The distance from airport A to airport C is 770.88 miles.
What is Cosine law?The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
Let x is the distance from airport A to airport C.
The other angle is,
= 73+36
= 109
Now, using cosine law,
x² = 550² + 390² - 2(550)(390)cos(109)
x²= 454600 + 139668.73
x= 770.88 miles
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Real estate ads suggest that 62% of homes for sale have garages 28% have swimming pools and 18% have both features. If a home for sale has a garage what’s the probability that it has a pool too?
Answer:
Step-by-step explanation:
The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool
Question 5 (1 point)
Match the expressions that are equivalent.
Column A
1/32
32
2
1/2
64
1/64
Column B
a. (2^3)(2^2)
b. 2^(-2) x 2^(-3)
C. (2^3) x (2^-3)
d. (2^2)^3
e. 2^2/2^3
f. 2^3/2^2
It should be noted that the correct matching of the expressions illustrated will be:
a. (2^3)(2^2) = 32
b. 2^(-2) x 2^(-3) = 1/32
C. (2^3) x (2^-3) = 1
d. (2^2)^3 = 64
e. 2^2/2^3 = 1/2
f. 2^3/2^2 = 2
How to illustrate the information?It should be noted that (2^3)(2^2) will be:
= 2³ × 2²
= 8 × 4
= 32
b. 2^(-2) x 2^(-3) will be illustrated as:
= 1/4 × 1/8
= 1/32
C. (2^3) x (2^-3)
= 8 × 1/8
= 1
d. (2^2)^3
= 4³
= 64
e. 2^2/2^3
= 4 / 8
= 1/2
f. 2^3/2^2
= 2³ / 2²
= 8 / 4
= 2
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You work at a sporting goods store and make commissions on the products you
help sell. If you earn a 5.5% commission on all regular priced items, and a 4.5%
commission on all items on sale, how much do you earn in a week where you sell
$8,800 worth of regular goods, and $10,650 worth of items that are on sale?
Answer:
963.25
Step-by-step explanation:
8,800x0.055=484
10,650x0.045=479.25
484+479.25=963.25
Attached as an image. Please help.
The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
How to find the solution of an ordinary differential equation with separable variablesHerein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:
dy / dt = 3 · y · (1 - y / 14)
dy / [3 · y · (1 - y / 14)] = dt
dy / [- (3 / 14) · y · (y - 14)] = dt
By partial fractions we find the following expression:
- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt
- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.
y = 14 / [1 - C · tⁿ], where n = - 14² / 3.
If y(0) = 10, then the particular solution is:
y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
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The graph shows the charges of an instructor. The
instructor charges an initial fee and then an hourly rate
for private lessons. Determine the instructor's hourly
charge from the graph.
What is the hourly charge?
O $1.00
O $4.00
O $7.00
O $8.00
Answer:
$8
Step-by-step explanation:
35 POINTS!!!
What is the measurement angle of angle C and D in the image
Answer:
c = 45 and e = 30
Step-by-step explanation:
Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45
Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.
We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.
Hope that answers your question
Keep You Warm Heating Service charges a flat rate of $50 per service call and an additional $1 per minute the technician is in your home. If the technician spends 60 minutes repairing your heating unit, which of the following will be your total service bill?
Answer:
$110
Step-by-step explanation:
Total bill = 1x+50, where x is the number of minutes
so if x=60, then
total bill is 1(60)+50 = $110
Example: Divide 3 loaves between 5 people First, divide two of the loaves into thirds... each person gets one third each, with one third left over Then divide the left-over third from the second loaf into fifths So, each person gets: 1/5 and the third loaf into fifths each person gets one fifth each each person gets a slice (one fifteenth) 1/15 3/5 The Egyptians used the approximated process to work on the area of a circle as shown in the picture. 1.4 Show the representation of the fractions on the second row. (2) 1.5 Show the algorithm/abstract strategy to justify the 3/5 found as the answer. (3)
The algorithm justifies the answer of 3/5 as the fraction each person gets.
Representation of the fractions on the second row:
From what you described, two of the loaves were divided into thirds.
This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.
Therefore, each person receives one fifth from this remaining third.
So, the representation of the fractions on the second row would be:
Each person receives 1/3 (one third) from the two loaves.
