a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.
b) The price of the security is $128.31.
a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:
PV = C / [tex](1+r)^n[/tex]
where PV is the present value,
C is the coupon payment,
r is the zero rate, and
n is the number of years to maturity.
We can solve for r by rearranging the formula:
r = [tex](C/PV)^{(1/n) }[/tex]- 1
Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:
For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.
For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.
For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.
For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.
For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.
Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:
PV = A × x
where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.
To solve for x, we can use the equation:
x = ([tex]A^{-1}[/tex]) x PV
where ([tex]A^{-1}[/tex]) is the inverse of matrix A.
Using this method, we can solve for the zero rates as follows:
[2.01% ]
[2.48% ]
[2.77% ] = x
[1.73% ]
[4.32% ]
PV = [tex]A^{-1}[/tex] x [98]
[101]
[103]
[101]
[103]
PV = [-0.0201]
[ 0.0248]
[ 0.0277]
[-0.0173]
[ 0.0432]
b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:
PV = [tex]C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4[/tex]
where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.
Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:
PV1 = $10 /(1+2.01 % [tex])^1[/tex] = $9.80
PV2 = $25/(1+2.48%[tex])^2[/tex] = $22.15
PV3 = $100/(1+1.73%[tex])^4[/tex] = $81.36
Then, the price of the security is the sum of the present values:
PV = $9.80 + $22.15 + $81.36 = $128.31
Therefore, the price of the security is $128.31.
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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
a culture contains 10,000 bacteria initially. after an hour the bacteria count is 25,000. (a) find the doubling period. (b) find the number of bacteria after 3 hours.
9.12 movie lovers, part ii. suppose an online media streaming company is interested in building a movie recommendation system. the website maintains data on the movies in their database (genre, length, cast, director, budget, etc.) and additionally collects data from their subscribers ( demographic information, previously watched movies, how they rated previously watched movies, etc.). the recommendation sys- tem will be deemed successful if subscribers actually watch, and rate highly, the movies recommended to them. should the company use the adjusted r2 or the p-value approach in selecting variables for their recommendation system?
The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.
To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.
In this case, the company should use the adjusted R² approach instead of the p-value approach.
The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).
Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.
It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.
This could result in a less accurate recommendation system.
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There is 6/8 of a cake
leftover after a birthday
party. How many 1/4
pieces can be made from
the leftover cake?
Answer: 3 pieces
Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.
Find the avatar rate of change f(x)=3√x-1 +2; 9 ≤ x ≤ 65
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
Which comparison is not correct?
A. 1 > -9
B. 3 < 6
C. -8 > -6
D. -3 < 4
Answer:
The comparison that is not correct is:
C. -8 > -6
This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.
The other comparisons are correct:
A. 1 > -9 (true, because 1 is greater than -9)
B. 3 < 6 (true, because 3 is less than 6)
D. -3 < 4 (true, because -3 is less than 4)
3 out of 7 questions. PLEASE help me.
Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar
Transforming the circles(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:
Translate the solid circle 2 units to the left and 2 units down.Dilate the solid circle by a scale factor of 2.Therefore, the blank spaces should be filled as follows:
Translate the solid circle 2 units to the left and 2 units down.
Dilate the solid circle by a scale factor of 2.
(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.
This is because all circles are similar
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A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
The product of two terms gives the walkway's area around the garden: 15x+13.5.
Define rectangleA rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.
Area of garden = 4(4.5x + 3.5) = 18x+14
The combined area of the garden and the walkway = 5.5(6x+5) =33x+27.5
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
Aw=combined area -Area of garden
=33x+27.5-18x-14
=15x+13.5
Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.
Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.
Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.
So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.
However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).
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Complete Question:
Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
Fifteen children split $9 among themselves so that each child receives the same amount. How much did each child receive?
The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.
Total number of children is equal to 15
Total amount of money distributed among 15 children = $9
To find out how much each child receives,
We can divide the total amount of money by the number of children.
In this case, there are 15 children and $9 to split.
So, the amount of money each child receives is equal to,
(Total amount of money )/ ( total number of children )
= $9 ÷ 15
= $0.60
Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.
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Grupo textil M & M destaca que los ingresos de este año vienen dados por la funcion f(x) = (x+2)(-x+9-3) donde "x" es el precio de cada unidad y f(x) es la ganancia expresada en dolares
Para entender mejor esta función, podemos expandirla y simplificarla:
f(x) = (x+2)(-x+6)
f(x) = [tex]-x^2 + 4x + 12[/tex]
Esta es una función cuadrática, lo que significa que tiene la forma de una parábola. El término cuadrático ([tex]-x^2[/tex]) hace que la parábola tenga una concavidad hacia abajo, lo que significa que el valor máximo de la función se encuentra en el vértice de la parábola.
Podemos encontrar el valor del precio de venta que maximiza la ganancia utilizando la fórmula x = -b/(2a), donde "a" es el coeficiente del término cuadrático y "b" es el coeficiente del término lineal.
En este caso, a = -1 y b = 4, por lo que:
x = -4/(2-1)
x = -4/-2
x = 2
Por lo tanto, el precio de venta que maximiza la ganancia es de 2 por unidad. Si se venden las unidades a este precio, la ganancia total sería de:
f(2) = [tex]-2^2 + 4(2) + 12[/tex]
f(2) = -4 + 8 + 12
f(2) = 16 dólares
Es importante tener en cuenta que la función f(x) también puede ser utilizada para calcular la ganancia total para cualquier precio de venta "x". Por ejemplo, si se venden las unidades a 3 por unidad, la ganancia sería:
f(3) = [tex]-3^2 + 4(3) + 12[/tex]
f(3) = -9 + 12 + 12
f(3) = 15 dólares
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ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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why would you use a trigonometric function to set-up an application problem instead of a non-trigonometric function
Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.
For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.
In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.
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angles of triangles- does anyone know how to do this?
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°
(4) m∠1=88°m∠2=42° m∠3=113°
What is an angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.
Define triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles.
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)
(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)
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Select the GCF of these numbers. 48 and 60 22 ·3 2· 112 32 23 · 5 13· 193 ·232
The GCF of 48 and 60 is 12
To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number
48 = 2^4 × 3
60 = 2^2 × 3 × 5
Next, we can identify the common factors of both numbers by looking at their prime factorization
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.
The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.
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The given question is incomplete, the complete question is:
Find the GCF of 48 and 60.
Given the quadratic equation x^(2)+4x+c=0, what must the value of c be in order for the equation to have solutions at x=-3 and x=-1 ?
Answer:
Step-by-step explanation:
If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,
(x - 3) (x - 1)
x^2 - x - 3x + 3
x^3 - 4x + 3 = 0
Your answer is 3
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
What is the answer to this problem?
The area of the shaded area is 3.27 ft²
How to the area of the shaded area?We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;
Area of shaded area = Area of sector - area of triangle
Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)
Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)
Area of shaded area = 3.27 ft²
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three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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The cost of 1 cup of tea and 6 cakes is £13. The cost of 1 cup of tea and 4 cakes is £9 a) How much do 2 cakes cost? b) How much does 1 cake cost?
The answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:
3 cupcakes + 1 tea = £9
3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5
1 cupcake = £7.5 ÷ 3 = £2.5
So 2 cupcakes would cost:
2 cupcakes = 2 × £2.5 = £5
Therefore, the answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
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Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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Sam makes tote bags for a school fundraiser. The fixed costs for making the bags is $30. The cost of the materials for each bag is $8.50. Sam can spend less than a total of $200 on the tote bags. Write an inequality that can be used to determine b , the number of tote bags that can be made.
when a researcher uses the pearson product moment correlation, two highly correlated variables will appear on a scatter diagram as what?
When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.
The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.
On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.
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in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.
Find the measure of the line segment indicated, assume that lines which appear tangent, are tangent.
Find FS
Possible answers —>
A. 17
B. 21
C. None of the other answers are correct
D. 18
E. 45
The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
UF × FS = VF × FT
8(10x - 1) = 9 × 16
80x - 8 = 144
80x = 144 + 8 {collect like terms}
80x = 152
x = 152/80 {divide through by 80}
x = 1.9
FS = 10(1.9) - 1 = 18
Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
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state the nameof this quadrilateral...70 points
Answer:
Step-by-step explanation:
its a rectanlge
Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)