Answer:
Step-by-step explanation:
Assuming the interest rate remains constant throughout the 10-year period, Rajesh will have enough money in the account to cover all of the required loan payments. The total amount of money he will withdraw over the 10-year period will be $30,000 (250 x 12 months x 10 years). At the end of the 10-year period, he will have $50,847.90 in the account, which is more than enough to cover the required loan payments.
Find the non-zero value of $c$ for which there is exactly one positive value of $b$ for which there is one solution to the equation $x^2 + \left(b + \frac 1b\right)x + c = 0$
The value of c in the quadratic = 1.
From this equation, we can easily see that for this equation to have one possible answer, this equation must be a perfect square trinomial, which results from an equation of the form [tex](x+1)^{2}[/tex].
We also know that [tex]b+\frac{1}{b}[/tex] is equal to the sum of the roots (since the coefficient of [tex]x^{2} = 1[/tex]) and the product of the roots = c.
We easily know that in a quadratic [tex]ax^{2} +dx+c=0[/tex], if this quadratic is a square, then [tex]\frac{d}{c} = \frac{2\sqrt{c} }{c}[/tex]
[tex]2\sqrt{c} = b + \frac{1}{b}[/tex]
We know that c is a perfect square, so that means [tex]b+\frac{1}{b}[/tex] has to have an integer value, and the only way this is possible is if b = 1.
Therefore, if b = 1,
[tex]2\sqrt{c} = b + \frac{1}{b}\\\sqrt{c} = 1\\c = 1[/tex]
Therefore, the value of c in the quadratic = 1.
To learn more about quadratic equations, visit the link:
brainly.com/question/30098550
#SPJ4
As the sample size becomes larger, the sampling distribution of sample mean approaches a:
a. binomial distribution
b. either binomial distribution or normal distribution
c. normal distribution
d. none of the above
As the sample size becomes larger, the sampling distribution of sample mean approaches a normal distribution.
As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution. This is known as the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean becomes more and more normal, regardless of the shape of the underlying population distribution. The sample mean is an unbiased estimator of the population mean and it follows a normal distribution when the sample size is large.
The binomial distribution is a probability distribution that describes the number of success in a fixed number of trials, each with the same probability of success. While the binomial distribution is used to model the number of successes in a fixed number of trials, it is not used to model the sample mean.
Therefore, the answer is option (c) normal distribution.
Learn more about normal distribution here: https://brainly.com/question/4079902
#SPJ4
How do you solve ratio problems?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
learn more about of ratio here
brainly.com/question/29201784
#SPJ4
1. Find the slope of the line.
−3x−4y=6
2. Find the slope of the line that is (a) perpendicular to the line that goes through points (6, -1) and (-4, -10).
The slope of the line in 1. is -3/4 and the slope of 2. is 9/10.
What is slope?Understanding what slope is is among the most crucial things to know about lines. The line's slope, also referred to as rise over run, is how "steep" it is. By dividing the difference between the y-values at two points by the difference between the x-values, we can determine slope. Understanding how to interpret graphs and create equations is necessary in order to comprehend the significance of the definition of slope.
The slope of the line = m in y = mx + b
−3x−4y=6
4y = -3x -6
y = (-3x -6)/4
y = -3x/4 -6/4
y = -3/4(x) -3/2
2. Slope formula = y₂ - y₁ = m(x₂ -x₁)
points (6, -1) and (-4, -10)
Substitute
-10 -(-1)= m(-4 -6)
m = 9/10
Thus, the slope of the line in 1. is -3/4 and the slope of 2. is 9/10.
Learn more about slope
https://brainly.com/question/3605446
#SPJ1
once a homework quiz is opened, how long does the student have to submit the quiz? group of answer choices 2 hours, but must submit the exam no later than the closing time. 3 hours, but must submit the exam no later than the closing time. 4 hours, but must submit the exam no later than the closing time. 5 hours, but must submit the exam no later than the closing tim
3 hours, but must submit the exam no later than the closing time.
The browser displays a notification banner for tests that have a due date to inform students when the test will be marked as incomplete (30 minutes prior, 5 minutes prior, and 1 minute prior).
The browser displays a notification banner for quizzes that are about to auto-submit (using an Until date or the natural course finish date) to inform students of this (30 minutes prior, 5 minutes prior, 1 minute prior, and 10 seconds prior).3 hours, but must submit the exam no later than the closing time.
If students are unable to finish a timed quiz in the full permitted time, the browser will display a notification banner.
