Answers
After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:
El = HG
EG = IF
From the knowledge provided above, we can formulate two equations in terms of x:
3x + 5 = HG
5x + 16 = IF
90 m HG F and 90 m EFG
Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.
Now that the formulas for HG and IF are equivalent to one another, we may find x:
3x + 5 = 5x + 16
2x = 11\sx = 5.5
Hence, x = 5.5 and m El H = 180.
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Related Questions
The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4.
Answers
The required graph is attached.
What is a graph?An organized representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
The modification looks like this.
Combining two transformations results in the transformation of
h(x) to -h(x) -4.
1. An X-axis-centered reflection. Every point (x, y) in h(x) is transformed into (x', y'), where x' = x and y' = -y. Hence, (x, y) (x, -y)
2. A 4-unit translation of each reflected point, where the x value remains constant, but the y value is translated downward to become y'-4 = -y -4
Every coordinate (x, y) in h(x) will be transformed to the following as a result of both transformations: (x, -y -4)
Given that the graph is made up of two straight lines that intersect at the origin, all we need to do is select any three points in h(x), determine their transformed coordinates, and then connect them using straight lines: h(x0 -h(X) - 4 (-2, 4) (-2, -4-4) =(-2, -8) (0, 0) (0, -0 - 4) =(0, -4) (4, 2) (4, (4, -6)
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A map of B.C. has a scale of 1:2 500 000. The actual distance between Nanaimo and Campbell River is approximately 86 mi. What is this distance on the map? Answer to the nearest sixteenth of an inch.
pls help! and show work.
Answers
Reduce fraction to its lowest terms:
= 43/1,250,000
= 0.0000344” or 3.44x10^-5
The nearest 16th of an inch would then essentially be 0.001”
A lightyear is the distance that light travels in one year. The speed of light is about 300 million m/s. The earth is about 150 million km from the sun. How long does it take a beam of light to travel from the sun to the earth?
Answers
The distance from the sun to the earth is approximately 150 million km.
To convert this to meters, we can multiply by 1,000 to get 150 billion meters (1 km = 1000 m).
Using the speed of light of 300 million m/s, we can calculate the time it takes for light to travel from the sun to the earth by dividing the distance by the speed of light:
Time = Distance / Speed of light
Time = 150,000,000,000 m / 300,000,000 m/s
Time = 500 seconds
Therefore, it takes about 500 seconds or 8.3 minutes for a beam of light to travel from the sun to the earth.
In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answers
Answer: 1.3
Step-by-step explanation:
Show that the semigroup of subsets of a monoid is also a monoid.
Answers
Let (M,*) be a monoid, which means that M is a set equipped with an associative binary operation * and an identity element e such that for all a, b, and c in M:
a*(bc) = (ab)*c (associativity)
ae = ea = a (identity)
We want to show that the semigroup of subsets of M, denoted by (P(M),•), where • is the set intersection operation, is also a monoid.
First, let's show that (P(M),•) is a semigroup. To prove that (P(M),•) is closed under the operation •, we need to show that for any A, B in P(M), A • B is also in P(M). This is true since A • B is a subset of M. Moreover, the operation • is associative, which means that for any A, B, and C in P(M), we have:
(A • B) • C = A • (B • C)
Therefore, (P(M),•) is a semigroup.
Next, we need to show that (P(M),•) has an identity element. The identity element for the semigroup (P(M),•) is the set M itself, since for any A in P(M), we have:
M • A = A • M = A
Therefore, (P(M),•) has an identity element.
Finally, we need to show that (P(M),•) satisfies the associative and identity properties of a monoid. Since we have already shown that (P(M),•) is a semigroup with an identity element, we only need to show that • is associative and that M is the identity element.
Associativity: For any A, B, and C in P(M), we have:
(A • B) • C = A ∩ B ∩ C
A • (B • C) = A ∩ (B ∩ C)
Since the intersection operation is associative, we have:
A ∩ (B ∩ C) = (A ∩ B) ∩ C
Therefore, (A • B) • C = A • (B • C), and • is associative.
Identity: For any A in P(M), we have:
M • A = M ∩ A = A
A • M = A ∩ M = A
Therefore, M is the identity element for (P(M),•), and (P(M),•) is a monoid.
Hence, we have shown that the semigroup of subsets of a monoid is also a monoid.
help fast
9 inches of ribbon is needed for wrapping one present. How many presents can be wrapped with 8 yards of ribbon?
9 presents
16 presents
32 presents
45 presents
Answers
Work Shown:
1 ft = 12 inches
3 ft = 3*12 = 36 inches
1 yard = 3 ft = 36 inches
8 yards = 8*36 = 288 inches
x = number of presents
9x = amount of ribbon
9x = 288
x = 288/9
x = 32
Solve n/6= 30/36 for the unknown quantity,n
Answers
Answer:
n=5
Step-by-step explanation:
First cross multiply to get:
36n = 180
Divide both sides by 36
36n/36 = 180/36
n=5
Find the perimeter of the composite figure.
Responses
33.4 cm
41.8 cm
70 cm
44 cm
Answers
8.4+8.4+10+5+10=41.8
Which function has an average change of -4 over the interval [-2,2]
Answers
Answer: B
Step-by-step explanation:
Find the distance in units, between P and R.
Express your answer as a square root.
Answers
Therefore , the solution of the given problem of unitary method comes out to be P and R are separated by 5 units.
What is an unitary method?One may use this common convenience, already-existing variables, or all important elements from the original Bishop customizable question that adhered to a particular method to achieve the goal. If so, there will be another chance to get in touch with the object. If it doesn't, all of the crucial elements that make up an expression proof outcome will be lost.
Here,
The triangle formed by the points P, Q, and R in the provided diagram is right-angled.
We can determine the length of PR, the hypotenuse of this triangle, using the Pythagorean Theorem.
PQ² + QR² = PR²
The illustration shows that PQ and QR each equal four units.
By replacing these numbers, we obtain:
=> PR² = 4² + 3²
=> PR² = 16 + 9
=> PR² = 25
When we square the two edges, we obtain:
=> PR = √25
=> PR = 5
As a result, P and R are separated by 5 units.
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A triangle has two side lengths of 6 cm and 4 cm. Select all the lengths that could be the third side.
Answers
The third side of the triangle can have any one of the following lengths:
2 cm < third side < 10 cm.
The triangle inequality theorem, which asserts that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, must be applied in order to find the potential lengths of the third side of the triangle.
We have sides of 6 cm and 4 cm in this instance. Hence, the third side's length must be smaller than the sum of the first two sides and bigger than the difference between them.
Contrast: 6 - 4 = 2 cm
Sum: 6 + 4 = 10 cm
As a result, the following are potential lengths for the triangle's third side:
Third side: 2 cm; length: 10 cm
Hence, the third side could be any length that falls within the range of 2 cm and 10 cm (exclusive).
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if you divide 50 by half and add 20 what is the sum?
Answers
Answer: 120
Step-by-step explanation: When 50 is divided by half, which is 100, and added 20 to it, it is 120
Answer:
45
step by step explaination:
Think about what same 2 numbers that, when added together make fifty. 25! so when you divide 50 by half, if equals 25. Then, add 25+20 to equal 45 :)
A toddler is playing with his toys in the bathtub. He is using a toy shaped like a rectangular prism, filling it with water to the top, and filling his other toys to overflowing.
Rectangular prism toy:
a. What is the volume of the rectangular prism toy?
b. What formula did you use to calculate your answer?
C. What formula did you use to calculate the volume of the cylindrical toy?
help
Answers
Therefore , the solution of the given problem of volume comes out to be a) 30 cubic inches , b)rectangular prism and c) cylinder volume is 108.6 cubic inches.
Explain volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The digits cm3 and in3 are two examples of cubic units. However, one can gauge an object's size using its bulk. Usually, the weight of an item is converted into mass measurements like kilogrammes or kilos.
Here,
a. By multiplying the rectangular prism toy's length, breadth, and height together, one can determine its volume:
Capacity is calculated using the formula LWH.
5 in. × 3 in. x 2 in.
thirty cubic inches of volume
Consequently, the rectangular prism toy has a capacity of 30 cubic inches.
b. I calculated the capacity of a rectangular prism using the following formula:
Capacity is calculated using the formula LWH.
c. The equation for a cylinder's volume is:
=> V = π x radius² x height
We can determine the radius using the following formula given that the cylindrical toy's height is 4 inches and its width, which is twice the radius, is 5.2 inches:
=> radius = circumference / 2.
=> radius=5.2 inches/two
=> radius: 2.6 inches
When we enter the numbers, we obtain:
Dimensions = 2.6 in x 2 in x 4 in
108.6 cubic inches of volume
Consequently, the cylindrical toy has a capacity of roughly 108.6 cubic inches.
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Use a truth table to determine whether the symbolic form of the argument on the right is valid or invalid.
Choose the correct answer below.
O The argument is invalid.
O The argument is valid.
r
p-q
9
Answers
The last column gives the truth values of the premises [(p -> q) ∧ (q -> r)] and (p -> r) ∧ [(p -> q) ∧ (q -> r)] . .
, as and the truth value of the conclusion (p -> r).
What is a truth table?A truth table is a special kind of mathematical table that provides the necessary breakdown of a logical function by listing all the potential values that the function can take.
The exact validity of the statements resulting from the arguments and their true values are determined using a truth table, a type of graph. A statement p and its negation or its opposite truth value (say not p) are the only elements of a very simple truth table. These items are identified by the symbol or .
p q r p -> q q -> r (p -> q) ∧ (q -> r) (p -> r) ∧ [(p -> q) ∧ (q -> r)]
T T T T T T T
T T F T F F F
T F T F T F F
TFFFFTFTFT
F T T T T T T
F T F T F F T
F F T T T T T
F F F T T T T
Each row of the table represents a possible combination of logical values for the variables p, q, and r. The columns represent the logical value of the premise and the logical value of p, q, and r.
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Please help with this pre calculus question
Answers
The distance between the points z₁ = 3+7i and z₂ = -5-2i is 12.04.
What is distance?Distance is the total movement of an object without any regard to direction.
To calculate the distance between the two complex expression, we use the
formula below
Formula:
d = √[(c-a)²+(d-b)²].................. Equation 1From the question,
Given the question
z₁ = 3+7iz₂ = -5-2iWhere:
a = 3b = 7c = -5d = -2Substitute these values into equation 1
d = √[(-5-3)²+(-2-7)²]d = √(64+81)d = √145d = 12.04Hence, the distance is 12.04.
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fin the missing value so that the two points have a slope of 1/7 (7,2) and (0,y)
Answers
Answer:
1/14
Step-by-step explanation:
three friends anna , manna and hanna are doing the decorations for matric farewell dance , anna puts up two-fifth of the decorations, manna puts one - fourth and hanna put up three - tenth of the decorations
Answers
The job is not yet complete at this stage, there is [tex]\frac{2}{40}[/tex] of the decoration is still left.
What is the percentage of job completion?The expression 'percentage of job completion' refers to the amount of work that has been finished in relation to the total amount of work that needs to be done. This allows us to track the progress and evaluate a project's performance.
We are told,
Anna: [tex]\frac{2}{5}[/tex] * [tex]40 = 16[/tex]
Manna: [tex]\frac{1}{4}[/tex] * [tex]40 = 10[/tex]
Hanna: [tex]\frac{3}{10}[/tex] * [tex]40 = 12[/tex]
Summing total individual progress:
[tex]16+10+12=38[/tex]
Fraction of job that still left to do:
[tex]1 - \frac{38}{40} = \frac{2}{40}[/tex]
This implies that there is still [tex]\frac{2}{40}[/tex] decoration left to do the total job.
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You've asked an incomplete question. The full question reads;
Three friends Anna, Manna, and Hanna are doing the decorations for matric farewell dance. Anna put up two-fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer.
The volume of a rectangular prism is given by the product of its length, width and height. A rectangular prism has a length of b^2 units, a width of a units, and a height ofab + c units. What is the volume of the rectangular prism?
Answers
The volume of the rectangular prism is expressed as a²b³ + ab²c
How to determine the volume of the prismSome of the properties of a rectangular prism are;
A rectangular prism has 6 faces, 12 edges and 8 verticesThe top and base of the rectangular prism are rectanglesIt also has three dimensions, that is, length width and height, making it look like a cuboidFrom the information given, we have that;
The formula for calculating the volume of a rectangular prism is expressed as;
Volume = length× width × height
Now, substitute the values into the formula, we have;
Volume = b² × a × ab + c
Multiply the values, we have;
Volume = ab²(ab + c)
Volume = a²b³ + ab²c
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Note that one of the x-values is negative. Find Σ [ x • P(x)]
Answers
Using the expected value of probability formula, the value of Σ[x•P(x)] is -0.65
What is the value of Σ[x•P(x)]The expected value of a probability distribution is a measure of the central tendency of the distribution. It is also known as the mean or the average value of the distribution.
To calculate the expected value, we multiply each possible outcome by its corresponding probability and then sum up the products. Symbolically, if X is a random variable with possible outcomes x1, x2, ..., xn and probabilities p1, p2, ..., pn, then the expected value of X, denoted E(X), is given by:
[tex]E(X) = \sum_{i=1}^{n} x_i p_i[/tex]
To find Σ[x•P(x)] we need to multiply each x-value by its corresponding probability and then sum up the products.
So we have:
Σ[x•P(x)] = (-1)(0.999) + (349)(0.001)
Σ[x•P(x)] = -0.999 + 0.349
Σ[x•P(x)] = -0.65
Therefore, Σ[x•P(x)] is equal to -0.65.
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Find the sum of the first ten terms
Does anyone think they can help me with this?
Answers
The sοlutiοn οf the given prοblem οf arithmetic mean cοmes οut tο be 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.
What is an arithmetic mean?A list's typical values, alsο referred tο as the οrganisatiοn ’s gοals, are determined by adding up each value οn the list. The percentage οf list cοmpοnents with the highest density is then used tο adjust these average numbers. Mathematical grοwth trends are cοmparable. The actual average οf the digits 5, 7, as well as 9 is 4, and the number 21 becοmes seven by adding three (there are presently a number οf three-digit numbers).
Here,
The series is a geοmetric sequence with the cοmmοn ratiο r = 3/2 and the first term a = 1. We are instructed tο use the fοllοwing fοrmula tο determine the sum οf the first ten terms:
= >S = a(1 - rⁿ) / (1 - r)
Inputting the numbers prοvided yields:
=> S = 1(1 - (3/2)¹⁰) / (1 - 3/2)
=> S = (1 - 59049/1024) / (-1/2)
=> S = (-59048/1024) * (-2) (-2)
=> S = 115.0625
Cοnsequently, 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.
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Find the common difference
Answers
Answer:
-1, -6, 13, 20 is an arithmetic sequence
d = 7
5, 12, 19, 26 is arithmetic sequence
d = 7
-3 - 9, -27, -81 is not an arithmetic sequence
Step-by-step explanation:
Common difference is the difference between successive terms and must be the same for all terms
-1, -6, 13, 20 is an arithmetic sequence with common difference:
6 - (-1) = 13 - 6 = 20 - 13 = 7
5, 12, 19, 26 is arithmetic sequence with common difference
12- 5 = 19 - 12 = 26 - 19 = 7
-3 - 9, -27, -81 is not an arithmetic sequence
The difference between successive terms is not the same
-9 - (-3) = -9 + 3= -6
but
-27 - (-9) = -27 + 9 = -18
In fact it is a geometric sequence where each term = x previous term
-9 = 3 x -3
-27 = 3 x -9
etc
Rewrite standard form y=3x^2 + 12x + 14 into vertex form
Answers
Answer:
(2,-2)
Step-by-step explanation:
Answer:
the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).
Step-by-step explanation:
To rewrite the quadratic equation y=3x^2 + 12x + 14 into vertex form, we need to complete the square.
First, we can factor out the coefficient of x^2, which is 3:
y = 3(x^2 + 4x) + 14
Next, we need to add and subtract a constant term inside the parentheses that will allow us to complete the square. We can do this by adding and subtracting (4/2)^2 = 4:
y = 3(x^2 + 4x + 4 - 4) + 14
Now we can write the first three terms inside the parentheses as a squared expression:
y = 3((x + 2)^2 - 4) + 14
Finally, we can simplify this equation by distributing the 3 and combining like terms:
y = 3(x + 2)^2 - 2
So the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).
Multiply (8+12t)(-3-6t)
Answers
Answer:
to multiply (8+12t)(-3-6t), we can use the distributive property and then simplify:
(8+12t)(-3-6t)
= 8(-3) + 8(-6t) + 12t(-3) + 12t(-6t)
= -24 - 48t - 36t + (-72t^2)
= -72t^2 - 84t - 24
Therefore, (8+12t)(-3-6t) = -72t^2 - 84t - 24.
Step-by-step explanation:
Answer:
[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to \underline{multiply} the given expression.}\\[/tex]
[tex]\textsf{We should use the \underline{FOIL Method.}}[/tex]
[tex]\Large\underline{\textsf{What is the FOIL Method?}}[/tex]
[tex]\textsf{The \underline{FOIL Method} is a method used to \underline{multiply 2 binomials together}.}[/tex]
[tex]\large\underline{\textsf{Foil Means:}}[/tex]
[tex]\textsf{Fronts - Front x Front.}[/tex]
[tex]\textsf{Outsides - Front x Inside.}[/tex]
[tex]\textsf{Insides - Inside x Front.}[/tex]
[tex]\textsf{Lasts - Inside x Inside.}[/tex]
[tex]\mathtt{(4x-3x)(5x-6x)}[/tex]
[tex]\textsf{4x - First front.}\\\textsf{-3x - First inside.}\\\textsf{5x - Second front.}\\\textsf{-6x - Second inside.}[/tex]
[tex]\large\underline{\textsf{Multiply using the FOIL Method:}}[/tex]
[tex]\mathtt{(8+12t)(-3-6t)}\\[/tex]
[tex]\mathtt{(8 \times -3)+(8 \times -6t) + (12t \times -3) +( 12t \times -6t)}[/tex]
[tex]\mathtt{-24+ -48t -36t-72t^{2}}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]
[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]
HELPP I NEED TO KNOW THIS
Answers
Answer:
45 pounds
Step-by-step explanation:
using the conversion
16 ounces = 1 pound , then
6 ounces = [tex]\frac{6}{16}[/tex] = [tex]\frac{3}{8}[/tex] pound
total pounds sold on Friday is then
( 40 × [tex]\frac{3}{8}[/tex] ) + (40 × [tex]\frac{3}{4}[/tex] )
= (5 × 3) + (10 × 3)
= 15 + 30
= 45 pounds
Find the real numbers that satisfy the equation |x| = -5/8
Answers
There are no real numbers, actual solutions to the equation |x| = -5/8.
What does the term "absolute value" mean?Several mathematical disciplines, including calculus, algebra, geometry, and number theory, employ the absolute value function. By removing the sign from a number or changing a complicated expression into a simpler one, it is frequently used to simplify expressions and equations. The distance between two points in n-dimensional space, where n is any positive integer, is also defined using the absolute value function. The absolute value function is also employed in many mathematical applications, including physics, engineering, economics, and finance, where it is utilised to describe quantities that can only have non-negative values.
There are no actual solutions to the equation |x| = -5/8. This is because |x| can never be negative because the absolute value function always returns a non-negative number. It follows that |x| cannot be equal to the negative integer -5/8.
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- Challenge:
A line through the points (2, 8) and (-2, k) has a slope of ¾. What is the value of k?
Answers
A line passing through the coordinates (2, 8) & (-2, k) does have a 34 slope. As a result, k has a value of 5.
A slope is what?The slope of a line governs its steepness. Rise over fall is a mathematical formula that describes slope.
We can construct an equation & solve for k using the slope formula:
if (x1, y1) & (x2, y2) are indeed the provided locations, slope is defined as (y2 – y1)/(x2 - x1).
Inputting the specified values results in:
¾ = (k - 8)/(-2 - 2) (-2 - 2)
By condensing this equation, we obtain:
3/4 = (k - 8)/(-4) (-4)
The result of multiplying all sides by -4 is:
-3 = k - 8
5 Equals k when we add 8 to both sides.
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3.) The line which is the graph of y = 2x -4 is transformed by the rule (x,y) (-x, -y). What is the
slope of the image?
Answers
The slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of the original line y = 2x - 4 is 2.
To find the slope of the image after the transformation, we can apply the transformation rule to two points on the original line, and then find the slope of the line passing through the images of those two points.
Let's choose two points on the original line:
Point 1: (0, -4)
Point 2: (1, -2)
Now we apply the transformation rule to each of these points:
Point 1 image: (-0, -(-4)) = (0, 4)
Point 2 image: (-1, -(-2)) = (1, 2)
The images of these two points lie on the line y = -2x + 4. The slope of this line is -2.
Therefore, the slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.
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Ryan wishes to purchase a new boat and can afford monthly payments of up to $500 per month. Finance is available, and the terms are that the loan lasts for 10 years and the annual interest rate is 13%. What is the maximum price for a boat that Ryan's budget can afford? Round your answer to the nearest hundred dollars.
Answers
Answer:
First, we need to calculate the total number of payments Ryan will make over 10 years, which is 10 years x 12 months/year = 120 months.
Next, we can use the formula for the present value of an annuity to calculate the maximum price of the boat:
PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)
where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the values we have:
PMT = $500
r = 0.13
n = 12 (since the loan is monthly)
t = 10
PV = $500 x [1 - (1 + 0.13/12)^(-12x10)] / (0.13/12)
PV = $44,484.72
Therefore, the maximum price for a boat that Ryan's budget can afford, rounded to the nearest hundred dollars, is $44,500.
1. Write an inequality to represent “a number (n) is at least four"
2. Graph your inequality.
Answers
Answer:
From what I remember, words like "at least" mean that that's the minimum, so it can be more than that, but not less than. So I believe the inequality that would best represent this is n ≥ 4.
Answer:
n>=4
Step-by-step explanation:
the personnel department of a large corporation reported 60 resginations during the last year. Carry out a test to determine if the number of resignations is uniform over the four seasons
Answers
Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.
What is Null hypοthesis?The null hypοthesis is statement that assumes there is nο significant difference between twο οr mοre sets οf data. It is statement that can be tested and either accepted οr rejected based οn statistical evidence.
Tο test whether the number οf resignatiοns is unifοrm οver the fοur seasοns, we can use the chi-squared gοοdness οf fit test. The null hypοthesis fοr this test is that the number οf resignatiοns is unifοrm οver the fοur seasοns
Here are the steps tο perfοrm the chi-squared gοοdness οf fit test:
Determine the expected frequencies:
Tο determine the expected frequencies, we need tο assume that the null hypοthesis is true. Since there are fοur seasοns, each seasοn is expected tο have 1/4 οf the tοtal number οf resignatiοns. Therefοre, the expected frequency fοr each seasοn is 60/4 = 15.
Calculate the test statistic:
The test statistic fοr the chi-squared gοοdness οf fit test is calculated using the fοrmula:
χ²=∑(O-E)²/E
Using the οbserved frequencies, we get:
χ² = (20 - 15)²/15 + (15 - 15)²/15 + (10 - 15)²/15 + (15 - 15)²/15
= 1.33
Determine the p-value:
The p-value fοr the calculated test statistic is 0.72.
Make a decisiοn:
Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.
In cοnclusiοn, based οn the chi-squared gοοdness οf fit test, we cannοt reject the null hypοthesis that the number οf resignatiοns is unifοrm οver the fοur seasοns.
To know more about Frequency visit:
brainly.com/question/30053506
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