The length of each wire is 12.8 feet
The television antenna makes an angle 90 with the ground
The height of the antenna is 10 feet
The wires are anchored to the base which is 8 feet
We need to calculate the length of the wires
The height of the wire can be calculated by using pythagoras theorem
h² = b² + p²
h² = 8² + 10²
h² = 64 + 100
h = √164
h = 12.8
Therefore, the length of each wire is 12.8 feet
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solve the equation 8-3(x + 4)= 2x +1
Answer:
x = -1
Step-by-step explanation:
8 - 3x - 12 = 2x + 1
-3x - 4 = 2x + 1
-5 = 5x
x = -1
The value of x in the equation 8-3(x+4)=2x+1 is -1.
Given equation 8-3(x+4)=2x+1
= 8-3x-12 = 2x+1
= -3x-4 = 2x+1
= -5x = 5
= x = -1
We will first solve the bracket which is -3(x+4) which will give us -3x-12 and then we will add this to 8 which will give us -3x-4. Next, we will move all the constants to one side and the terms with x to one side which will give us -5x=5. Finally, we will divide the whole equation by -5 and we will get the answer of x as -1.
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g in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. calculate the expected value to two decimals.
Using the concepts of probability, we got that 0.4286 is the probability that the battery life for an iPad Mini will be 10 hours or less which is about 42.86%.
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12
[tex]f_X(x)=[/tex](1/3.5)8.5<x<12
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
F(10)=[tex](x-A)/(B-A)[/tex]
F(10)=(10-8.5)/(12-8.5)
F(10)=1.5/3.5
F(10)=0.4286
Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286
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(Complete question)
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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What is the slope of a line parallel to the line whose equation is 3x+4y=36
Answer:
3/4
Step-by-step explanation:
Get into y=mx+b
Subtract 3x
4y=3x+36
Divide by 4
y=3/4x+9
Parallel= 3/4
Perpendicular= -4/3
Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.
Calculation
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's x-intercept: x= 5
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]
The chart for : 4x-9y = 20
see the attachment
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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4
What is meant by fraction?A fraction is a portion of a whole. In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator. In a simple fraction, both are integers.A complex fraction has a fraction in either the numerator or denominator. In a proper fraction, the top number is less than the lowest common.A fraction pretty much tells us how many parts of a whole we have. A fraction is identified by the slash that is written between the two numbers. Designers have a top number, the quaternion, and a bottom number, the denominator. For instance, 1/2 is a fraction.Given
x, 4x - 9y = 20
x = 20 + 9 /4 y
Steps
4x - 9y = 20
Add 9 y to both sides
4x - 9y + 9y = 20 + 9y
Simplify
4x = 20 + 9y
Divide both sides by 4
4x/4 = 20/4 + 9y/4
Simplify
x = 20 + 9y /4
Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.
x = 20 + 9y /4
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CORE
SKILL
ADVANCED
If a is inversely related to the square of b, and a = 3 when bis
8, which of the following is another possible value for a and b?
(A) a = 4, b = 12
(B) a = 12, b = 4
(C) a = 8, b = 3
(D) a = 2, b = 4
(E) a = 6, b = 4
Another possible values for a and b are a = 12 and b = 4
How to find another possible value for a and b?
A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: a is inversely related to the square of b, and a = 3 when bis
8.
This can be written as:
a α 1/b²
a = k/b² (where k is a constant)
k = ab²
since a = 3 and b = 8.
Thus, k = 3 × 8² = 3 × 64 = 192
For a value to be another possible value for a and b, they must give k = 192 when substituted into the equation k = ab²:
a = 4, b = 12: k = 4 × 12² = 576
a = 12, b = 4: k = 12 × 4² = 192
a = 8, b = 3: k = 8 × 3² = 72
a = 2, b = 4: k = 2 × 4² = 32
a = 6, b = 4: k = 6 × 4² = 96
The values that produce k = 192 are a = 12 and b = 4. Therefore, another possible value for a and b is a = 12 and b = 4. So option B is the answer
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The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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i will literally do ANYTHING for doordash mcdonalds literally Anything for 20 dollars
Answer: Nice
Step-by-step explanation:
In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.
The length (in cm) of the hypotenuse is 17 cm.
What is Pythagoras' theorem?According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
H² = P² + B²
Let the hypotenuse = H
Shortest side = B
Third side = P
So, according to the question
H = 2B +1 ..... (1)
P = 2B -1 ..... (2)
Use Pythagoras' theorem,
H² = P² + B²
(2B+1)² = (2B-1)² + B²
4B² + 1 + 4B = 4B² + 1 - 4B + B²
4B = - 4B +B²
B² =-8B
B = - 8
But the length cannot be negative, so B = 8 cm
The length of the shortest side = 8 cm
So the hypotenuse will be
H = 2B + 1
= 2(8) + 1
= 17 cm
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A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.
Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.
Enter your inequality without a thousands separator.
