Answer:
$ 546.00
Step-by-step explanation:
Simple Interest = P x r x t
where t = number of years
r = interest rate per year as a decimal
P = amount invested(deposit)
We are given that r = 7.8% per year = 7,8/100 = 0.078
However, since this is the yearly interest, the monthly interest = 0.078/12
The time period is 42 months
Initial deposit = $2,000
Therefore interest
I = 2000x (0.078/12) x 42 = $ 546.00
Answer the following questions
The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;
(a) 5·x + 3·y = 10
2·x + 6·y = 10
(b) Length of each Plan A workout: 1.25 hours
Length of each Plan B workout: 1.25 hours
What are linear system of equations?A linear system of equation consists of two or more linear equations that share common variables.
(a) The number of Plan A workouts Mary trained on Wednesday = 5
Number of Plan B workouts she trained on Wednesday = 3
The total time (in hours) Mary trained both workouts on Wednesday = 10
Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;
5·x + 3·y = 10
Similarly, the number of Plan A workouts trained on Thursday = 2
Number of Plan B workout trained on Thursday = 6
The duration of training of all workouts on Thursday = 10 hours
Therefore, we get;
2·x + 6·y = 10
The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;
5·x + 3·y = 102·x + 6·y = 10(b) The first equation from the system of equations indicates that we get;
5·x + 3·y = 10
3·y = 10 - 5·x
y = (10 - 5·x)/3Plugging the value of y above into the second equation from the system of equations, we get;
2·x + 6·y = 10
2·x + 6 × ((10 - 5·x)/3) = 10
2·x + 2·(10 - 5·x) = 10
2·x + 20 - 10·x = 10
20 - 8·x = 10
8·x = 20 - 10 = 10
x = 10/8 = 1.25
The length of each Plan A workout, x = 1.25 hoursy = (10 - 5·x)/3,
x = 1.25, therefore;
y = (10 - 5 × 1.25)/3 = 1.25
y = 1.25
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In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
The statements are (a) False, (b) True and (c) False
What are Right Angles?Right angles are angles whose measure is 90 degrees.
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
(a) ∠AHB and ∠AHG are vertical angles.
Vertical angles are angles which are formed on the opposite sides of two intersecting lines.
∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.
So the statement is false.
(b) ∠EHF and ∠DHE are adjacent angles.
∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.
So the statement is true.
(c) The measure of ∠FHG is equal to the measure ∠DHF.
We know that DG is a straight line.
∠FHG and ∠DHF are linear pair of angles.
So, ∠FHG + ∠DHF = 180°
Given that ∠FHG is right angle.
90° + ∠DHF = 180°
∠DHF = 180° - 90°
∠DHF = 90°
So the statement is true.
Hence the statements (a), (b) and (c) are false, true and true respectively.
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Your question is incomplete. The complete question with the figure is given below.
The table shows the total numbers of visitors to a website t days after it is online.
a. Determine wether the table represents an exponential growth function, an exponential decay function, or neither.
b. How many people will have visited the website after it is online 47 days? Round to the nearest whole number.
a) The table represents an exponential growth function.
b) The number of people that will have visited the website after 47 days online is given as follows: 17,716 people.
How to model the exponential function?An exponential function is modeled as follows:
y = a(b)^x.
In which:
a is the initial value.b is the rate of change.The parameters for this problem are given as follows:
a = 11000.b = 12100/11000 = 1.1. > 1 -> exponential growth.Considering that the reference day is the day 42, the function is defined as follows:
y = 11000(1.1)^(x - 42).
Hence, after day 47, the number of visitors is given as follows:
y = 11000 x (1.1)^5.
y = 17,716.
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Graph h(x)=−x2+3.
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.
A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.
The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.
To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:
h(-2) = -(-2)^2 + 3
h(-2) = 4 + 3
h(-2) = 7
So the point (-2, 7) is also on the parabola.
With the vertex and one other point on the parabola, you can now graph the parabola.
Step-by-step explanation:
The triangle below is equilateral. Find the length of side � x in simplest radical form with a rational denominator. x 6
The length of the side is 12 units in simplest radical form with a rational denominator.
What is an equilateral triangle?A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.
Given:
The triangle given in the image is an equilateral triangle.
That means the angle measure of the triangle is 60° each.
And all the sides are equal.
