Find the simple interest on $50,000 for 2 years at 7%
Answer:
$7,000
Explanation:
To find the simple interest on any principal, we use the formula:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]From the given question:
• Principal = $50,000
,• Rate= 7%
,• Time = 2 years
Therefore:
[tex]\begin{gathered} \text{Interest}=\frac{50,000\times7\times2}{100} \\ =\$7,000 \end{gathered}[/tex]The simple interest is $7,000.
help please
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample 50 of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
5 9 10 2 2 2 2 7 7 7 7 6 7
8 9 9 2 10 2 7 6 9 8 10 9 2
7 5 7 2 2 7 7 6 2 10 8 2 6
6 9 5 2 10 7 10 2 2 6 6
Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.
Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:
(4.29, 7.71).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the meaning of the parameters are:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:
[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Hence the lower bound of the interval is given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]
The upper bound of the interval is given by:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]
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Over the interval [0,2pi), what are the solutions to cos(2x)=cos(x)? Check all that apply.
Answer:
x = 0 and 2pi/3
Explanation
Given the expression
cos(2x)=cos(x)
In trigonometry expression;
cos2x = 2xos^2x - 1
Substituting into the equation given;
cos(2x)=cos(x)
2xos^2x - 1 = cos x
Rearrange
2xos^2x - 1 - cosx - 1 = 0
Let P = cosx
2P^2 - P - 1 = 0
Factorize
2P^2 - 2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P+1 = 0 and P-1 = 0
P = -1/2 and 1
Recall that P = cosx
-1/2 = cosx
x = cos^-1(-1/2)
x = 120 degrees = 2pi/3
If P = 1
cosx = 1
x = cos^-1(1)
x = 0
Hence the value of x that satisfies the equation is 0 ad 2pi/3
15
A principal needs to order 1,437 T-shirts for students at her school. She rounds to the nearest hundred
to estimate the number of T-shirts to order. Will there be enough T-shirts for all the students? Explain.
There will not be enough T-shirts for all the students
How to determine if the T-shirts will be enough?From the question, the given parameters are:
Number of T-shirt = 1437
From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred
When the number of T-shirts is approximated to the nearest hundred, we have
Approximation = 1400
By comparison, 1400 is less than 1437
This means that the T-shirts will not be enough
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given AC=XZ and AB=XY prove BC=YZ
Explain how knowing the linear factor establishes that f(10) multiple of 12.
f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10
f(10) multiple of 12 is given as:
The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.
f(10) = (10+2)(100+20+2)
= (12)(122)
= 1220+244
= 1464
Hence, f(10) is a multiple of 12
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Keandre wants to buy a new pair of shoes that costs $220. In order to earn money for this, Keandre babysits his neighbor for $10 an hour. He also has saved up his monthly allowance which totals $50. What is the minimum number of hours he should babysit in order to be able to afford the shoes?
Answer:
Step-by-step explanation:
$220=$10x+$50
x= hours
subtract $50 from both sides making sure to cancel the right side
$220-$50=$10x
$170=$10x
Divide both sides by $10 to leaving x by itself on the right side
$170/$10=x
17hrs=x
The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Cost of new pair of shoes = $220
In order to earn money for this, Keandre babysits his neighbor for $10 an hour.
And, He also has saved up his monthly allowance which totals $50.
Now,
Let number of minimum hours = x hour
So, We can formulate;
⇒ $10x + $50 = $220
Solve for x as;
⇒ $10x + $50 = $220
Subtract 50 both side, we get;
⇒ $10x + $50 - $50 = $220 - $50
⇒ $10x = $170
Divide by 10 both side, we get;
⇒x = 17
Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
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Translate the sentence into an equation. Use the variable w for the unknown number.Two times the sum of a number and 7 equals 6.
we have that
Two times the sum of a number and 7 -----> 2(w+7)
Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6
the answer is
2(w+7)=6Multiply. Write your answer in scientific notation.
2.(4 × 10³)
help meeeeeee pleaseee !!!!
The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:
y = -5*x + 3
How to find the linear function?We can find a general linear function in the slope-intercept form as:
y = m*x + k
Where m is the slope and k is the intercept of the y-axis.
If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:
m = (-7 - 18)/(2 + 3) = -5
So the line is something like:
y = -5*x + k
To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:
-7 = -5*2 + k
-7 = -10 + k
-7 + 10 = k
3 = k
So the linear function is:
y = -5*x + 3
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A cricket pitch measures $1$ chain by $10$ feet. What is the area of a cricket pitch in square feet?
