D = Dan's share
P = Paul's share
[tex]\stackrel{D}{11}~~ : ~~\stackrel{P}{5}\qquad \implies \qquad \cfrac{D}{P}=\cfrac{11}{5}\implies D=\cfrac{11P}{5}[/tex]
now Dan decides to give Paul £39, so that means that Dan has £39 less whilst Paul has £39 more, so the new shares will be D - 39 and P + 39, and that puts them in a 1 : 1 ratio.
[tex]\stackrel{D-39}{1}~~ : ~~\stackrel{P+39}{1}\qquad \implies \qquad \cfrac{D-39}{P+39}=\cfrac{1}{1}\implies D-39=P+39 \\\\\\ \stackrel{\textit{substituting from the 1st eqution}}{\left(\cfrac{11P}{5} \right)-39~~ = ~~P+39}\implies \cfrac{11P}{5}=P+78\implies 11P=5P+390 \\\\\\ 6P=390\implies P=\cfrac{390}{6}\implies \boxed{P=65}[/tex]
I need help please and thank you
Answer: y-intercept is 6 and x intercept is 2
Step-by-step explanation:
The slope formula explains it all. I have nothing to explain.
The top of the hill rises 115 feet over -167 what is the altitude of the top of the hill
Find the surface area of the triangular prism. A drawing of a triangular prism. The base is a right triangle with base 9 inches, height 12 inches, and third side 15 inches. The height of the prism is 29 inches
The surface area of the triangular prism is 891 square inches, calculated by finding the area of each face (two triangular and three rectangular) and adding them up.
To find the surface area of the triangular prism, we need to find the area of each face and add them up.
The triangular prism has two identical triangular faces and three rectangular faces. The triangular faces have base 9 inches, height 12 inches, and hypotenuse 15 inches. The area of each triangular face can be found using the formula for the area of a triangle:
Formula for area of each triangular face = (1/2) x base x height
= (1/2) x 9 x 12
= 54 square inches
The prism also has three rectangular faces, each with length equal to the base of the triangle (9 inches) and width equal to the height of the prism (29 inches). The area of each rectangular face can be found using the formula for the area of a rectangle:
Area of each rectangular face = length x width
= 9 x 29
= 261 square inches
Hence, the triangular prism's total surface area is:
Total surface area = 2(Area of each triangular face) + 3(Area of each rectangular face)
= 2(54) + 3(261)
= 108 + 783
= 891 square inches
Therefore, the surface area of the triangular prism is 891 square inches.
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write the decimal number in standard form. eight hundred three and one hundred thirty-three thousands
The standard form of the given decimal number is 803,133.
The given decimal number in words is "eight hundred three and one hundred thirty-three thousands". We have to write this decimal number in standard form. So, let's do it below.
The standard form of a decimal number is the way it's written normally, such as 3,040.00 instead of 3.04 × 103. To write the decimal number in standard form, we have to represent it in the form of a sum of its place values, which have a power of ten (10).
Therefore the standard form of the given decimal number is 803,133.
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The angle of elevation to a nearby tree from a point on the ground is measured to be 54° How tall is the tree if the point on the ground is 52 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
Therefore, the tree is 78.14 feet tall. Rounded to the nearest hundredth of a foot, the answer is 78.14 feet.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental part of geometry and is used in many areas of science, engineering, and technology.
by the question.
A represents the top of the tree, and the line segment AB represents the height of the tree, which we want to find. The angle of elevation, which is the angle between the ground and the line of sight to the top of the tree, is 54°. The distance from the point on the ground to the tree is 52 feet, which we'll call d. Finally, h represents the distance from the ground to the point where the line of sight intersects the tree.
Using trigonometry, we know that:
tan (54°) = h/d
We can rearrange this equation to solve for h:
[tex]h = d * tan (54)[/tex]
Plugging in the values we know, we get:
[tex]h = 52 * tan (54) = 78.14[/tex]
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Calculate the volume of a pie
that has flat sides so that it is
shaped like a cylinder. The pie
has a radius of 3 inches and a
height of 2 inches.
