Simple interest analysis reveals that
a) The installment was $321.53 per month.
b) The total amount of the payments is $11,575.
c) Interest was paid of $1,575.
How to find the Calculation?After t years, the amount of simple interest is calculated using:
A(t) = p(1 + rt)
that where:
The initial deposit is known as the primary, or P.
The interest rate in decimal form is r.
In this issue:
Hence, a $10,000 loan.
APR of 5.25%, which equals 3 years, therefore
Item c:
The result is A(3), so:
A(t) = P( 1 + rt)
A(3) = 10000[ 1 + 0.0525(3)]
A(3) = 11575
The total amount of the monthly installments is $11,575.
Item d:
I = A(3) - P = 11575 - 10000 = 1575
When interest is calculated, the principal is removed, so:
Interest was paid of $1,575.
Item b:
36 payments were made over a period of 3 years, or 3 x 12 months.
Item a:
11575/3 = 321.53
The amount due each month was $321.53.
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Decide whether each equation is true for all, one, or no values of x.
The description of each equation in comparison with its' right hand side is;
A) True for all values of x.
B) True for no values of x.
C) True for no values of x.
D) True for no values of x.
E) True for all values of x.
F) True for no values of x.
G) True for no values of x.
H) True for all values of x.
How to solve Linear equations?
A) We are given the equation;
7x - 5
This can also be written as; -5 + 7x and so the right hand side is true.
B) We are given the equation as 5x - 7.
There is no 4 in the equation and so the right hand side is wrong.
C) We are given the equation as -3x + 5.
The coefficient of x is -3 and not -4 and so the right hand side is wrong.
D) We are given the equation as;
3x - 32 + 4(4x - 2463)
By basic inspection, the right hand side cannot be true because we can see a very huge value in this bracket.
E) We are given the equation as 7x - 9 + 3(6x + 3)
Expanding the bracket gives;
7x - 9 + 18x + 9 = 25x
Thus, the right hand side is correct.
F) We are given the equation as 3x + 9
The equation does not contain -4 and 20 and so the right hand side is wrong.
G) We are given the equation as 10(2x - 3)
Multiplying the bracket gives 20x - 30. Thus, the right hand side is wrong
H) We are given the equation as 4(4x + 3) - 3x
Multiplying out the bracket gives us;
16x + 12 - 3x = 13x + 12
Thus, the right hand side is correct.
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Write 3/4 in simplest form a decimal and percent
Answer:
1/ In decimal, 3/4 is 0.75
2/ In percent, 3/4 is 75%
Step-by-step explanation:
1/ take 3 divided by 4, and you will get 0.75 as an answer for decimal
2/ For percent, 3/4 is simple for of 75%/100%
a sports analyst claims that the mean batting average for teams in the american league is not equal to the mean batting average for teams in the national league because a pitcher does not bat in the american league. what hypothesis test would be used to test that batting average for teams in the american league is not equal to the batting average in the national league?
Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.
As given in the question,
Given : Mean batting for American league is not equal to Mean batting for National league.
Here two teams are given representing sample size of the population.Hypothesis tests help us to make decisions or conclusion about the value of the given parameters, such as the population mean. Based on it two approaches are used for conducting a hypothesis test one is the critical value and the P-value test.If in the given data population standard deviation (σ) can be calculated, a hypothesis test used for one population mean is z-test. A z-test represents the hypothesis test which is used to test a population mean, μ, against a considered population mean, μ₀.Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.
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The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3,300 every night to cover all expenses. Let d represent the number of adult tickets sold at $7.50. Let s represent the number of student tickets sold at $4.50 each. If all 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3,300? At one performance there were two times as many student tickets sold as adult tickets. If there were 360 tickets sold at that performance, how much below the goal of $3,300 did ticket sales fall??