(Useful information: there are $3$ feet in a yard, and there are $22$ yards in a chain.)
Area of the cricket pitch is 660 square feet
Given
1 chain is equal to 10 feet
There are 3 feet in a yard
And 22 yards in a chain
Hence it is evident that
One chain is equal to 22 x 3
1 chain = 66 Feet
Area of a rectangle is Length x Width
Length = 66
Width = 10
Hence Area = 66 x 10
Area = 660 Square feet
Hence area of the cricket pitch is 660 square feet.
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a standard number cube number 1 through 6 on east side is rolled 3 times what is the probability of rolling a 2 on all three rolls express your answer as a fraction
the probability of getting a 2 tree times is
[tex]\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{216}[/tex]The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1997 his card was worth $6.36. The value has increased by $1.93 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2007
?
Part a: The relationship between x and y can be represented as y = 6.36 + 1.93x
Part b: The relationship between x and y is proportional
Part c: The value of the card in 2007 will be $25.66
Worth of the card in 1997 = $6.36
Increase in value each year = $1.93
Let x be the number of years the player has been in retirement and y be the value of the cards in dollars
Formulating the equations we get the following:
Value of the card = Worth of the card in 1997 + Increase in value each year*Number of years the player has been in retirement
Part a:
y = 6.36 + 1.93x
Part b:
The relationship between x and y is proportional as the increase in the value each year leads to an increase in the worth of the card
Part c:
Value of the card in 2007:
The number of years the player has been retired will be 10 years in this case
Formulating the equation we get the following:
y = 6.36 + 1.93(10)
= 25.66
So, the value will be $25.66
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The sum of two whole numbers is 63. The difference between the numbers is less than 10. Find as many solutions
Answer:
hmmph..
(32, 31)
(33,30)
(34, 29)
(35, 28)
(36,27)
(37, 26)
Step-by-step explanation:
That all I got....
Your lunch in the hospital cafeteria cost $6.50. How much will you spend each week if you average spending $6.50 per meal every day for your five day work week?
Which two values of x are roots of the polynomial below?
4x² - 6x+1
A. x = -6-√52/16
B. x = 6+ √20/8
C. x = 6-√20/8
D. x = -8-√28/6
E. x = -8+ √28/6
F. x = -6 + √52/16
Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.
What in mathematics is a polynomial?
Sums of terms with the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.4x² - 6x+1 = 0
x = -b ± √b² - 4ac/2a
x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4
x = -( 6) ± √36 - 16/8
x = - 6 ± √20/8
So, roots are x = - 6 + √20/8 and x = - 6 - √20/8
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A square napkin has sides of length 8 inches. To the nearest inch, what is the length of the diagonal of the (1
napkin?
O8 inches
09 inches
O11 inches
O16 inches
The length of the diagonal of the napkin is 11 inches.
Here, we are given that a square napkin has a side of length 8 inches.
All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.
Thus, by using Pythagoras theorem, we can form the following equation-
[tex]side^{2} + side^{2} = diagonal^{2}[/tex]
Let the diagonal of the square be d. Then, we have-
[tex]8^{2} +8^{2} =d^{2}[/tex]
64 + 64 = [tex]d^{2}[/tex]
128 = [tex]d^{2}[/tex]
[tex]d^{2}[/tex] = 128
d = [tex]\sqrt{128}[/tex]
d = [tex]8\sqrt{2}[/tex]
the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,
d = 8 × 1.41
= 11.28
Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.
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12. In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. If mZTVQ = 5x - 22 and mZTVQ = 3x + 10, for which value of x is PQ parallel to RS? P_ R W A. 6 B. 16 C. 24 D. 28
ANSWER:
The value of x is 16
STEP-BY-STEP EXPLANATION:
With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.
Thanks to this we can make the following equality:
[tex]5x-22=3x+10[/tex]Solving for x:
[tex]\begin{gathered} 5x-3x=22+10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}[/tex]Answer:
16 is the answer
9y-(2y-3)=5(y-2)+2
Should equal ‘no solution’
[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]
ATTACHED IS THE SOLUTION OF Y
BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.
What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이
To complete the square, we want a number such that:
[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]because in this way we can writte the square as follows:
[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]Hence the answer is the last option:
[tex](\frac{7}{2})^2[/tex]write the following in the form a+bi (2+5) - (-6 +bi)
The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi
How to evaluate the expression?The expression is given as
(2+5) - (-6 +bi)
The above expression is a complex expression
So, we have the following expression
(2+5) - (-6 +bi)
Remove the brackets in the above expression
So, we have the following expression
(2+5) - (-6 +bi) = 2 + 5 + 6 - bi
Evaluate the like terms in the above equation
So, we have the following expression
(2+5) - (-6 +bi) = 13 - bi
Hence, the solution to the complex expression is 13 - bi
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A coin has 2 sides: heads (H) and tails (T). A bag has 3 balls: 1 red (R), 1 green (G), and 1 blue (B). You toss a coin and randomly pick a ball. What is the sample space?
The space sample is the total quantity of possible results
for each toss there are 3 possible results
so the total results are 2x 3 = 6
The only option with 6 elements is B
so the answer is B.
Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.
Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)
Answer:
slope would be 4/1
Step-by-step explanation:
its rise over run, so up 4 and out 1
have a good day!
I just need to make sure 1-9 are correct so if you could confirm please.9 b)
Given:
[tex]2x^2+3x+9=0[/tex]To find:
The roots.
Explanation:
Here,
[tex]\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}[/tex]Using the quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]On substitution we get,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{(3)^2-4(2)(9)}}{2(2)} \\ =\frac{-3\pm\sqrt{9-72}}{4} \\ =\frac{-3\pm\sqrt{-63}}{4} \\ =\frac{-3\pm3i\sqrt{7}}{4} \end{gathered}[/tex]Therefore, the solutions are,
[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]Final answer:
The solutions are,
[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]
I inserted a image of the question I’m very confused and need help with homework so I do good on test
To find the magnitude of a vector we use the following equation
[tex]\lvert\vec{v}\rvert=\sqrt[]{(v_x)^2+(v_y)^2}[/tex]This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:
In the case of your exercise, the values would be
[tex]\begin{gathered} v_x=x \\ v_y=y \\ \lvert\vec{v}\rvert=\sqrt[]{(x_{})^2+(y)^2} \end{gathered}[/tex]A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas, Houston, and San Antonio (see figure).
If the actual distance from San Antonio to Houston is approximately 192 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.
a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given that the actual distance from San Antonio to Houston is approximately 192 miles.
The scale factor from the map to the real world is;
(actual)/( map) = (192mi)/(3 in) = 64 mi/in
Then the actual distance from Dallas to Houston will be;
(3.75 in)(64 mi/in) = 0.058 mi
And from Dallas to San Antonio, the distance will be;
(4.125 in)(64 mi/in) = 0.064 mi
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The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
a. Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meet its goal.
b. List three different combinations of tickets sold that satisfy the inequalities.
The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)
How to graph the systemFrom the question, we have the following parameters that can be used to determine system of inequalities
An adult ticket = $15Student ticket = $11. Auditorium capacity = 300 ticket-holdersAmount from sales = at least $3630 from ticket sales.Represent the adult with y and the students with x
So, we have the following representations
x + y ≤ 300 ---- the ticket holders cannot exceed the capacity
11x + 15y ≥ 3630 --- the total sales cannot be less than $3630
x ≥ 0 -- the number of students cannot be negative
y ≥ 0 -- the number of students cannot be negative
Write out the inequalities
x + y ≤ 300
11x + 15y ≥ 3630
x ≥ 0
y ≥ 0
Next, we represent the inequalities on a graph
See attachment for the graph of the inequalities
The combinations from the graphTo get the combination, we make use of the coordinate points that are in the shaded region of the graph
Using the above as a guide, we have
(70, 200), (150, 140) and (140, 150)
There are other points too
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result step by step of this simple but yet hard for me exercise
Answer:
The anser is
Step-by-step explanation:
DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y
a line goes through the point (5, -7) and has slope m = -3. write the equation that represents the line.
We are given the following information
Slope of the line = m = -3
The line passes through the point (5, -7)
Recall that the equation of a line in the point-slope form is given by
[tex](y-y_1)=m(x_{}-x_1)[/tex]Where m is the slope and (x₁, y₁) is a point on the line.
Let us substitute the given values into the above equation
[tex]\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=-3x+8[/tex]