Answer:
56.54 inches
Step-by-step explanation:
If the radius is 3 inches, to find the area of the circle your equation would be A = (pi) x r^2
Your equation would look like this:
A = (pi) x 3^2
A = 28.27
Now to get the volume of the pie, you would multiply 28.27 x 2 which gives you an answer of 56.54 inches.
if a random variable follows a normal distribution, what is the probability that the random variable is 1.96 standard deviations below the mean? select answer from the options below 97.50% 95.00% 96.25% 98.75%
The total probability is 2.5% + 2.5% = 5.0%, which is equivalent to 0.05 or 95.00% in decimal form.
If a random variable follows a normal distribution, the probability that the random variable is 1.96 standard deviations below the mean is 95.00%.Step-by-step explanation:
Z-value for 1.96 standard deviations below the mean can be calculated as follows:
Z=(x-μ)/σ=(-1.96)
Where x is the value of the random variable, μ is the mean, and σ is the standard deviation.To find the probability, we can use a standard normal distribution table.
The table gives the probability of a standard normal random variable Z being less than or equal to a given value, denoted by P(Z ≤ z).
The Z-value we calculated is -1.96, so we look up the corresponding probability in the table:
P(Z ≤ -1.96) = 0.025.
The probability that the random variable is 1.96 standard deviations below the mean is therefore:
P(Z ≤ -1.96) = 0.025 = 2.5%
However, since we are interested in the probability that the random variable is exactly 1.96 standard deviations below the mean, we need to use a two-tailed test.
The probability of being below the mean by 1.96 standard deviations is 2.5%, and the probability of being above the mean by 1.96 standard deviations is also 2.5%.
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-5
-4
-3
A
7
-1
6-
5
4
3-
2
1
O
4
2
-3
-4
-5
-6
-7
A
B
2 3 4 SX
Shape A can be transformed to shape B by
a reflection in the x-axis followed by a
translation
(8)
Find the value of c and the value of d.
C =
d =
The value of c is equal to 4.
The value of d is equal to 0.
What is a reflection across the x-axis?In Geometry, a reflection across or over the x-axis is modeled and represented by the following transformation rule (x, y) → (x, -y). Therefore, a reflection across or over the x-axis would maintain the same x-value while the sign of the y-value would change from negative to positive or positive to negative as the case may be.
One of the vertices of triangle A is given by:
(x, y) → (x, -y)
A (-1, -1) → A' (-1, -(-1) = (-1, 1)
When a translation is applied to triangle A', one of the corresponding or resulting vertices of triangle B is given by:
B (3, 1)
A' (-1 + c, 1 + d) → B (3, 1)
-1 + c = 3
c = 3 + 1
c = 4.
1 + d = 1
d = 0
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Select all that are a radius of circle O.
A) OC
B) OB
C) PQ
D) AB
The parts that are called radius as shown from the diagram are: OC and OB (option A and B)
How do i know which part of the circle is called radius?The radius of a circle is defined as the distance from the center of the circle to any point on the circumference. However, the radius is also obtained by dividing the diameter of a circle by 2
Now, we shall consider the diagram given to determine the distance from the center to the circumference (i.e radius). This is shown below:
Line PQ is not a radius since it does not start from the centerLine OA is called a radius since it starts from the centerLine OB is called a radius since it starts from the centerLine OC is called a radius since it starts from the centerConsidering the options given from the question, we can conclude that the parts of the circle which is called the radius are: OC and OB (option A and B)
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A survery showed that 12 out of 20 homeowners in the neighborhood had HBO TV subscription. If there are 320 homeowners in the neighborhood, how many could be expected to have a HBO subscription?
Answer:
192
Step-by-step explanation:
320/20=16
12x16=192
I NEED HELP ON THIS ASAP! PLEASE IT'S DUE TODAY!!!
Answer:
below
Step-by-step explanation:
A (0,8)
B (8,0)
C(0,-8)
D(-8,0)
AB ( 4, 4 )
8/2 , 8/2
(x1+x2/2, y1+y2/2)
BC ( 4,-4 )
8/2 , -8/2
CD ( -4,-4 )
-8/2 -8/2
AD ( -4,4 )
-8/2 8/2
The polygon formed is a square because they all have sides with same lengths
If it was repeated it will still be a square
Help me with this math problem please
Part a: ∠ABE and ∠DBE share a ray EBC as EBC is a straight line.
Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the vertical angles.