By using simultaneous linear equation, it can be calculated that-
200 adult tickets and 400 student tickets were sold
In another performance, ticket sale falls $1320 below the goal of $3300
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a simultaneous linear equation needs to be solved
Here, d represents the number of adult tickets and s represents the number of student tickets
Their auditorium holds 600 people
d + s = 600 ..... (1)
Price of adult ticket = $7.50
Price of student ticket = $4.50
Total price = $(7.50d + 4.50s)
By the problem,
7.50d + 4.50s = 3300
5d + 3s = 2200 ..... (2)
Multiplying (1) by 3
3d + 3s = 1800.... (3)
Subtracting (3) from (2)
2d = 400
[tex]d = \frac{400}{2}[/tex]
d = 200
Putting the value of d in (1)
200 + s = 600
s = 600 - 200
s = 400
Now,
At one performance there were two times as many student tickets sold as adult tickets.
Total tickets sold = d + 2d = 3d
By the problem-
3d = 360
d = [tex]\frac{360}{3}[/tex]
d = 120
s = 2 [tex]\times[/tex] 120 = 240
Number of student ticket sold = 240
Number of adult ticket sold = 120
Total cost = 240 [tex]\times[/tex] 4.50 + 120 [tex]\times[/tex] 7.50
= $1980
Fall in ticket sale = $(3300 - 1980) = $1320
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373646351636646475753626266374747574884x848484893990299149440505944330309877=?
Answer: 1
Step-by-step explanation:
Answer:
totally not confused whatso ever
Step-by-step explanation:
45 points pls help
In the equation y=mx +b
What is the meaning of the M and the b. Explain in your own words what kind of thinking are you engaged in
In the equation y = mx + b, the meaning of the m and the b is
m is the slopeb is the y interceptWhat is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + b
How to determine the meaning of m and bInformation gotten from the question include
In the equation y = mx + b
m = ? and b = ?
y = mx + b
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
b = y intercept
therefore m and b are the slope and y intercept respectively
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help pls explain!!!!!!!!!!!!
The value of the given logarithmic expression is -142.20.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the logarithmic values as,
log₃ (t) = 5.44
log₃ (y) = 11.03
log₃ (z) = 7.74
Now, the value of the expression can be written as,
12 log₃ (z⁷ / y⁵t²)
= 12 { log₃ (z⁷) - [ log₃ (y⁵) + log₃ (t²) ] }
= 12 { 7log₃ (z) - [ 5log₃ (y) + 2log₃ (t) ] }
= 12 [7×7.74 - (5×11.03 + 2×5.44)]
= 12 [ 54.18 - (55.15 + 10.88)]
= 12(54.18-66.03)
= 12 × (-11.85)
= -142.20
Hence, the value of the given expression is -142.20.
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Which table represents a function? Choose all that apply.
Hint: there are 3 correct answers
Answer:a,b,c
Step-by-step explanation:easy work just trust me
The vertex is always the highest point of a function.
True false question.
True
False
Answer:
False!
Step-by-step explanation:
See picture for examples.
if F,B, and D are midpoints of EC, AC, and AR respectively, then …
The lengths of the parts of the median lines FA, BE, CD, that extends from the vertices of the triangle ΔACE to the midpoints of the sides EC, AE, and AC are;
A. G is called the centroid of the triangle ΔACE
B. G is also the center of gravity of a uniform density triangle. The correct option is True; T
C. GF = 5
D. DC = 18
E. GB = 7
What is a median of a triangle?A median of a triangle is a line segment that extends from a vertex of a triangle to the midpoint of the side opposite the vertex
The midpoints of the sides of the triangle = F, B, and D
The midpoint of EC = F
The midpoint of AC = B
Midpoint of AE = D
A. The lines CD, BE, and FA are called median lines
The point of intersection of the three median lines of a triangle is the centroid of the triangle.
The point G is called the centroid of the triangleB. The centroid of a triangle and center of gravity of the triangle are located at the same position in a uniformly dense triangle, therefore, G is the center of gravity, True, T
C. In the relationship of a median, we get;
AG = (2/3)·FA
GF = (1/3)·FA
Therefore, AG = 2·(GF)
GF = 0.5 × AG
GF = 0.5 × 10 = 5
GF = 5
D. DG = (1/3) × DC
Therefore; DC = 3 × DG
DG = 6, therefore, DC = 3 × 6 = 18
DC = 18
E. EB = 21
GB = (1/3) × EB
Therefore; GB = (1/3) × 21 = 7
GB = 7
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You are designing a rectangular poster to contain 48 in^2 of printing with a 3-in margin at the top and bottom and a 1-in margin at each side. What overall dimensions will minimize the amount of paper used?