To find the value of x:
Sin(60/2)° = opposite/ hypotenuse.
Sin30° = x/6
x = 6/Sin30°
[tex]x = \frac{6}{1/2}[/tex]
x = 6(2)
x = 12
Therefore, the value of x is 12 units.
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The complete question:
The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.
The image is given below.
HELPPPP PLS I NEED HELP
According to the given information the lateral surface area of given cylinder is 725.34 in².
What can you say about a cylinder?In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.
What three qualities does a cylinder have?A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.
As we know that the lateral surface area of cylinder (A) = 2πrh
Given
D = [tex]16\frac{1}{2}[/tex]in
h = 14in
r = D/2
= 33/4 in
A = (2 × 3.14 × 33 × 14) / 4
= 2901.36 /4
= 725.34 in²
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Please solve quickly thanks
Answer:
Step-by-step explanation:
I believe that you put the right answer in.
The temperatures, in °C , at midnight on 10 consecutive days were 4, 1, 0, –2, –1, –3, 1, –2, 3, –1. (a) Find the difference between the highest and the lowest temperature
Answer:
7 degrees C
Step-by-step explanation:
To solve this question, we can start by ordering the temperatures from least to greatest:
4, 1, 0, -2, -1, -3, 1, -2, 3, -1 --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4
the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:
4-(-3) = 4+3=7
The difference is 7 degrees C.
If the percentage increase between 2017 of 9,640,000 and 2018 of 9,960,000 continued in 2018 and 2019 , how many households would be there be in 2019 ? Round to the nearest ten thousand
Answer:
Step-by-step explanation:
To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:
(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%
So, the number of households increased by 3.125% from 2017 to 2018.
To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:
9960,000 * (3.125 / 100) + 9960,000 = 10,298,800
Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.
Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). If necessary, round to three decimal places
The statistical measurement known as the Z-score describes the connection between a value and the mean of a set of values and the required z-score to the three decimal places is −2.714.
What is the z-score?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score.
Standard deviations from the mean are used to measure Z-score.
A Z-score of zero means the data point's score is the same as the mean score.
Your observed value is 2.5 standard deviations from the mean if your Z-score is 2.5, and so on.
Your value is more closely aligned with the mean the closer your Z-score is to zero.
Your value is further from the mean the farther your Z-score is from zero.
So, let's say Rosetta wins the game on Thursday with 110 points.
When x=110, the z-score is -2.714.
The average is 148.
You can see from this z-score that x=110 is 2.714 standard deviations away from the mean.
This formula can be used to determine the z-score:
z = x−μ/σ
=110−148/14
=−38/14
≈−2.714
Therefore, the required z-score to the three decimal places is −2.714.
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Based on the scatter plot above, which three statements are true?
A
The graph shows a positive association.
B
The graph shows a negative association.
C
As the cost of a t-shirt increases, the # of t-shirts sold increases.
D
As the cost of a t-shirt increases, the # of t-shirts sold decreases.
E
There is a linear association shown.
F
There is a nonlinear association shown.
G
There is no correlation shown on the scatter plot.
The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.
What is a nonlinear?A nonlinear system is one in mathematics and science where the change in the output is not proportional to the change in the input. Since the majority of systems are fundamentally nonlinear, engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems. A nonlinear equation is one in which the highest degree of any term is two or more. For instance, 3x2. + 2x + 1 = 0, 3x + 4y = 5, is an example of a nonlinear equation since equation 1 has the greatest degree of 2, while equation 2 involves variables x and y. Anything connected to a line is considered linear. To construct a line, one uses all of the linear equations. Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.To learn more about nonlinear refer to:
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The shape of the distribution of the number of clase friends for the males is best characterized as
The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).
What are shapes called in math?Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza
What are the basic shapes?The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.
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graph the inequality p < -8.
Answer:
I have graphed it and attached an image in the explanation part.
Step-by-step explanation:
Question 5b
A trailer truck carries 11, 430 bottles, each weighing 14 ounces. To the nearest ton,
how much weight does the truck carry?
The truck carries
tons.
The total weight of the bottles the truck carries is 6020 ounces.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
2 + 1x + 4y = 7 is an expression.
3 + 3x + 3 = 7 is an expression.
We have,
Number of bottles the truck carries = 430
One bottle weight = 14 ounces
Now,
The total weight of the bottles.