Know more about time management
https://brainly.com/question/24662469
#SPJ4
Which graph represents the function of f(x) =9x²-36/3x +6
The graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2. That is the second graph of the second picture gives the graph of the function.
What is y-intercept?The point at which a graph crosses the y-axis is known as the y-intercept. It is, in other words, the value of y when "(x=0)" occurs. Using the slope and a specified location, determine the y-intercept of a linear function.
Determine the graph's gradient and a point first. Enter a linear equation in slope-intercept form (y = mx + b) once this is finished. Rewrite the equation using the supplied point (x, y) and slope (m), inserting the correct values for x, y, and m.
The function is:
f(x) = (9x^2 - 36)/3x + 6
Simplify that function to a linear function for all x for which 3x + 6 ≠ 0
3x = - 6
x = -2
So, for x ≠ - 2, you can do:
f(x) = (9x^2 - 36) / 3x + 6
f(x) = 9(x^2 - 4) / 3x + 6
f(x) = 3(x + 2)(x - 2) / x+2
f(x) = 3(x - 2) = 3x - 6
Hence, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2. That is the second graph of the second picture.
Learn more about intercept here:
https://brainly.com/question/14180189
#SPJ1
Work out the unknown value
[tex] {8}^{a} \times {8}^{a} = {8}^{ - 12} [/tex]
[tex]a \: = [/tex]
Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).
Find the unknown value in the proportion ?Unknown value.Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).
The variable can be separated from the equation by performing inverse operations.Adding and multiplying are the opposites of subtracting and dividing, respectively.
Starting with the proportion:
12/? = 4/3
Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
To learn more about unknown value refer
https://brainly.com/question/29272503
#SPJ1
a rectangular box with a square base is made from 216 ft2 of material. which dimensions will result in a box with the largest possible volume?
height = 14.5 ft and width = length = 3.2 ft in a box with the largest possible volume
Let the side of the square base is a and the height of the box is h.
The material required to make the box is equal to the total surface area of the box.
Area of base = a²
Cost of square base is $ 2 per ft²
So, the cost of making base = 2a²
Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah
Cost of making walls and the top is $ 1 per ft²
So, the cost of making walls and the top = 1 x ( 3a² + 2ah)
Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah
According to the question
144 = 5a² + 2ah
.... (1)
The volume of the box is V = length x width x height
V = a x a x h
V = 72 a - 2.5 a³ from equation (1)
Differentiate both sides with respect to a.
dV/da = 72 - 7.5 a²
Put, it equal to zero for maxima and minima
7.5 a² = 72
a = 3.2 ft
Put in equation (1)
h = 14.5 ft
So, the dimensions of the box are
height = 14.5 ft
width = length = 3.2 ft
learn more about of height here
https://brainly.com/question/15393365
#SPJ4
HELP I ONLY HAVE TELL 12 QUICK I HAVE OTHER QUIZZES TOO
Answer:
by 5
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
What is the product of radical 5 and 10 radical 30 in simplest radical form
The product of radical 5 and 10 radical 30 in simplest radical form is 50√6
What is Expression?An expression is combination of variables, numbers and operators.
We need to find the product of radical 5 and 10 radical 30 in simplest radical form
It can be written as √5×10√30
√a.√b=√ab
√5×10√30
10√5×30
10√150
10√25×6
10.5√6
50√6
Hence, the product of radical 5 and 10 radical 30 in simplest radical form is 50√6
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
Answer:
What the other dude said:
The product of radical 5 and 10 radical 30 in simplest radical form is 50√6
Step-by-step explanation:
Heeeeeeeeelp, what is x?
Answer:
right angle
Step-by-step explanation:
Answer:
its 34
Step-by-step explanation:
Did it yesterday and got it right.
Determine the equation of a parabola with vertex (-2, -11) and point (-4, 5).
3 marks
Answer (vertex form): y=4(x+2)^2 - 11
Answer (standard form): y=4x^2 + 16x + 5
what is the reciprocal of -2/7
Answer: -3.5 is the reciprocal
Answer:
= 7/-2
= -7/2
Step-by-step explanation:
The reciprocal number results from dividing the number 1 ny the original number, in this case:
original number = -2/7
reciprocal number = 1 / (-2/7) = (1*7)/-2 = 7/-2 = -7/2
What are the characteristics of an absolute value graph?
There are six characteristics of an absolute value graph.