Explain about the vertical angles?Angles that are opposing each other whenever two lines connect are known as vertical angles. According to the vertical angles theorem, vertical angles are consistently congruent.
When two lines in geometry connect, four angles are created. Vertical angles are those that are not next to one another or that are opposing one another. Since they always utilize the same measure, vertical angles are unique.
Postulate for Angle Addition: When two neighbouring angles combine to make a straight line, its result is 180°.
The given angles:
∠ABE = ∠DBE (vertical angles)
Part a: ∠ABE and ∠DBE share a ray EBC .
Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the vertical angles.
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I need help show work
The probability of landing in the color green is P = 0.41, and out of 160 spuns, we can expect to get the color green 66 times.
What is the probability of the spinner landing on green?We have a table and we want to use it to find the probability of the spinner landing on green.
It is equal to the quotient between the number of times that we got green and the total number of times that we spun the spinner.
We got green 325 times, and the total number is:
T = 116 + 325 + 359
T = 800
Then the probability is P = 325/800 = 0.41
b) If it is spun 160 times, then we will get 0.41 times 160 green landings, it is:
160*0.41 = 65.6
This can be rounded up to 66, we can expect to land in the green section 66 times.
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what is 8,842 round to the nearest hundred
Answer: 8800
Step-by-step explanation:
Rounds down because 42 is less than 50
Question 5 Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation (-4, 2); y = -x+6
Step-by-step explanation:
If it is parallel to the line y = -x + 6, they have the same gradient and the gradient is the coefficient of x which is -1.
We use the equation y=mx+c
Y is 2
M is -1
X is -4
2 = (-1×-4) + c
2 = 4 + c
C = 2 - 4 = -2
Y = -x -2
PLEASE HELP!!!!!! I REALLY NEED THIS ANSWER!!! ILL GIVE BRAINLIEST IF IT POPS UP!
Memorize Psalm 19:1 through 6.
When you have memorized these verses, recite them with expression to either your teacher or parent. Then, write these verses in your own words to show that you understand them.
"The heavens proclaim God's glory; the skies proclaim the work of his hands." They pour forth speech day after day, and unveil knowledge night after night. They have no speech, no words, and no sound is heard from them. Nonetheless, their voice reaches all over the world, and their words reach all the way to the ends of the planet. God has set up a tent for the sun in the heavens. It's like a newlywed emerging from his bedroom, or a champion joyful to run his race. It rises at one end of the heavens and circles back; nothing is bereft of its warmth."
This paraphrase captures the essence of the verses, emphasizing the declaration of God's glory through the beauty and order of the heavens, the continuous revelation of knowledge, and the symbolism of the sun's journey across the sky.
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Which expression is an equivalent expression for 2(6y – 4)?
Answer:
12y-8
Step-by-step explanation:
Mark wants to order a pizza. Drag and drop the correct number or phrase into each box to complete the explanation for which is the better deal. Round your answer to the nearest cent. Use 3.14 for . Donnie's Pizza Palace Diameter (in.) Cost ($) The 10-inch pizza costs about 0.13 10-inch 10 10 ? & per square inch. The 16-inch 16 20 10 13 0.1 c per square inch while the 16-inch pizza costs about pizza is a better deal. 4
The 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.
Donnie's Pizza Palace Diameter (in.) Cost ($) Cost per Square Inch ($/in²)
10-inch 10 10 0.13
16-inch 16 20 0.1
To determine which pizza is the better deal, we need to compare the cost per square inch of each pizza.
For the 10-inch pizza:
Cost per square inch = Cost / (π x [tex](diameter/2)^2)[/tex]
Cost per square inch = 10 / [tex](3.14 x (10/2)^2)[/tex] ≈ $0.13
For the 16-inch pizza: Cost / (πx x [tex](diameter/2)^2)[/tex]
Cost per square inch =[tex]20 / (3.14 x (16/2)^2) ≈ $0.10[/tex]
Therefore, the 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.
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two trains leave stations 418 miles apart at the same time and travel toward eact other. once treain trevels at 85 mph and the ohter treavels at 105 mph. how long willit take for the two trains to meet
It will take 2.2 hours for the two trains to meet.
We can find the time taken by the two trains to meet by using the formula,
large Time=Distance/Speed
Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.
Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.
Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.