Each person receives 1/5 (one fifth) from the remaining third.
Algorithm/Abstract strategy to justify the 3/5 found as the answer:
To find the final answer of 3/5, we can follow the steps you provided:
Divide two loaves into thirds, giving each person 1/3.
Divide the remaining third from the second loaf into fifths, giving each person 1/5.
Combining the fractions, each person has 1/3 + 1/5.
To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:
1/3 = 5/15 (multiplying numerator and denominator by 5)
1/5 = 3/15 (multiplying numerator and denominator by 3)
Now, we can add the fractions:
5/15 + 3/15 = 8/15
Therefore, each person receives 8/15 of a loaf.
Simplifying this fraction, we get 3/5.
Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.
what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.
Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.
What is the cultural Strain?Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.
Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.
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A simple random sample of college students was performed recently in which the students were asked to self identify as to whether they are binge drinkers or not. In a 1995 study it was found that about 44% of students were self identified as such and the researcher believed that this number has increased. In this study 7851 of the 17592 students interviewed self identified as binge drinkers. A 90% confidence interval of the estimated binge drinking rate is
Answer:
The 90% confidence interval is \(0.445< p < 0.456\)
Step-by-step explanation:
From the question we are told that
The sample size is \(n = 17592\)
The number of binge drinkers is \(k = 7851\)
Given that the confidence level is 90% then the level of significance is mathematically represented as
\(\alpha = (100 - 90)\%\)
\(\alpha = 0.10\)
The critical value of \(\frac{\alpha }{2}\) from the normal distribution table is \(Z_{\frac{\alpha }{2} } = 1.645\)
The sample proportion is mathematically represented as
\(\r p = \frac{ 7851}{ 17592}\)
\(\r p = 0.45\)
Generally the margin of error is mathematically represented as
\(E = Z_{ \frac{x}{y} } * \sqrt{\frac{\r p(1 - \r p )}{n} }\)
\(E =1.645 * \sqrt{\frac{ 0.45 (1 - 0.45 )}{17592} }\)
\(E =0.00617\)
The 90% confidence interval is mathematically represented as
\(\r p -E < p < \r p +E\)
\(0.45 -0.00617 < p < 0.45 + 0.00617\)
\(0.445< p < 0.456\)
In the given circle, the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4 : 5. What is the degree measure of angle BCD?
The degree measure of angle BCD is 130.
What is the measure of angle?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Given: the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5.
We can let ∠AEB be 4x and ∠ABE be 5x because they are in the ratio 4: 5.
When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by the triangle sum theorem,
= 4x+5x+90 = 180
x = 10 and
∠ABE = 50.
∠ABE =∠BED because they are alternate interior angles and AB||ED.
Opposite angles in a cyclic quadrilateral are supplementary,
so ∠BED + ∠BCD = 180
Use substitution to get ∠ABE + ∠BCD = 180
50 + ∠BCD = 180
∠BCD = 130
Hence, the degree measure of angle BCD is 130.
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line m and point p are graphed on the coordinate grid below. which equation represents a line that passes through point p and is parallel to line m?
The equation of the graphed on the coordinate grid parallel to line M y = x and passing through the point P(4, -7) is equal to y = x - 11.
As given in the question,
Equation of the line M is given by :
y = x
Slope of the line M by comparing it with standard equation of the line with slope m is given by :
y = mx + c
Equation of the line M is y = x
Here m = 1
Slope of the required line is m₁ = 1 as it is parallel to line M
Equation of the required line which passes through ( x₁ , y₁) = ( 4, -7) with slope m₁ = 1 is given by:
y - y₁ = m₁( x - x₁)
⇒ y + 7 = 1( x - 4)
⇒ y= x - 4 -7
⇒ y= x - 11
Therefore, the equation of the required line which is parallel to line M and passing through point P is equal to y = x - 11.
Line M is graphed on the coordinate grid. y = x. Which equation can be used to represent a line parallel to M passing through the point P(4, -7)?
A. x = 4 B. x = -7 C. y = -7 D. y = 4
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what is the least common deno minator 2/5 and 3/2
Answer: 10
Step-by-step explanation: The common denominator for these two
fractions is simply the least common multiple for the two denominators.
