At the donut shop the cost for a dozen donut holes and a glass of milk is $3.50. The cost for three dozen donut holes and four glasses of milk is $11.80 which pair of equations can be used to determine D (the cost for donut holes) and M (the cost for the milk)
Answer:
Step-by-step explanation:
12 D + M = 3.50
3*12 D +4M = 11.80
the pair of equations are
12 D + M = 3.50
36 D +4M = 11.80
Answer:
I need points lol 2=yx thank you for letting me spam
Finding A Value. Solve For A In The Triple Integral. Ƒ³0 Ƒ3 0-ª-y² ∫4 0-x-y² Dzdxdy = 14 /15
The value of A in the triple integral ∫∫∫ Ƒ dV = 14/15 is A = -15(14/15) / (16y+64y³/3).
To find the value of A in the triple integral ∫∫∫ Ƒ dV, where the limits of integration are given, and the result is equal to 14/15, we need to evaluate the integral and solve for A.
Let's compute the given triple integral step by step. We have ∫∫∫ Ƒ dV = ∫[0 to 4] ∫[0 to x] ∫[0 to -x-y²] Adzdxdy. Integrating with respect to z first, we obtain ∫[0 to 4] ∫[0 to x] -A(x+y²) dydx. Integrating with respect to y, we have ∫[0 to 4] [-A(xy+y³/3)] dx. Finally, integrating with respect to x gives [-A(x²y+xy³/3)] evaluated from 0 to 4.
Evaluating the upper limit, we get [-A(16y+64y³/3)]. Plugging in the lower limit, we have [-A(0+0)] = 0. Thus, the result of the triple integral is [-A(16y+64y³/3)]. Setting the result equal to 14/15, we have [-A(16y+64y³/3)] = 14/15. Rearranging the equation, we get -A(16y+64y³/3) = 14/15.
To solve for A, we divide both sides of the equation by (-16y-64y³/3), resulting in A = -15(14/15) / (16y+64y³/3). Therefore, the value of A in the triple integral ∫∫∫ Ƒ dV = 14/15 is A = -15(14/15) / (16y+64y³/3).
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help with this pleased
Answer:
Kite A ascends to a height of 36 feet
Step-by-step explanation:
21 + 15 = 36
Answer:
Kite A is now at 36 feet.
Step-by-step explanation:
Ascend means go up, so adding 15 to 21 gives you your answer.
You buy a "gold" ring at a pawn shop. The ring has a mass of 0.014 g and a volume of 0.0022 cm^3. The standard density of gold is 19,300 kg/m^3. Is the ring solid gold?
Answer:
Below
Step-by-step explanation:
.014 g / .0022 cm^3 = 6.364 gm / cc = 6364 kg/m^3
density is too low to be pure gold
21) Answer the question using the information given. Special cube-shaped dice are manufactured having side lengths of in. The dice are stored in rectangular prism boxes. What is the greatest number of dice that will fill the box? 405 dice 1,755 dice 1,026 dice
Answer: Hello your question is missing some details but I will provide a general solution based on the scope of the problem and you can plugin the missing value
answer = Volume of rectangular prism box / volume of cube
Step-by-step explanation:
To determine the number of Dice that will fit in the rectangular prism box
First : calculate the volume of the cube box ( dice )
volume of a Cube box : V = L^3 where L = side length
next : calculate the volume of the rectangular prism box
volume of rectangular prism box = L * b * h
L= length , b = width , h = height
final step : Divide the volume of the rectangular prism box by the volume of the cube box ( dice )
= ( L * b * h ) / ( L^3 )
Lily has walked 2 miles. Her goal is to walk 6 miles. Lily plans to reach her goal by walking 3 miles each hour h for the rest of her walk. Write an equation to find the number of hours it will take Lily to reach her goal.
Answer: \(1\dfrac13\) hours
Step-by-step explanation:
Lily's goal to walk = 6 miles
Lily has walked 2 miles.
Let h= number of hours it will take Lily to reach her goal.
She walk 3 miles an hour.
Total miles she can walk in h hour = 3h
According to the question,
\(3h +2 = 6\) (Required equation)
Subtract 2 from both sides , we get
\(3h = 4\)
Divide both sides by 3 , we get
\(h=\dfrac43=1\dfrac{1}{3}\)
Hence, it will take \(1\dfrac13\) hours to reach her goal.