The inequality expression of the volume of the balloon is V < 4,400
How to determine the inequality expression?From the question, we have the following statement:
The initial volume of the balloon is 4,400 cubic centimeters
Also, we understand that:
The balloon leaks out over time
This means that the volume of air in the balloon decreases over time.
So, we have the following representation
V = Less than the initial volume
Rewrite as
V < 4400
Hence, the volume of the balloon at any time after it starts leaking is V < 4,400
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[tex]a(n)=a(n-1)-5[/tex]a(n)=a(n-1)-5
The first five terms of the arithmetic sequence with the formula a(n) = a(n - 1) - 5 is; -5, -10, -15. -20, -25
What is the nth term of the arithmetic sequence?
The general formula for an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
aₙ is the nth term of the sequence
Now we are given the formula for the nth term of a sequence as;
a(n) = a(n - 1) - 5
Thus;
1) First term is when n = 1;
a(1) = a(1 - 1) - 5
a(1) = -5
2) Second term is when n = 2;
a(2) = -5(2 - 1) - 5
a(2) = -5 - 5
a(2) = -10
3) Third term is when n = 3;
a(3) = -5(3 - 1) - 5
a(3) = -15
4) Fourth term is when n = 4;
a(4) = -5(4 - 1) - 5
a(4) = -20
5) Fifth term is when n = 5;
a(5) = -5(5 - 1) - 5
a(5) = -25
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Complete question is;
Write the first five terms sequence defined by a(n) = a(n - 1) - 5
if the probability of a is 0.45 and the probability of the intersection of a and b is 0.15, then the probability that b will occur given that a has occurred is:
The probability that b will occur given that a has occurred is 2/5 as the probability of a is 0.45 and the probability of the intersection of a and b is 0.15.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
P(A)=0.45
P(A∩B)=0.15
P(A∪B)=1
P(B)=1-(0.45+0.15)
=1-0.60
=0.4
=2/5
With a probability of 0.45 and a and b's intersection having a 0.15 probability each, the likelihood that b will happen given that a has happened is 2/5.
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Alyssa misses 2% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 63?
Answer: 3150
Step-by-step explanation:
We know that 50×2%s is 100%, so 50×63 should result in the total amount of throws she attempts, which is 3150.
Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
Larissa is standing at point L Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
What is the Segment Addition Postulate?The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.
This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.
By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:
LP + PR = LR
LP = LR - PR
Substituting the given parameters into the formula, we have;
LP = 12 - 4
LP = 8.
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Complete Question:
Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
LP = 16 because 12 + 4 = 16 according to the addition property of equality.
LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.
PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.
PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
Answer: Lp = 8
Step-by-step explanation:
Got it right
A: 10:00 am a truck started traveling from point A with a speed of 40mph. 3 hours
and 10 minutes later a car started to drive from point A in the same direction
with an
average speed of 60mph. At what time will the car catch up with
the truck?
Answer:h
Step-by-step explanation:
ihlug
Question 10 of 10
Which of the following is the solution to | x | +5 ≤1?
OA. No solution
OB. xs-4
C. All values are solutions *
OD. xs-4 and x ≥ −6
The solution of | x | +5 ≤ 1 is option C, All values are solutions
We need to find the solution of | x | +5 ≤ 1
Upon removing the modulus function, the term presnet within it can be either negative or positive
considering it as postive
| x | +5 ≤ 1
x + 5 ≤ 1
x ≤ 1 - 5
x ≤ -4
considering it as negative
| x | +5 ≤ 1
-x + 5 ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x ≥ -4
Therefore, the solution of | x | +5 ≤ 1 is All values are solutions
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Part A: Timothy said that triangle KLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy correct? Explain your answer or show your work by listing the coordinates of the primage and image and showing the scale factor
Part B: Are the two triangles similar? Explain.
a. Timothy is correct regarding the dilation, considering the vertices of each triangle.
b. The two triangles are similar, as they have congruent angle measures.
What is a dilation?A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.
The effects of a dilation are given as follows:
Congruence is lost, as the side lengths will be different due to the multiplication by the scale factor.Similarity is kept, as the side lengths are proportional, hence the angles remain constant.The vertices of each triangle in this problem are given as follows:
Triangle KLM: K(-1,3), L(8,4) and M(10,-3).Triangle K'L'M': K'(-1.5, 4.5), L'(12, 6) and M'(15, -4.5).The scale factor is obtained by the division of any of the equivalent factors, hence:
k = 4.5/3 = 1.5.
Confirming that Timothy's statement regarding the scale factor of the dilation is correct.
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equation of the line that passes through the points (1,-4)(1,−4) and (5,-1)(5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(1, −4) and (5, −1)
The equation of the line that passes through (1, −4) and (5, −1) will be given as,
(y + 4) = [(−1 + 4) / (5 − 1)](x − 1)
y + 4 = (3/4)x − 3/4
y = (3/4)x + 13/4
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
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One share of kimcos common stock pays an annual dividend of 1. 43. Today kimco closed at 19. 09 with a net cahnge of +0. 72. The stock yield yesterdays closing price is about 8
With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.