Since our denominators of 5 and 2 have no factors in common,
our least common denominator is 5 · 2 or 10.
5. Which of the following rules could represent a transformation that mapped one shape onto another
to establish their congruence?
A) K(x,y) ---->(x-3,3y)
C) K(x, y) ---->(-y,x+2)
B) K(x, y)
--->(2x, y)
D) K(x, y) - - - - > (5x, 5y)
Answer:
i think it’s C
Step-by-step explanation:
What is
-2.3 -
(4.5 – 3)?
2.3
1.3
10.3
-3.3
Answer:
-3.8
Step-by-step explanation:
-2.3 - 1.5 = -3.8
If ABCD is dilated by a factor of 3, thecoordinate of B' would be:5С43B.21-5 4 3-2 -1 012345-1-2DB' = ([?],[])-3
First, find coordinate B.
B= ( -2,2 )
Multiply each coordinate by the dilation factor 1/2
B'= ( -2 * 1/2 , 2 * 1/2 )
B'= ( -1, 1 )
How many solutions of the linear equation 5x + 3y = -5 has ?
Answer:
You can solve it yourself
Step-by-step explanation:
By using demos graphing calculator
Help
look at the picture
\(x7 - 2 \: or \: x \leqslant - 3\)
A construction worker is painting
walls. He has 4 ½ gallons of paint.
All of the walls are the same size and
each require 3/4 gallon of paint. How
many walls will the construction
worker be able to repaint with that
amount of paint?
A.
B.
C.
D.
4 walls
5 walls
6 walls
7 walls
The construction worker will be able to repaint 6 walls with 4 ½ gallons of paint. Option C
To determine how many walls the construction worker will be able to repaint with 4 ½ gallons of paint, we need to divide the total amount of paint by the amount required per wall.
The worker has 4 ½ gallons of paint, which can be written as 4 + 1/2 gallons.
Each wall requires 3/4 gallon of paint.
To find the number of walls that can be repainted, we divide the total amount of paint by the amount required per wall:
Number of walls = (Total amount of paint) / (Amount required per wall)
Plugging in the values, we have:
Number of walls = (4 + 1/2) gallons / (3/4 gallon)
To simplify the division, we can convert the mixed number 4 1/2 to an improper fraction:
Number of walls = (9/2) gallons / (3/4 gallon)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Number of walls = (9/2) gallons * (4/3 gallon)
Simplifying the multiplication:
Number of walls = (9 * 4) / (2 * 3) = 36/6 = 6
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The upper-left coordinates on a rectangle are
(−4,4)
(4,4)
20 units.
Draw the rectangle on the coordinate plane below.
The rectangle has a length of 8 units along the top and bottom sides, and a height of 6 units along the vertical sides.
What is a rectangle?A rectangle is a four-sided flat shape with four right angles (90 degree angles) between the sides. It is a type of quadrilateral, which means a shape with four sides.
According to question:To find the length of the sides of the rectangle, we can use the distance formula:
d = √((x2 - x1)²+ (y2 - y1)²)
Using the coordinates (-4,4) and (4,4) for the two endpoints of the top side of the rectangle, we get:
d = √((4 - (-4))² + (4 - 4)²) = 8
Since the top side has length 8 and there are two top and two bottom sides of equal length, the perimeter is:
20 = 28 + 2L
where L is the length of one of the vertical sides. Solving for L, we get:
L = (20 - 2*8)/2 = 2
Therefore, the length of the vertical sides of the rectangle is 2 units.
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The length of rectangle is 8 units on the x-axis, and the width of rectangle is 4 units along the y-axis.
What is a perimeter of rectangle?The whole distance encircling a rectangle's edge is known as its perimeter. It is the total of the measurements of the rectangle's four sides.
The formula for calculating the perimeter P of a rectangle with length L and width W is as follows:
P = 2L + 2W
According to question:
To find the length of the sides of the rectangle, we can use the distance formula:
\(d = \sqrt{((x_{2} - x_{1} )^2+ (y_{2} - y_{1})^2)}\)
Using the coordinates (-4, 4) and (4, 4)
\(d = \sqrt{((4 - (-4) )^2+ (4 - 4)^2)}\) = 8 units
L (length) = 8 Units
So, the length of the horizontal sides (x-axis) of the rectangle is 8 units.
then, the top side has length 8 and there are top and bottom sides are equal length, the perimeter is: P = (8+8) + 2W
20 = 16 + 2W
where, L is the length of one of the vertical sides. Solving for L, we get:
W = (20 - 16)/2 = 2
So, the length of the vertical sides (y-axis) of the rectangle is 2 units.