The equation to find the number of hours it will take Lily to reach her goal is (2 + 3h = 6) and this can be determined by using the given data.
Given :
Lily has walked 2 miles. Her goal is to walk 6 miles. Lily plans to reach her goal by walking 3 miles each hour h for the rest of her walk.The following steps can be used in order to determine the equation to find the number of hours it will take Lily to reach her goal:
Step 1 - The linear equation can be formed in order to determine the number of hours it will take Lily to reach her goal.
Step 2 - Let the number of hours be 'h'.
Step 3 - So, the linear equation that represents the given situation is given below:
2 + 3h = 6
Step 4 - Simplify the above equation in order to determine the value of 'h'.
3h = 4
h = 4/3 hours
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How many 4-letter combinations containing 3 consonants and 1 vowel can be made from this set if all the letters in a combination must be unique? {R, E, L, O, A, D} A. 30 B. 48 C. 72 D. 90
Answer: C. 72
Step-by-step explanation:
The set is:
{R, E, L, O, A, D}
if we separate it into consonants and vowels, we have
consonants: {R, L, D}
vowels : {E, O, A}
Now, we want combinations of 3 consonants and one vowel.
we have 4-letters combinations, let's fixate the first letter as the vowel,
for this first letter, we have 3 options {E, O, A}
for the second letter, a consonant, we also have 3 options {R, L, D}
for the third letter, we also need to choose a consonant, but now we have 2 options (because we already selected one)
for the fourth letter, we have only one option.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 3*3*2*1 = 18
But remember that this is the case where the vowel is fixed for the first letter, we have 4 positions where the vowel can be (first, second, etc)
So the actual number of combinations is:
C*4 = 18*4 = 72
The correct option is C.
'SOMEBODY PLEASE HELP I WILL GIVE YOU A BRAINLIEST
PROP/CONSTANT
A factory makes 36 cookies in 12 mins. How many cookies can they make in ONE minute?
6 cookies
4 cookies
3 cookies
2. A bathtub leaks 1/2 cup of water every 1/4 minute. How many cups of water leak every minute?
3 1/2 cups
1 cup
2 cups
3. 5 glazed donut has 750 calories altogether. How many calories are in TWO donuts?
300 calories
150 calories
450 calories
4. A cell phone company charges $70 for 2 months of service, and $210 for 6 months of service. What is the constant rate (per month) for the service?
$40 per month
$35 per month
$55 per month
5. Which is the formula to find the constant of a chart?
k = y/x
y = kx
x = k/y
6. A chart is not considered proportional if...
the chart has too many large numbers
the x values are bigger than the y values
if the y values are bigger than the x values
if there is no constant (k)
Use the chart below for questions 7 and 8
7. Is the chart above proportional?
Yes
No
8. Determine the constant(k) of the chart.
k = .75
k = 1.75
k = 2.15
Doesn't have a constant
Use the chart below to answer questions 9 - 12.
9. Is the chart above proportional?
8 points
Yes
No
10. Determine the constant(k) of the chart?
10 points
k = 5
k = 4
k = .25
11. Which formula satisfies an equation for Y.
y = 4x
y = .25x
y = 5x
12. Find the value of y when x is 49.
12.25
196
80
18
Answer:
1. 3 cookies
2. 2 cups
3. 300 calories
4. $35 per month
5. k = y/x
6. If there is no constant (k)
Step-by-step explanation:
1. The number of cookies the factory makes in one minute = (The number of cookies the factory makes in 12 minutes)/(12 minutes)
∴ The number of cookies the factory makes in one minute = 36 cookies/(12 minutes) = 3 cookies/minute
The correct answer is 3 cookies
2. The number of cups of water that leak every minute = (The number of cups of water that leak in 1/4 minute) × (The number of 1/4 minute per minute)
The number of cups of water that leak every minute = 1/2 cup per 1/4 minute × 4_1/4 minute per minute
The number of cups of water that leak every minute = 1/2 × 4 = 2
The number of cups of water that leak every minute = 2 cups
3. 5 glazed donuts contains 750 calories
∴ 1 glazed donuts contains 750/5 = 150 calories
2 = 2 × 1 glazed donuts will contain 2 × 150 = 300 calories
4. The charge of the cell phone company for 2 months = $70
The charge of the cell phone company for 6 months = $210
The constant rate per month = The rate of change of the cell phones companys charges
∴ The constant rate per month = (210 - 70)/(6 - 2) = 140/4 = 35
The constant rate (per month) for the service = $35 per month
5. The formula to find the constant of a chart, k = y/x
6. A chart is not considered proportional if there is no constant (k)
A team of doctors claim to have developed a medicine that will with 80% effectiveness stop the growth of a skin cancer on rats. To test the medicine on a wide scale, a random sample of 400 cancer infested rats is treated. The cancerous growth was entirely stopped on 310 rats. Test against their claim using a=.05.
The evidence from the test does not support the claim that the medicine is 80% effective in stopping the growth of skin cancer on rats.
Is the claim of 80% effectiveness supported by the test?Null hypothesis (H0): The medicine is not effective, and the true proportion of rats with the cancerous growth stopped is equal to or less than 80%.
Alternative hypothesis (Ha): The medicine is effective, and the true proportion of rats with the cancerous growth stopped is greater than 80%.
Given:
Sample size is 400 and 310 rats had their cancerous growth stopped.
We will calculate the sample proportion (p) of rats with the growth stopped:
p = 310/400
= 0.775
To perform the hypothesis test, we are using test statistic formula: z = (p - p) / √(p(1-p)/n)
Data:
p = 0.80 = (80%)
n = 400.
z = (0.775 - 0.80) / √(0.80*(1-0.80) / 400)
= -0.025 / √(0.16/400)
= -0.025 / √0.0004
= -0.025 / 0.02
= -1.25
Using a significance level (α) of 0.05, we will compare the test statistic to the critical value from the standard normal distribution. The critical value for a one-tailed test at α = 0.05 is 1.645.
Since -1.25 < 1.645, we do not have enough evidence to reject the null hypothesis.
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What is the value of x???
The value of x, the exterior angle, is 44°.
Given is a triangle ABC with two opposite interior angles 14° and 30° we need to find the value of x which is the exterior angles,
The sum of the measures of the interior angles of a triangle is always 180 degrees.
Since you have two opposite interior angles given, which are 14° and 30°, you can find the third interior angle by subtracting the sum of these two angles from 180°:
180° - (14° + 30°) = 136°
Now, let's consider the exterior angle, which is supplementary to the interior angle.
The sum of an interior angle and its corresponding exterior angle is always 180 degrees.
Therefore, the value of the exterior angle, x, can be found by subtracting the corresponding interior angle from 180°:
x = 180° - 136° = 44°
So, the value of x, the exterior angle, is 44°.
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Answer:
44°
Step-by-step explanation:
The second theorem states that the exterior angle is equal to the sum of the two interior angles that are not adjacent to it. This second theorem is particularly important because it allows us to prove that the sum of the interior angles of a triangle is a straight angle.
so
Angle x = 30 + 14 = 44°
a) Calculate the size of angle x in the diagram
below.
b) Work out the bearing of A from B.
The angle x in the diagram is 98 degrees.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.
Therefore, let's find the angle of x using the angle relationships as follows:
The size of the angle x can be found as follows:
82 + x = 180(same side interior angles)
Same side interior angles are supplementary.
Hence,
82 + x = 180
x = 180 - 82
x = 98 degrees
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Determine the probability that the first child of clara and charles will be a boy with hemophilia. express your answer as a fraction (example 1/8).
The probability that the first child of Clara and Charles will be a boy with hemophilia is 1/4.
How to calculate the probability?It shouldbe noted the dominant and recessive alleles is given as H and h. It should be noted that A and a also represent the tyrosinase alleles.
The father of Clara had hemophilia.
Therefore, the probability that the first child of Clara and Charles will be a boy with hemophilia will be:
= 1/2 × 1/2
= 1/4.
Therefore, the probability is 1/4.
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In humans, hemophilia (OMIM 306700) is an X-linked recessive disorder. The dominant and recessive alleles represented by H and h . Albinism is an autosomal recessive condition . A and a represent the tyrosinase alleles. A healthy woman named Clara (II-2), whose father (I-1) has hemophilia and whose brother (II-1) has albinism, is married to a healthy man named Charles (II-3), whose parents are healthy. Charles's brother (II-5) has hemophilia, and his sister (II-4) has albinism. The pedigree is shown.
Determine the probability that the first child of clara and charles will be a boy with hemophilia.
PLSSSS HELP WILL GIVE BRAINLIEST
ILL FRIEND U
ILL GIVE 5 STARS AND A THANKS
Answer:
12 / (-15) goes in the first box.
12 / 15 goes into the second box
15 / -12 goes into the third box
and 15 / 12 goes into the fourth box
Step-by-step explanation:
Answer:
if im not mistaken the order should go
1.15/12
2.12/(-15)
3.12/15
4.15/(-12)
Step-by-step explanation:
if wrong or i made a mistake please tell me :)
what is foci of ellipse calculator?
An ellipse's form is determined by two locations inside the ellipse known as its foci.
The lengths of the main and minor axes of an ellipse may be used to calculate its foci.
The foci of an ellipse may be calculated using a variety of online calculators.
These calculators normally ask the user to enter the main and minor ellipse axes' lengths before calculating the foci's coordinates. Depending on the calculator in question, some may additionally ask for more details like the ellipse's eccentricity or center of rotation.
Understanding an ellipse's shape and characteristics requires knowing its foci since they are what characterize an ellipse.
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A pool with 12,000 gallons is drained at 4 gallons per minute.?
A.Proportional
B.Non Proportional
Answer:
proportional
Step-by-step explanation:
good luck!
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The gift shop at a science museum sells lollipops that are made to look like the planets.
Each lollipop is
shaped like a sphere and has a radius of 12 mm.
What is the volume of each lollipop?
Either enter an exact answer in terms of pi or use 3.14 for pi.
Answer:
\(volume = 2304\pi \ mm^3\\\\volume = 7234.56 \ mm^3\)
Step-by-step explanation:
Radius , r = 12mm
\(Volume = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (12^3)\\\\\)
\(=\frac{4}{3} \pi \times 1728\\\\= 4\pi \times 576\\\\= 2304 \pi \ mm^3\\\\or \\\\= 7234.56 \ mm^3\)
Which expression uses the associative property to make it easier to evaluate 8(3)? O A. 80 ) O 8 B. (8-5) O c. (2-3) OD. (8) 2
The associative property tells us that a product of three numbers written as:
\(a\cdot(b\cdot c)\)Is the same as if we multiply them in the order:
\((a\cdot b)\cdot c\)So, applying this property to:
\(8\cdot(\frac{1}{2}\cdot\frac{1}{3})\)We will get:
\((8\cdot\frac{1}{2})\cdot\frac{1}{3}\)Therefore, the answer is option B.
1. What position in the distribution corresponds to a z-score of =1.20? A. Below the mean by 1.20 points B. Selow the mean by a distance equal to 1.20 standard deviations C. Above the mean by 1.20 points D. Above the mean by a distance equal to 1.20 standard deviations
The correct answer is option D. Above the mean by a distance equal to 1.20 standard deviations .What is z-score? A z-score is also known as the standard score and is used to calculate the probability of a score occurring within a normal distribution's distribution.
It is a measure of how many standard deviations a data point is from the mean. It is denoted by the letter “Z.”Z-score calculation formula isz = (x- μ) / σ Where,
x = Score
μ = Mean
σ = Standard deviation
In this question, the z-score given is 1.20, which means it is 1.20 standard deviations above the mean. Therefore, option D. Above the mean by a distance equal to 1.20 standard deviations is the correct answer to the given question.
A z-score is the number of standard deviations that a data point is from the mean of a distribution. To solve this problem, we'll first need to determine the position in the distribution that corresponds to a z-score of 1.20. The formula for calculating z-score is z = (x - μ) / σwhere z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation. Using this formula, we can solve for the raw score that corresponds to a z-score of 1.20. We know that the z-score is 1.20, so we can substitute that value in for z:1.20 = (x - μ) / σWe also know that the mean is 0 (since z-scores are calculated based on a standard normal distribution with a mean of 0 and a standard deviation of 1), so we can substitute that value in for μ:1.20 = (x - 0) / σSimplifying the equation,
we get: 1.20σ = x Now we know that the raw score is equal to 1.20 standard deviations above the mean. So the correct answer is D. Above the mean by a distance equal to 1.20 standard deviations.
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the angle of elevation from a rowboat moored 75 feet from a cliff is 73.8 degrees.find the height of the cliff to the nearest foot.
The height of the cliff is approximately 269 feet.
We will be using the tangent function to find the height of the cliff.