An absolute value function is a function of the form f(x) = |x|. The graph of an absolute value function has the following characteristics:
It is symmetric about the y-axis, since changing the sign of x (from positive to negative or vice versa) does not change the value of |x|.It has a "V" shape, with the vertex located at the origin (0,0).As x moves away from 0 along the x-axis, the y-coordinate of the graph increases in value.As x moves towards 0 along the x-axis, the y-coordinate of the graph approaches 0.The graph does not cross the x-axis.The range of the function is all non-negative numbers.Learn more about Graphs:
https://brainly.com/question/9286643
#SPJ4
the measure of two supplementary angles of a triangle are in the ratio 4:11. what is the measure of the larger angle?
According to the given information the supplementary angle are 132 and 48.
Are indeed the supplementary angles 90 or 180?Two angles are referred to as supplementary angles because they combine to generate a linear angle when their total is 180 degrees. When two angles add up to 90 degrees, however, they are considered to be complimentary angles and together they make a right angle.
What do complimentary and additional angles mean?If the total of two angles is 90 degrees or greater, they are complementary; if the sum is 180 degrees or greater, they are supplementary. Given that they are in the same ratio, we will call one angle 11x whilst the other is 4x.
They add up to [tex]11x+4x=15x={180}^\circ\rightarrow x=12[/tex]
So one angle is [tex]11\cdot12={132}^\circ[/tex]
And the other is [tex]4\cdot12={48}^\circ[/tex]
Check: [tex]132+48=180[/tex]
To know more about supplementary angles visit:
https://brainly.com/question/13045673
#SPJ4
steve wants to download a selection of new music. how many ways can steve select three rock songs, five alternative songs, and six rap songs from a list of five rock songs, six alternative songs, and nine rap songs?
Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.
1. To select three rock songs from a list of five, use the formula for combinations: nCr = 5Cr = 5!/ (3!*2!) = 10
2. To select five alternative songs from a list of six, use the formula for combinations: nCr = 6Cr = 6!/ (5!*1!) = 6
3. To select six rap songs from a list of nine, use the formula for combinations: nCr = 9Cr = 9!/ (6!*3!) = 84
4. To find the total number of selections, multiply the individual combinations: 10 x 6 x 84 = 11,250
Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
how many liters of a 15% alcohol solution must be mixed with 30 liters of a 40% alcohol solution to obtain a 30% solution
Answer: 20 liters
Step-by-step explanation:
Let the number of liters of 15% alcohol solution be [tex]x[/tex].
[tex]0.15x+30(0.4)=0.3(x+30)\\\\0.15x+12=0.3x+9\\\\12=0.15x+9\\\\0.15x=3\\\\x=20[/tex]
PLEASE HELPPPP!!! (-2/3)^4 evaluate.
(-2/3)^4 evaluates to (1/81) or 0.012345679012345678.
In the given figure, △ADE ∼ △ABC. Which triangle similarity theorem justifies
this similarity? Show proof toyour answer.
a. Using the figure below, name the three similar triangles.
b. Write the proportions that exist among corresponding parts of similar
By similarity theorem The three similar triangles are △CLB~△LUB~△CUL
(B) The proportions in corresponding parts of similar are in △CLB~△LUB: CL/LU=LB/UB=CB/LB and in △CLB~△CUL:CL/CU=LB/UL=CB/CL
What is similarity theorem?Triangle similarity in Euclidean geometry. According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
In the given figure, △ADE~△ABC.
1. ∠D≅∠B
2. DE II BC converse of basic proportionality
3. ∠E ≅ ∠C corresponding angle are congruent
4. ∠DAE≅∠BAC reflexive property
5. △ADE ≅△ABC (AAA similarity theorem)
The three similar triangles are-
△CLB~△LUB~△CUL
The proportions that exist among corresponding parts of similar
→ In △CLB~△LUB
CL/LU=LB/UB=CB/LB
→ In △CLB~△CUL
CL/CU=LB/UL=CB/CL
→ In △LUB~△CUL
LU/CU=UB/UL=LB/CL
To learn more about similarity theorem visit:
brainly.com/question/14926756
#SPJ4
3/8 in simplest form as a fraction
3/8 is already in its simplest form as a fraction. The numerator, 3, and denominator, 8, have no common factors other than 1. To simplify a fraction to its simplest form, you divide both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 3 and 8 is 1, so there's no need to simplify further. Therefore 3/8 is already in its simplest form.
Answer:
3/8 is already in its simplest for as both numerator n denominator does not have any common factor
A manufacturer offers a 25/20 chain
discount if the invoice subtotal is above
$1,000. If the list price is $52 per item,
what is the total price of the first invoice
that activates the chain discount?
The total price of the first invoice that activates the chain discount is $624.