The distance covered by the second train in time "t"=105t.
So, the total distance covered by both the trains in time "t" is,
Distance covered = 85t+105t=190t.
But we know the distance between the two trains is 418 miles.
Therefore,190t = 418
Now, solve for "t"t = 418/190t = 2.2 hours
Therefore, the two trains will meet in 2.2 hours.
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I need all the help in the world
Triangle XYZ will be translated to X'Y'Z' and the coordinates of Z' are (6,7).
Describe transformation.A transformation known as a translation involves shifting each point in an image uniformly in one direction. It is also a type of transformation where every point in a figure is moved by the same amount in the same direction, producing a new figure that is identical to the original.
From the graph,
The coordinates of X are (7, 11)
The coordinates of Y are (10, 14)
The coordinates of Z are (8, 7)
When triangle XYZ is translated to X'Y'Z', the X-coordinate is given as (5, 11), which means the X-coordinate shifts left 2 points, so we need to subtract 2 from X-coordinate and keep Y-coordinate as it is.
Therefore the coordinate of the triangle X'Y'Z' are as follows,
The coordinates of X' are (7-2, 11) = (5,11)
The coordinates of Y' are (10-2, 14) = (8, 14)
The coordinates of Z' are (8-2, 7) = (6, 7)
Therefore the coordinates of Z' are (6,7)
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The trapezoid has base lengths of 8 inches and 9 inches. The height of the trapezoid is 13 inches.
Answer:
110.5 inches
Step-by-step explanation:
A=( a + b) / 2 h
A = (8 + 9) / 2 x 13
A = 17 / 2 x 13
A = 110.5 inches
What skills concepts did you use to solve the radical equations?
Solving radical equations requires a strong foundation in algebraic concepts and techniques, as well as knowledge of exponents and radicals.
Several mathematical skills and concepts required to solve radical equations are as follow,
Knowledge of exponents,
Radical expressions involve exponents, which are fundamental to solving these equations.
Understanding of the properties of radicals,
Knowing the properties of radicals.
How to simplify them or manipulate them to isolate the variable, is essential in solving radical equations.
Algebraic manipulation,
In solving radical equations, use algebraic manipulation techniques.
Such as factoring or multiplying by conjugates, to isolate the variable and solve for it.
Familiarity with solving equations,
Process of solving a radical equation is similar to that of solving any other equation.
Follow standard algebraic procedures, such as combining like terms, applying inverse operations, and checking our solutions.
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Ten people (labeled 1-10) have purchased raffle tickets for a fundraiser. However, they did not all purchase the same
number of tickets. One ticket is to be selected at random. Which of the following could be the probability distribution for
the winning ticket?
C
1
0.10
1
2
0.01 0.01
2
0.10
1
3
4
5
6
0.10 0.10 0.10 0.10
3
4
5
0.05 0.07 0.68
1
2
0.125 0.125
6
0.01
2 3
4
5
6
7 8 9 10
0.01 0.11 0.02 0.12 0.03 0.13 0.04 0.14 0.05 0.15
3
0.125
7
8 9 10
0.10 0.10 0.10 0.10
5
7 8 9 10
0.05
0.03 0.01 0.08
6
4
7
9
10
0.125 0.125 0.125 0.125 0.125 0.125 0.125
8
The correct option is A: the probability distribution for the winning ticket:
1 2 3 4 5 6 7 8 9 10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
Explain about the probability distribution?A frequency distribution that has been idealised is a probability distribution.
Each individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value for a particular variable appears.The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:Zero denotes impossibility.1 denotes a certainty.Total people = 10 (1 - 10)
One ticket is selected at random from each person.
As the selection is independent events of each other, each will have the same probability.
So,
probability = favourable outcome / total outcome.
probability = 1/10
probability = 0.10.
Thus, the correct option is A: the probability distribution for the winning ticket:
1 2 3 4 5 6 7 8 9 10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
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the speeds of four vehicles were measured at the midpoint of a roadway section as 55, 50, 74, and 78 mph, respectively. if all vehicles were traveling at constant speed over this roadway section, what was the space-mean speed (rounded to the nearest mph) for the four vehicles?
The space-mean speed of the four vehicles is approximately 64 mph.