Draw a right triangle with the rowboat at one corner, the cliff's base as the adjacent side, and the cliff's height as the opposite side.
The angle of elevation (73.8 degrees) is between the rowboat and the cliff's base.
We are given the adjacent side (75 feet) and we need to find the opposite side (height of the cliff).
To do this, we will use the tangent function:
tan(angle) = opposite side / adjacent side
Plug in the given values:
tan(73.8) = height / 75
Solve for the height:
height = tan(73.8) * 75
Calculate the value:
height ≈ 269.4 feet
Round the height to the nearest foot:
height ≈ 269 feet.
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Ria drinks x number of glasses of milk, each containing y mL each day. Sharan drinks 2x number of glasses of milk, each containing -y/2)} mL each day. Who drink more amount of milk each day?
I will give brainlist if you give the correct answer.
Ria and Sharan drank drank equal amount of milk
How to work itGiven data
Ria drinks x number of glasses of milk, each containing y mL each day
Sharan drinks 2x number of glasses of milk, each containing -y/2)} mL each day
Ria
x glass contains y ml. hence Ria took xy ml of milk each day
Sharan
2x glass contains y/2 ml. hence Sharan took xy ml of milk each day
comparing both shows that they both contains xy ml of milk each day. Therefore Ria and Sharan took equal amount of milk each day
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Jenna collects stamps. She puts the same number of stamps on each page and then inserts each page into one of her two stamp books. One of her stamp books has a total of 840 stamps. The other has 1008. What is the largest number of stamps that Jenna could be putting on each page
168 is the largest number of stamps that Jenna could be putting on each page
What is the Greatest Common Factor?
The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
So the largest number of stamps that Jenna could be putting on each page
would be gcd of 1008 and 840.
840 = 2 x 2 x 2 x 3 x 5 x 7
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.
∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.
Hence 168 is the largest number of stamps that Jenna could be putting on each page
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Juan y Alfredo desayunan en la misma cafetería, Juan asiste cada 15 días y Alfredo cada 27 días. Considerando que hoy coincidieron, ¿dentro de cuánto tiempo volverán a encontrarse?
Teniendo en cuenta el mínimo común múltiplo, considerando que hoy coincidieron, dentro de 135 días Juan y Alfredo volverán a encontrarse.
Mínimo común múltiploEl mínimo común múltiplo de dos o más números es el múltiplo más pequeño que esos números tienen en común.
En otras palabras, el mcm es la cifra más pequeña que satisface la condición de ser múltiplo de todos los elementos de un conjunto de números.
El mínimo común múltiplo se suele expresar como m.c.m. (a, b), siendo a y b los números.
Para calcular el mínimo común múltiplo de dos o más números, debes:
descomponer los números en factores primos.escoger todos los factores (comunes y no comunes), elevados a la máxima potencia. Es decir elegir todos los factores, pero los que se repitan se escogen elevados a la máxima potencia (repetidos la mayor cantidad de veces).multiplicar los factores elegidos para obtener el mínimo común múltiplo.Tiempo en que Juan y Alfredo vuelven a encontrarseEn este caso debes encontrar el mínimo común múltiplo entre 15 y 27, correspondientes a los días que Juan y Alfredo asisten a la misma cafetería.
Descomponiendo cada número en factores primos se obtiene:
15= 3× 5
27= 3× 3× 3= 3³
Escogiendo los factores (comunes y no comunes), elevados a la máxima potencia, y multiplicándolos se obtiene:
m.c.m(15,27)= 3³× 5= 135
Finalmente, considerando que hoy coincidieron, dentro de 135 días Juan y Alfredo volverán a encontrarse.
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What method can be used to prove the triangles below are congruent?
Answer:
A. SAS
Step-by-step explanation:
- SAS is side, angle, side.
- when both triangle are compared, both triangles are similar in their: (the point face upward)
• left-side (one line)
• upper angle
• base / down-side (two lines)
What order do I put the numbers in
We have following associations:
m ∠ADC + m ∠CDB = 180° → Definition of linear pair∠ADC is supplementary to ∠CDB → Definition of supplementary angles 2 · m ∠BDC = 180° → Substitution property of equalitym ∠BDC = 90° → Division property of equalityHow to complete the proof of a geometric theorem
In this question we need to fill the blanks of a given proof by understanding and taking advantage of the most important axioms and theorems of Euclidean geometry and real algebra. In this case, a linear pair is the combination of two angles whose sum equals 180°, and those angles are always supplementary.