To minimize the amount of paper used to create a rectangular poster with a given amount of printing and specific margins, you can use the formula for the area of a rectangle to determine the dimensions that will minimize the area of the poster.
In this case, the area of the poster must be at least 48 square inches to contain the printing, and the margins at the top and bottom must be 3 inches each, for a total of 6 inches. The margins at the sides must be 1 inch each, for a total of 2 inches. Therefore, the minimum area of the poster is 48 + 6 + 2 = 56 square inches.
To minimize the amount of paper used, we want to find the dimensions of the poster that will have the smallest possible area while still satisfying the constraints on the margins and the amount of printing. We can do this by using the formula for the area of a rectangle:
A = lw
where A is the area of the rectangle, l is the length, and w is the width.
In this case, we want to find the length and width that will minimize the area of the rectangle while still satisfying the constraints on the margins and the amount of printing. We can do this by setting the area of the rectangle equal to the minimum area we calculated above (56 square inches) and then solving for the length and width:
A = lw = 56
lw = 56
We can then use the constraints
Lines c and d are parallel lines cut by transversal p.
Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.
∠2 is congruent to ∠6 based on corresponding angle theorem.
What is corresponding angle theorem?Corresponding angles are formed when two parallel lines are intersected by a transversal line.The corresponding angles theorem states that "when a line intersects two parallel lines, the corresponding angles in the two regions of intersection are congruent."Assume that A, B, and C are distinct lines. Then A and B are parallel if and only if the corresponding angles of intersection of A and C, as well as B and Care, are equal.So here ,
Since in this question they are corresponding angles of parallel lines cut by a transversal, they are ∠2 ≅ ∠6 according to the Vertical Angles Theorem.
The complete question is : "Lines c and d are parallel lines cut by transversal p. Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8. Which must be true by the corresponding angles theorem?"
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Find the point where the line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39
The plane 13x + 11y + 20z = 39 is where the line x = t, y = 1 + t, and z = 1 t cross (2,3,-1).
What is plane?A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions. In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used.
Here,
13t+11(1+t)+20(1-t)=39
13t+11+11t+20-20t=39
4t+31=39
4t=8
t=2
x=2, y=3, z=-1
The line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39 at (2,3,-1).
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A kite flys in the air has an 11-ft line attached to it. It line pulled cast a 10ft shadow. Find the height of the kite. If necessary
Answer:
Step-by-step explanation:
Due to the cast of the shadow regardless of that the line will still be 11 feet due to the lines length
A project calls for a 50 in. long board to be cut into three pieces. The first piece must be twice the length of the second piece. The third piece is 10 in. shorter than the second piece. How long must each piece be?
Answer:
Step-by-step explanation:
la première planche = 2x
la deuxième = x
la troisième = x-10
1ere planche + 2eme planche + 3eme planche = 50 pouces
donc :
(2x) + x + (x-10) =50
4x-10 = 50
4x-10+10 = 50 +10
4x = 60
4x diviser par 4 = 60 diviser par 4
x=15
la première planche = 30
la deuxième = 15
la troisième = 5
30+15+5=50
Please someone help me I need help
Answer:
Yes
Step-by-step explanation:
Since the point is in the intersection area (purple) of the lines it is a solution.
a quadratic equation can be written in vertex form or in standard form sometimes one form is more beneficial than the other Identify which form would be more helpful if you needed to do each task listed below and explain why. A .factor the equation. B graph the parabola.C identify the vertex minimum or maximum of the parabola D and solve the equation using the quadratic formula
a. In order to factor the equation, the vertex form needs to be expanded to the standard form first, to obtain the factors of the equation
b. The parabola is easily graphed with the information on the vertex given in the vertex form of the quadratic equation
c. The vertex, minimum or maximum of the parabola are easily obtained in the vertex form of the quadratic equation
d. The quadratic formula is defined based on the standard form of the quadratic equation
Answer:
[tex]\huge{\boxed{\text{A) Standard form}}}\\\huge{\boxed{\text{B) Vertex Form}}}\\\huge{\boxed{\text{C) Vertex Form}}}\\\huge{\boxed{\text{D) Standard Form}}}\\[/tex]
Step-by-step explanation:
Vertex form is represented as: [tex]f(x) = a(x-h)^2+k[/tex], where the vertex of the parabola is (h, k).
Standard form is represented as [tex]f(x) = ax^2+bx+c[/tex], where a, b, and c are constants.
A) When factoring an equation, the sum of the roots is equal to b and the sum of the roots is equal to c, meaning standard form is the beneficial.
B) When graphing a parabola, vertex form is extremely beneficial, as it provides the vertex of the parabola, and the direction in which it opens. If "a" is positive, the vertex opens upward, while when "a" is negative, the vertex opens downward. As such, graphing is greatly eased with this information.
C) As is evident from the name, vertex form is the best for identifying the vertex of a parabola, as it is explicitly shown via the constants h and k.
D) The quadratic formula directly uses the constants a, b, and c, so working in standard form is more beneficial, as it removes the effort of solving for each constant.
Hope it helps :) and let me know if you want me to elaborate.
The question is linked below, please respond asap its due really soon
The Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.
Define Domain and Range
The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. Domain = the set of all x-coordinates Range = the set of all y-coordinates The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range.Given expression is,
f(x) = -1/4x³ + 4x - 3
In this x ∈ R, so
Domain = (-∞,∞) , { x|x ∈ R }
Range = (-∞,∞) ,{ y|y ∈ R }
Hence, the Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.
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Plot the point on this function with an x-value of 6.
What is the y-value of this point?
Answer:
7
Step-by-step explanation:
Answer:7
Step-by-step explanation:
Go to 6 on the x value and then follow that line up until you reach the purple line. Then go to the left and see what the y vaule is(Height)
The triangle has a perimeter of 65 feet. What are the lengths of sides l,m,
and n
The system of equations that represents this situation is 65= _________?
Answer:
65 = l + m + n
Step-by-step explanation:
The perimeter of a triangle is the sum of its 3 sides:
65 = l + m + n
Rewrite the following equation in slope-intercept form. y − 9 = –10(x − 10)
Answer:
y = -10x + 109
Step-by-step explanation:
Given equation,
→ y - 9 = -10(x - 10)
The slope-intercept form is,
→ y = mx + b
Rewrite in slope-intercept form,
→ y = mx + b
→ y - 9 = -10(x - 10)
→ y - 9 = -10x + 100
→ y = -10x + 100 + 9
→ [ y = -10x + 109 ]
Hence, answer is y = -10x + 109.
i pray for help i hope someone see this
Answer:
Step-by-step explanation: Step one is distributive property because you distribute the numbers inside the parenthesis. Step 2 is communitive property because you switch the order. Step 3 is conbine-like terms. Step 4 is the addition property of equality. Step 5 is the division property of equality. Hope this helps!
what is the equation of the line that passes through the point(-6,-7) and has a slope of 1/3
Answer:
The equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:
x - 3y + 15 = 0
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
To find the equation of the line that passes through the point (-6, -7) and has a slope of 1/3, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
Plugging in the given values, we have:
y - (-7) = (1/3)(x - (-6))
Which simplifies to:
y + 7 = (1/3)x + 2
Multiplying both sides by 3, we have:
3y + 21 = x + 6
Subtracting 21 and 6 from both sides, we have:
3y - x - 15 = 0
Therefore, the equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:
x - 3y + 15 = 0
A drone is flying over a
baseball field, directly between
first and second base. The angle
of elevation from first and second
base to the drone is 77° 9' and
65° 45' 18", respectively.
If the bases are 90 feet apart,
find the height of the drone.
The height of the drone would be about 132.92 feet.
What is a tangent ratio in trigonometry?