The given information about the speeds of four vehicles measured at the midpoint of a roadway section are as follows:Vehicle Speed (mph)A 55B 50C 74D 78The space-mean speed of the four vehicles can be found out by the following formula:Space-mean speed = {Sum of the individual speeds of the vehicles}/{Number of vehicles}Space-mean speed = (55 + 50 + 74 + 78)/4Space-mean speed = 257/4Space-mean speed ≈ 64 mph (rounded to the nearest mph)
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What is the volume of a cake box that is 12 inches long, 9 inches wide, and 6 inches high? (1 point)
a
102 cubic inches
b
252 cubic inches
c
648 cubic inches
d
972 cubic inches
help
The volume of the cake box is c. 648 cubic inches.
Define volumeVolume refers to the amount of space occupied by an object or a three-dimensional figure. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).The volume of an object can be determined by multiplying its length, width, and height if it has a regular shape such as a rectangular prism or cube.
A rectangular box's volume is equal to its length, width, and height.
Substituting the given values, we get:
Volume of a cake box = 12 inches x 9 inches x 6 inches
Volume = 648 cubic inches
Therefore, the volume of the cake box is 648 cubic inches.
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rewrite 0.266666666 recurring in a fraction
The equivalent fraction of the given repeating decimal is: 4/25
How to write a recurring decimal as a fraction?A recurring Decimal is defined as a decimal number only that consists of digits repeating after a fixed interval after the decimal.
Let a/b denote the unknown fraction
Thus:
a/b = 0.266666666... ------(1)
Multiply both sides of the equation by 10 to produce
10a/b = 2.66666666... -----(2)
Multiply both sides of the equation 1 by 100 to produce:
100a/b = 26.6666666... -----(3)
Subtract eq 2 from eq 3 to get:
90a/b = 24
a/b = 24/90
a/b = 4/15
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4x-3y=18 I need the work to be shown please
Answer:
[tex]x = \frac{3(6+y)}{4}[/tex]
Step-By-Step Explanation:
First Step:
[tex]4x=18+3y[/tex]
Second Step:
[tex]x = \frac{18+3y}{4}[/tex]
Last Step:
[tex]x = \frac{3(6+y)}{4}[/tex]
Can you please solve this
this is only 8th grade math
A man left on a trip of 450 kilometres at 10 am. He stopped for a rest for
40 minutes and had another break of an hour for lunch. What time did he
finish the trip, if he was travelling at an average speed of 50 kilometres per
hour?
Therefore, the man finished his trip at 8:40 pm with total travelling time of 10 2/3 hours.
What is fraction?In mathematics, a fraction is a representation of a part of a whole or a ratio between two quantities. It consists of two numbers, a numerator and a denominator, separated by a horizontal line, also called a fraction bar or a vinculum. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts that make up the whole.
Here,
We can solve this problem using the formula:
distance = rate x time
Let's start by finding the time it took for the man to travel 450 kilometers at an average speed of 50 kilometers per hour:
time = distance / rate
time = 450 km / 50 km/h
time = 9 hours
So the man spent 9 hours travelling. However, he also took two breaks: a 40-minute rest and a 1-hour lunch break. We need to convert these times to hours to include them in our calculation.
40 minutes is equal to 40/60 = 2/3 hours, and 1 hour is simply 1 hour. So the total time the man spent travelling, including the breaks, is:
total time = 9 hours + 2/3 hours + 1 hour
total time = 10 2/3 hours
To find the finishing time, we add the total time to the starting time of 10 am:
finishing time = 10 am + 10 2/3 hours
finishing time = 8:40 pm (rounded to the nearest minute)
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What organ system contains the heart and blood vessels?
The circulatory system's primary functions are listed above. Service for the body's cells is provided by the heart, blood, and blood vessels.
Through the system of veins, arteries, and capillaries, blood transports carbon dioxide towards the lungs (for expiration) and takes up oxygen. Both liquid and solid components make up your blood. Water, salts, and protein make up the liquid component, known as plasma.
Plasma makes up most of your blood. Red blood cells, white blood cells, and platelets make up the solid portion of your blood. The oxygen from your lungs is carried to human tissues and organs by red blood cells (RBC).
The study on quality, organization, location, and change is what arithmetic is all about. Mathematicians look for patterns and come up with new theories.
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