Thus, we have following associations:
m ∠ADC + m ∠CDB = 180° → Definition of linear pair∠ADC is supplementary to ∠CDB → Definition of supplementary angles 2 · m ∠BDC = 180° → Substitution property of equalitym ∠BDC = 90° → Division property of equalityTo learn more on Euclidean theorem: https://brainly.com/question/13104788
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The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
The parameters are:
x is the number of successese = 2.71828 is the Euler number\(\mu\) is the mean in the given interval.The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
\(\mu = 3500 \times 0.0004 = 1.4\)
The probability that 2 or fewer cars will be stolen is:
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)
In which:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)
\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)
\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)
Then:
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)
0.8335 = 83.35% probability that 2 or fewer will be stolen.
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A building manager is buying gravel and mulch for landscaping. He can spend no more than $250 and must cover at least 200 square feet. Gravel costs $2 per square foot, and mulch costs $0.25 per square foot. If the building manager wants to purchase only one material, can he? Explain your answer.
Answer:
No, the building manager cannot purchase only one material. The maximum amount he can spend is $250, and 200 square feet of gravel would cost $400, which is more than the budget allows. Similarly, 200 square feet of mulch would cost only $50, which is far less than the budget allows.
Step-by-step explanation:
What is the perimeter of △ABC? Round each step to the nearest tenth. Enter your answer in the box. units A coordinate grid containing triangle A B C with points A begin ordered pair five comma negative one end ordered pair, B at begin ordered pair negative one comma one end ordered pair, C at begin ordered pair zero comma negative three end ordered pair.
ΔABC
A(-3, -1), B(0, 3), C(1, 2)
Find
the length of the perimeter of ΔABC to the nearest tenth
Solution
The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.
The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us
... AB² = 3² +4² = 9 +16 = 25
... AB = √25 = 5
You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.
LIkewise, segment AC has coordinate differences of ...
... C - A = (1, 2) -(-3, -1) = (4, 3)
These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.
Segment BC has coordinate differences ...
... C - B = (1, 2) -(0, 3) = (1, -1)
The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is
... BC = √(1² +1²) = √2 ≈ 1.4
So the perimeter of the triangle ABC is
... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units
_____
Please be aware that the advice to "round each step" is bad advice, in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.
In this problem, the only number that is not an integer is √2, so it doesn't really matter.
17.2(20+45)-3/4 (12)
Answer:
17•2×65 - 3/4×12
1118 - 36/4
1118 - 9
1109
Answer:
1109
Step-by-step explanation:
I put it here, cause didnt see the answer box until now,
but, this is the answer
Please input the Answer, With explanation.
Answer:
86 / 6 = 14.33
14.33 * 4 = 57.33
(round to 58)
1. Calculate the value of a 10 year bond with a face value of AUD 100, annual coupons of AUD 10, when the market yield (yield to maturity) is 11%.
a.
AUD 100
b.
AUD 94.11
c.
AUD 138.61
d.
AUD 88.70
e.
AUD 83.72
f.
AUD 106.42
The present value of a 10 year bond with a face value of AUD 100 and annual coupons of AUD 10, when the market yield (yield to maturity) is 11% is AUD 94.11.
Calculate the present value of the annual coupon payments. The present value of a perpetuity is equal to the periodic payment (in this case, AUD 10) divided by the discount rate (in this case, 0.11)P = C / r
P = AUD 10 / 0.11
P = AUD 90.91
Calculate the present value of the face value. The present value of the face value is equal to the face value (in this case, AUD 100) divided by (1 + the discount rate raised to the number of periods remaining (in this case, 10)). P = F / (1 + r)n
P = AUD 100 / (1 + 0.11)10
P = AUD 38.65
Add the present value of the annual coupon payments and the present value of the face value to get the present value of the bond. Present Value of Bond = Present Value of Coupons + Present Value of Face Value Present Value of Bond = AUD 90.91 + AUD 38.65Present Value of Bond = AUD 129.56
Present Value of Bond = Present Value of Coupons + Present Value of Face Value Present Value of Bond = AUD 90.91 + AUD 38.65 Present Value of Bond = AUD 129.56
Therefore, the present value of the bond is AUD 129.56 or AUD 94.11 after rounding to two decimal places.
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