The tangent ratio is the ratio of the opposite side to the adjacent side of a right triangle. Same to the sine and cosine ratios, tangent ratios can be used to calculate the angles and sides of right-angle triangles.
Given that the angle of elevation from the first and second base to the drone is 77° 9' and 65° 45' 18", respectively.
[tex]77^o9'=77\frac{9}{60}=77.15^o[/tex]
[tex]65^o 45' 18"=65+\frac{45}{60}+\frac{18}{3600}\\\\65^o 45' 18"=65.755^o[/tex]
tan 77°9 = h/AD and tan 65.75°=h/DB
AD + DB = 90
h/tan 77°9 + h/65.75° = 90
Solving this we get
h ≈ 132.92 feet.
Hence, the height of the drone would be about 132.92 feet.
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It costs £5.33 for 650g of beef steak. What is the price per kg?
Answer: 8.20
Step-by-step explanation:
1kg = 1000g
take 650 divided by 1000 = 0.65kg
Then take 5.33 divided by 0.65 = 8.20
What is the sampling method that involves taking a random selection of people from a defined population?.
Simple random sampling is a sort of probability sampling in which a subset of participants from a population is randomly chosen by the researcher. There is an equal opportunity for selection for every person in the population. Then, information is gathered from as much of this random subset as is feasible.
What is simple random sampling, and why is it significant?
One technique researchers employ to select a sample from a broader population is a simple random sampling.
If there is an equal chance that any subject in a population will be chosen, this strategy is effective. In order to draw general conclusions about a group, researchers choose basic random sampling.
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Question 5 of 6Maximize the objective function P = 5x + 3y for the given constraints.
x ≥ 0
y ≥ 0
3x + 6y ≤ 48
2x + 8y ≤ 56
On solving the provided question, we got that - The maximized value of the objective function is 38
what is function?Relationships between a group of inputs and one output per input are referred to as functions. A function is, to put it simply, a connection between inputs that are all connected to the same output. There is a domain and a codomain, or scope, for every function.
Given is the objective function:
Max P = 5x + 3y
The following are the constraints:
3x + 6y ≤ 48
2x + 8y ≤ 56 \sx ≥ 0 y ≥ 0
We employ the graphical method to achieve this.
The graph of the constraints is included as an attachment.
The graph leads us to the following doable point:
[tex](x,y) = (4,6)[/tex]
[tex]Substitute 4 for x and 6 for y in the objective function.\\Max P=5x+3y[/tex]
so,
[tex]P = 5x4+x6\\P = 38[/tex]
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I need help on this question.
Answer:
x=43
Step-by-step explanation:
Since the two interior angles of a triangle always add up to the exterior angle (d=a+b btw if u dont understand what i mean), x+90=133
x=133-90
x=43
a chemical engineer wants to compare the hardness of four blends of paint. six samples of each paint blend were applied to a piece of metal. the pieces of metal were cured. then each sample was measured for hardness. in order to test for the equality of means and to assess the differences between pairs of means, the analyst uses a one-way anova with multiple comparisons, finding a resulting f test statistic of 6.02 with a p-value of .034. what is the appropriate statistical conclusion?
The appropriate statistical conclusion is that there is sufficient evidence to conclude that the means are different.
How to interpret the test results?The null and the alternative hypothesis for this problem are given as follows:
Null hypothesis: means are equal.Alternative hypothesis: means are different.The p-value and the significance level for this problem are given as follows:
p-value: 0.034.Significance level: 0.05. (this is the standard when the significance level is not stated).As the p-value is less than the significance level, there is enough evidence to reject the null hypothesis, thus the appropriate statistical conclusion is that there is enough evidence to conclude that the means are different.
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Which of the following is approximately equal to the sum of the addition problem below?
8/9 + 9/10
A.
8/10
B.
1
C.
2
D.
1/2
Answer: 2
Step-by-step explanation:
[tex]\frac{8}{9} \approx 1\\\\\frac{9}{10} \approx 1\\\\\therefore \frac{8}{9}+\frac{9}{10} \approx 1+1=2[/tex]