= Number of bottles x Weight of one bottle
= 430 x 14
= 6020 ounces
Thus,
The total weight of the bottles the truck carries is 6020 ounces.
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LMNO is a parallelogram. If NM = x + 37 and OL = 5x + 9 find the value of x.
The value for the variable x in the parallelogram is equal to 7.
How to evaluate for the variable x in the parallelogramThe parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.
We shall evaluate for variable x as follows:
5x + 9 = x + 37
5x - x = 37 - 9 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7
Therefore, the value for the variable x in the parallelogram is equal to 7.
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The value of the variable x is 7
How to determine the valueIt is important to note that the opposite sides of a parallelogram are congruent or equal in length.
Then, for the parallelogram LMNO
NM is parallel to OL
Now, substitute the values, we get;
NM = OL
x + 37 = 5x + 9
collect like terms
x - 5x = 9 - 37
subtract the like terms
-4x = -28
Make 'x' the subject
x = 7
Hence, the value is 7
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10. Susan has $800 in her bank account. Every week, she withdraws $100 for spending money.
A) What is the rate of change (or slope) in this situation?
B)
How much will she have left in her account after five weeks?
A) The rate of change in this situation is -$100 per week.
B) She will have $300 left in her account after five weeks.
Use the formula d= vt + 16t2, where d is the distance in feet, v is the initial velocity in feet per second, and it is the time in seconds.
An object is released from the top of a building 480 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
Answer:
5 seconds
Step-by-step explanation:
d = vt + 16t² , that is
vt + 16t² = d
substitute d = 480, v = 16 into the equation
16t + 16t² = 480 ( divide through by 16 )
t + t² = 30 ( subtract 30 from both sides )
t² + t - 30 = 0 ← in standard form
(t + 6)(t - 5) = 0 ← in factored form
equate each factor to zero and solve for t
t + 6 = 0 ⇒ t = - 6
t - 5 = 0 ⇒ t = 5
t > 0 , then t = 5
the object will hit the ground 5 seconds later
Answer:
5 seconds.-------------------------
As per given we have:
d = 480 ft,v = 16 ft/s.Substitute these into given equation and solve for t:
480 = 16t + 16t²30 = t + t²t² + t - 30 = 0t² + 6t - 5t - 30 = 0t(t + 6) - 5(t + 6) = 0(t + 6)(t - 5) = 0t + 6 = 0 or t - 5 = 0t = - 6 or t = 5The first value of t is discarded as time can't be negative, so the answer is 5 seconds.
Of the 125 persons applying for a certain job at data processing center,79 had previous work experience and 62 had college degree, while 38 has both work experience and college degree.
i)How many applicants did not have college degree
ii)how many applicants did not have experience
iii) how many applicants had college degree but no experience
iv)how many applicants had either college degree or experience but not both
1. the number ( of people without college degree ) = 125 - (24 +38)= 63
2. number of people without experience ) = 125- ( 41+38) = 46
3. number ( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
number of people that have previous work experience only) = 79-38 = 41
number ( of persons that have college degree only) = 62- 38 = 24
1. the n( of people without college degree ) = 125 - (24 +38)= 63
2. n( of people without experience ) = 125- ( 41+38) = 46
3. n( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
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DUE TODAY PLS I JUST NEED HELP
Answer:
(a)
smaller value = 125 ft
larger value = 250 ft
(b)
31250 ft²
Step-by-step explanation:
(a)
In total, the farmer used 875ft worth of fencing.
In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x
This means 7x=875ft. Dividing both sides by 7, we find x=125ft
The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".
(b)
Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:
125ft * 250ft = 31250 ft²
Answer:
(a)
smaller value =125 ft
larger value = 250 ft
(b)
31250 ft?
i need help on this pleaseee!!
The value of each variable in the quadrilateral can be found such that :
y = 73 degrees z = 101 degrees How to find the value of the variables ?Angle 107 degrees and z degrees will add up to 180 degrees which means that the value of z is:
= 180 - 107
= 73 degrees
Using this value of z as 73 degrees, we can then solve for y because the sum of the interior angles of a quadrilateral need to add up to 360 degrees.