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Which of these expressions is equivalent to z + z+z + z?
A.4z
B.4+z4
C.4+z
D.4z4
Answer:
A. 4z
Step-by-step explanation:
The expressions is equivalent to z + z+z + z would be 4z. so option A is correct.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
Given expression
z + z+z + z
All the terms are like terms, by adding all of them
z + z+z + z
= 4z
Thus, The expressions is equivalent to z + z+z + z would be 4z. so option A is correct.
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A necklace and earrings cost $144. Six necklaces and five pairs of earrings cost $825
Step-by-step explanation:
let necklace : x
let earrings : y
x+y=144 -1st eqn
6x+5y=825 -2nd eqn
y=144-X -3rd eqn
substitute eqn into 2nd eqn
6x+5(144-x)= 825
6x +720-5X =825 (expanded)
X = 825-720
X =105
substitute "X=105" into 1st eqn
(105)+y=144
y= 144-105
y=39
1 necklace = 105$
1 pair of earrings = 39$
(to check back: substitute the value into the original eqn)
What are the roots of the polynomial function x^4 +7x^2-144=0
Answer:
Step-by-step explanation:
\(x^4+7x^2-144=0\\x^4+16x^{2} -9x^{2} -144=0\\x^{2} (x^{2} +16)-9(x^{2} +16)=0\\(x^{2} +16)(x^{2} -9)=0\\(x^{2} -(-16))(x^{2} -3^2)=0\\(x^{2} -16 \iota^2)(x+3)(x-3)=0\\(x^{2} -(4\iota)^2)(x+3)(x-3)=0\\(x+4\iota)(x-4\iota)(x+3)(x-3)=0\\x=\pm4 \iota,\pm3\)
6 people are evenly sharing 5 blueberry muffins.
How many blueberry muffins should each person get?
Choose 1 answer:
Each person will get 1.2 of the Blueberry muffins
How to calculate the number of blueberry muffins each person will get ?The number blueberry muffins in 5
6 people wants to share the 5 blueberry muffins
Therefore the number of blueberry muffins each person will get can be calculated by dividing 6 by 5
= 6/5
= 1.2
Hence each person will get 1.2 blueberry muffins if the muffins are shared equally.
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You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?
According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.
To find the effective annual yield, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.
To calculate the effective annual yield, we can use the following formula:
Effective Annual Yield = (1 + r/n)ⁿ - 1
Plugging in the values, we get:
Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1
Effective Annual Yield = 0.0649 or 6.49%
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stefan and misha have a car washing business. Stefan could wash the cars by himself in 6 hours and misha could wash the cars by himself in 5 hours. stefan starts washing the cars by himself, but he needs to go to his football game after 2.5 hours. misha continues the task. how long did it take misha to finish washing the cars?
11B. Long Beach Towing Company charges $40 plus $5 per mile to
tow a car. The Five-Star Towing Company charges $70 plus $2 per
mile. After how many miles the charges for the two companied will
be the same?
Answer:
The charges will be the same after 10 miles.
Step-by-step explanation:
Long Beach Towing Company:
Charges $40 plus $5 per mile. So after x miles, the charge will be of:
\(L(x) = 40 + 5x\)
Five-Star Towing Company:
Chargers of $70 plus $2 per mile. So after x miles, the charge will be of:
\(F(x) = 70 + 2x\)
After how many miles the charges for the two companied will be the same?
This is x for which:
\(L(x) = F(x)\)
So
\(40 + 5x = 70 + 2x\)
\(5x - 2x = 70 - 40\)
\(3x = 30\)
\(x = \frac{30}{3}\)
\(x = 10\)
The charges will be the same after 10 miles.
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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Any Answers and explanation to this?
Answer:
give a thanks first and then ill tell you
Step-by-step explanation:
Answer:
Maybe it's D) or c) if not i'm du.mb and sorry
Step-by-step explanation: