equation
m² - 9m + 3 = 0.
Answers
Answer: 2 real solutions
Step-by-step explanation:
The discriminant is [tex](-9)^2 -4(1)(3)=69[/tex].
Since the discriminant is positive, there are 2 real solutions.
model the expression on the number line by drawing an arrow -3- 2 1/2
Answers
A model of the given expression on a number line is represented by a number line with open circle on point negative 11 over 2 (-11/2) and arrow shaded to the left.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
From the information provided, we have the following mathematical expression:
x = -3 - 2 1/2
x = -3 - 5/2
x = -11/2 or -5.5.
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Roberto is applying for a mortgage. He has a monthly gross income of $3,500. The home he would like to buy has monthly payments for the following: $1,000 mortgage, $150 property taxes, $75 homeowners insurance premium, and $75 mortgage insurance premium. Roberto also has other monthly debts totaling $500 per month. Based on the Federal Housing Administration (FHA) total fixed payments-to-income ratio, would he qualify for the mortgage loan?
Answers
Based on the Federal Housing Administration's (FHA) total fixed payments-to-income ratio, Roberto would not qualify for the mortgage loan.
What is the fixed payments-to-income ratio?The Federal Housing Administration (FHA) allows 31% of a person's income to settle housing costs (as the front-end ratio) and 43% (as the back-end ratio) towards housing expenses and other long-term debt.
Monthly gross income = $3,500
Monthly payments for Housing:
Monthly mortgage = $1,000
Property taxes = $150
Homeowners insurance premium = $75
Mortgage insurance premium = $75
Total monthly housing costs = $1,300
Other monthly debts per month = $500
Total monthly payments = $1,800
Minimum front-end ratio = 31% = $1,085 ($3,500 x 31%)
Maximum back-end ratio = 43% = $1,505 ($3,500 x 43%)
Thus, using the FHA fixed payments-to-income ratio, Roberto would not qualify.
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5. If you were told that a specific tire could roll 200 yards in 27.28 revolutions, what is the radius of the tire?
Answers
The number of revolutions = Total distance divided by its circumference
The radius of the tire is 1.167 yards.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The area of a circle is given as πr².
We have,
The number of revolutions = Total distance divided by its circumference
Total distance = 200 yards
Revolutions = 27.28
A tire is in the form of a circle.
So,
The circumference of the tire.
= 2πr
Now,
27.28 = 200 yards / 2πr
2πr = 200 yards / 27.28
r = 200/(27.28 x 2 x 3.14)
r = 200 / 171.32
r = 1.167 yards.
The radius of the tire is 1.167 yards.
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The product of two consecutive integers is 110. Find the integers. Note: There are two sets of answers. The first set contains only positive answers and the second one contains only negative answers. Provide the answers in ascending order (smaller numbers first, greater numbers second)
Answers
Answer:
10 and 11
or
-11 and -10
Step-by-step explanation:
Which of these equations is linear
A. -3x+y=8
B. y=x²-3
C. 4y-2x³=0
D. 3=xy+9
Answers
Answer:
a) -3x + y = 8
Step-by-step explanation:
Now we have to,
→ find which of these equations is linear.
Format of linear equation,
→ Ax + By = C
Then the linear equation is,
→ Ax + By = C
→ -3x + y = 8
Hence, answer is -3x + y = 8.
Answer:
A. -3x + y = 8
Step-by-step explanation:
Definition of a Linear Equation:
A linear equation is an equation for a straight line.The highest power of its variables is always one.Each variable is multiplied by a constant only.A. -3x + y = 8This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.
B. y = x² - 3This is not a linear equation as the highest power of the term in x is 2.
C. 4y - 2x³ = 0This is not a linear equation as the highest power of the term in x is 3.
D. 3 = xy + 9This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.
what is 4 divided by 3.48
pls help
Answers
The solution to 4 divided by 3.48 is 0.87
DivisionDivision in mathematics is the method of dividing large numbers into smaller numbers or par
Step 1: Rewrite the question in mathematical terms then
[tex]\frac{3.48}{4}[/tex]= 0.87
Therefore, answer to the division is 0.87
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5 (a) (b) Identify the nature of two stationary points for y=4x³ - 96x² +576x.
Answers
Answer: (0,0) (12,0)
Step-by-step explanation:
y=4x³-96x²+576x
Let y=0
Hence,
4x³-96x²+576x=0
Divide both parts of the equation by 4:
x³-24x²+144x=0
x(x²-24x+144x)=0
x=0
Thus, (0,0)
x²-24x+144=0
x²-2(x)(12)+12(12)=0
x²-2(x)(12)+12²=0
(x-12)²=0
x-12=0
x=12
Thus, (12,0)
Given that x(a + bx)(a − bx) = 25x - 4x³, find the value of b-ª
Answers
Answer:
[tex] {2}^{ - 5} [/tex]
Step-by-step explanation:
Please see picture on how to do it
You give tours on the Great Lakes and talk about points of interest.
Answers
The Great Lakes are the world's largest group of freshwater lakes by total area and second-largest by total volume.
What are the Great Lakes?The Great Lakes, also known as the Great Lakes of North America or the Laurentian Great Lakes are a series of large interconnected freshwater lakes with sea-like characteristics in North America's mid-east region that connect to the Atlantic Ocean via the Saint Lawrence River.
Superior, Michigan, Huron, Erie, and Ontario are the names of five lakes that are located on or near the Canada-United States border. Lakes Michigan and Huron are joined hydrologically at the Straits of Mackinac. The Great Lakes Waterway allows for modern water travel.
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can u help me with this
Answers
Answer:
Step-by-step explanation:
220.5-(12.8+20.25+18.2+25.5)
220.5-(76.25)
143.75 lbs of ice left
Perimeter of the rectangle is 136 units . Find vaule of z
4z+3. 3z+2
Answers
Then 4z+3+3z+2= 136
7z+3+2=136
7z+5=136
Then u move the +5 to the other side (but when u move it…. U have to change the + to a -)
Then it becomes 7z =136-5
7z= 131
Then divide 131 by 7
Z= 131/7
=18.7(round up to 3 significant figures)