The value of y variable is therefore:
= 360 - 83 - 103 - 73
= 101 degrees
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity…..
the displacement is 23.14m and the velocity is 21.28m/s
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The given equation y = 25t - 1.86t²
at t = 1
So the displacement y = 25-1.86 = 23.14
to find velocity dy/dt = 25- 2(1.86)t
v = 25 - 3.72 = 21.28m/s
Hence the displacement is 23.14m and velocity is 21.28m/s
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Use calculator to find 61.6 to the nearest hundredth
Answer : 61.60
Step-by-step explanation:
Answer:61.60
Step-by-step explanation:
i just typed it in
the table shows the rate at which justin can make widgets. how many widgets can justin make in 36 minutes?
The number of widgets that Justin can make in 36 minutes is given as follows:
y = 36k.
In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: number of minutes.Output y: number of widgets.The constant is obtained as follows:
k = y/x.
For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:
y = 36k.
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please help question below
Answer:
Step-by-step explanation:
22
The square root of a number is greater than the square of the number. For what set of numbers is this true?.
The set of numbers for which the statement that the square root of a number is greater than the square of the number is true, is equals to (0,1). So, right choice is option (a).
In mathematics, when we multiplying the number by itself, the result is called square of number. This is usually equivalent to raising a number to the power of 2. For example, square of 4 is 4² = 16. The square root of a number is that factor of a number which when multiplied by itself the original number. Square root of number is usually equivalent to raising a number to the power of 1/2. It is represented using the symbol '√'. Now, we have to check the options and determine where square root of a number is greater than the square of the number.
a) (0, 1), if we plug f(x) = √x , x∈(0,1) and g(x) = x² , x∈(0,1) on calculator then we get, the value of f(x) is greater than g(x), i.e, x = 1/2 , f(1/2) = 0.70 and g(1/2) = 0.25.
b) [0, 1], if we plug x = 0 then f(0) = 0 , g(0) = 0
that is f(x) is greater than and equal to g(x). But we have to consider only greater than not equal.
c) [1,∞), closed bracket again represents equality which is not consider. So, statement is false for it.
d) (1,∞), here number inbetween 1 and infinite but not for all reals it is true that square root of a number is greater than the square of the number, for example x = 2 , f(2) =1.414, g( 2) = 4 implies f(x)< g(x) for x = 2. So, the statement is false for it.
Hence, required option is option (a).
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Complete question :
The square root of a number is greater than the square of the number. For what set of numbers is this true?
a) (0, 1)
b) [0, 1]
c) [1, ∞ )
d) (1,∞)
You can work a total of no more than 32 hours each week at your two jobs. Tutoring pays $7 per hour and babysitting pays $8 per hour. You need to earn at least $256 each week to pay your bills.
Let X = the number of hours tutoring. Let Y = the number of hours babysitting
Answer: The correct system of linear inequalities that represents this situation is:
X + Y ≤ 32 (to represent the maximum number of hours you can work)
7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)
X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)
Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.
Step-by-step explanation:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040. Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
The average hourly wage for police officers is $30.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.
In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.
Assume that police officers generally work 40 hours a week.
There are 52 weeks in the year.
The average hourly wage for police officers is,
= 62040 ÷ (52 x 40)
= 62040 / 2080
= 29.8
≈ $30
Therefore, $30 is the hourly wage.
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Square ABCD has diagonal AC with vertices A(1, 1) and C(3, — 1). Find the coordinates of the
remaining vertices.
The coordinates are
Answer:
The coordinates of the remaining vertices are (1, -1) and (3, 1).
Step-by-step explanation:
A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles. Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.
If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:
[tex](x_A, y_C)=(1,-1)[/tex][tex](x_C, y_A)=(3,1)[/tex]gerry's drawer has two black socks and 4 blue socks. if he selects two socks without looking what is the probability that both socks are black
Find echelon form of this augmented matrix written so 1's on the diagonal
1 -1 2 400
1 0 0 900
1 -3 7 -300
The echelon form of the given augmented matrix with 1's on the diagonal is:
1 -1 0 1000
0 1 0 1100
0 0 1 300
What is the echelon form of this matrixTo find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:
Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:
1 -1 2 400
0 1 -2 500
0 -2 5 -700
Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:
1 -1 2 400
0 1 -2 500
0 0 1 300
Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:
1 -1 0 1000
0 1 0 1100
0 0 1 300
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