How to calculate the Dividend Yield?
To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.
Dividend Yield = Annual Dividends Paid Per Share / Price Per Share
According to the given question:
Net change = today's price - yesterday's price
0.72 = 19.09 - yesterday's price
∴ Yesterday's price = 19.81
Stock dividend yield
= (1.43/19.81) x 100
= 7.2%
Therefore the stock yield of yesterday's closing price is 7.2%
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23.45+1.9-5.78-2.6 ?
Answer:
16.97
Step-by-step explanation:
x represents the number
of comic books Priya buys
at the store, all at the same
price, and y represents the
amount of money (in
dollars) Priya has after
buying the comic books.
By using the concept of equation of line in slope intercept form, it can be obtained that
a) x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
y- intercept is 20
This means, Priya had $20 before buying any comics
b) Slope = -4
This means Priya's money has been decreasing by $4 after buying one comics
c) Equation of line
y = -4x + 20
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
x represents the number of comic books Priya buys at the store
y represents the amount of money (in dollars) Priya has after buying the comic books.
a)From the figure, it is clear that x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
From the figure, it is clear that y- intercept is 20
This means, Priya had $20 before buying any comics
b) The line passes through (5, 0) and (0, 20)
Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4
This means Priya's money has been decreasing by $4 after buying
one comics
c) Equation of line
y - 0 = -4(x - 5)
y = -4x + 20
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Complete Question
The figure has been attached-
aisha wants to buy apples and raspberries to make a fruit tart. apples cost $3 per pound and raspberries cost $2.75 per pound. how many pounds of fruit does she buy if she buys 3 pounds of apples and 2.5 pounds of raspberries? how many pounds of fruit does she buy if she buys xx pounds of apples and yy pounds of raspberries?
Answer:
6.4
Step-by-step explanation:
I guessed and got it right.
The front elevation of a solid shape is a triangle. The side elevation of the solid shape is a triangle. The plan view of the solid shape is a circle. Write the name of the shape.
Answer:
Cone
Step-by-step explanation:
The Angles are all triangle-shaped, but the bottom is circle-shaped.
James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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you wish to survey people who have brought in their cars for service during the past month. you decide to choose a random sample of gas stations in the city and then survey all customers from those stations who had work done during the past month. this procedure is an example of which type of sampling?
An illustration of "Cluster sampling" is the practice of selecting a random sample of the city's gas stations, and then surveying every station's patrons.
Define the term Cluster sampling?In cluster sampling, a population is divided into clusters, which have been smaller groups. They but choose a sample at random from these clustersOften employed to investigate huge populations, typically those that are substantially geographically distributed, cluster sampling is a probability sampling technique. Often, clusters used by researchers have been groups like cities or schools.As per the given question.
People who brought their autos in for service over the past month should be surveyed. You make the decision to selecting a haphazard sample of the city's petrol stations, after which you interview all of their patrons whom have work done on their vehicles well within previous month.Thus, an implementation of "Cluster sampling" is the practice of randomizing sample of the city's gas stations, and thereafter surveying every station's patrons.
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lins bike travels 100 meters when her wheels rotate 55 times . whats the circumferences of her wheels
Answer:
Using formula to calculate the circumference of wheel: c=d/n
where
D is the distance bike travel
n is the number of times rotation
C is the circumference of the wheel
As per the statement:
Lin’s bike travels 100 meters when her wheels rotate 55 times.
here, n = 55 rotation and D = 100 meter.
then by definition:
meter c=100/55=20/11
Therefore, the circumference of her wheel is 1 9/11
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -9 ≤ x ≤ -4?
Answer:
2.4
Step-by-step explanation:
You want the average rate of change on the interval [-9, -4] for the graphed function.
Average rate of changeThe average rate of change (m) is the slope of the line between the points at the ends of the interval. For function f(x) on interval [a, b], this is ...
m = (f(b) -f(a))/(b -a)
ApplicationFor the function f(x) on the interval [-9, -4], the average rate of change is ...
m = (f(-4) -f(-9))/(-4 -(-9)) = (-4 -(-16))/5 = 12/5 = 2.4
The average rate of change of f(x) on [-9, -4] is 2.4.
Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=2x5−x3+x2+4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down
The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11
How to determine the transformation of the function?The equation of the function is given as
f(x) = 2x⁵ - x³ + x² + 4
The sequence of transformations is given as follows:
Reflection across the y-axisVertically stretched by a factor of 3Translate down by 1 unitWhen the above transformations are combined, we have:
g(x) = 3f(-x) - 1
So, we have
3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1
This gives
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1
Expand
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11
So, we have
g(x) = -6x⁵ + 3x³ + 3x² + 11
Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11
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