What is percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A manufacturer offers a 25/20 chain discount if the invoice subtotal is above $1,000.
If the list price is $52 per item.
now, to get the discount he must buy at least = 1000/52= 20 items
= 20 x $52
= $1040
Thus, (1040) (1-25%)(1- 20%)
= 1040 x 0.75 x 0.80
= 624
Hence, the total price is $624.
Learn more about Percentage here:
https://brainly.com/question/29306119
#SPJ1
1. The hypotenuse of a right triangle has length of 34cm. The sum of the lengths of the other two legs is 46cm. What are their lengths?
The length of the other two sides are 16 and 30.
What is right-angle triangle ?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
let one angle be x
the other angle be 46-x
as the sum of the angles is 46
x² + (46-x)² = 34²
2x² - 92x + 46² - 34² = 0
x² - 46x + 480 = 0
x² - 16x - 30x + 480 = 0
x(x-16) - 30 (x - 16) = 0
(x-30)(x-16) = 0
x = 30 or x = 16
To learn more about right-angle triangle from the given link
https://brainly.com/question/64787
#SPJ1
y=x, y=x^2, y=x^3, y=|x,| y=1/x, y=x, y=e^x, y=1/1+e^-x, y=ln(x), y=floor(x), y=sinx, y=cosx
12. three functions that are bounded above
Answer:Three functions that are bounded above are y = x^2, y = x^3, y = e^x.
y = x^2 is a parabola that opens upward and has a vertex at the origin (0,0). As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.
y = x^3 is a cubic function that also opens upward. As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.
y = e^x is the exponential function where e is Euler's number (approximately 2.718). As x increases, y will increase towards positive infinity, so the function is bounded above by positive infinity.
Step-by-step explanation:
a nutritionist believes that 10% of teenagers eat cereal for breakfast. to investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. she would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. what are the values of the test statistic and p-value for this test?
On solving the provided question, we can say that random sample the conditions for interference are met.
what is random sample?selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.
Yes, the conditions for interference are met.
To know more about random sample visit:
https://brainly.com/question/29852583
#SPJ4
Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
Find the proability of getting a full house ( 3 cards of one denomination and 2 of another) when 5 cards are dealt from an ordinary deck. Answer as a fraction
The probability of a “full house” is 6 / 4165.
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
For example, the probability of flipping a fair coin and it landing on heads is 0.5, or 50%. The probability of rolling a fair die and getting a 6 is 1/6, or about 16.67%.
A “full house” (3 cards of one kind and 2 cards of another kind)
Since there are 13 sets of each type, we have to select any 2 kinds of it.
The probability becomes =[tex]\frac{2 X 13C2 X4C3X 4C2 }{52 C5}[/tex]
On simplification,
= 3744 / 2598960
= 6 / 4165
=0.00144
So the probability of a “full house” is 0.00144.
To know more about probability refer to:
brainly.com/question/11234923
#SPJ4
given the following: p(a) =0.3 p(b) = 0.2 p(a and b) = 0.4 which of the following is true?
Group of answer choices a. A and B are independent and disjoint.
b. A and B are independent. c. A and B are disjoint. d. A and B are neither disjoint nor independent.
By applying independent and disjoint events theory, it can be concluded that A and B are neither disjoint nor independent (option D).
In probability, based on the occurrences, there are two types of events: independent and disjoint events.
If events are unrelated, they are considered independent events. Thus P(A and B) = P(A) * P(B)If events are mutually exclusive, which means they never occur at the same time, they are considered disjoint events. Thus the sum of the probabilities of each occurring, P(A and B) = 0. While P(A or B) = P(A) + P(B)Now we observe the data given:
p(a) = 0.3
p(b) = 0.2
p(a and b) = 0.4.
First, we check the independence. Here p(a and b) = 0.4. Whereas, if a and b are independent events, then:
p(a and b) = p(a) * p(b)
= 0.3 * 0.2
= 0.06
Since the value is different, we can conclude that events A and B are not independent.
Second, we check whether these events are disjoint events. Since the value of p(a and b) is not 0, these events are disjoint events.
Therefore, we can conclude that a and b are neither disjoint nor independent (option D)
To learn more about independent and disjoint events, click here: https://brainly.com/question/15668045
#SPJ4
a norma window has the shape of a rectangle surmounted by a semicircle of diameter equal to the width of the rectangle. if the perimeter of the window is 10m what is the dimension will admit the most lighT
The dimensions that will admit the most light are, the breadth of the rectangular window is [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is [tex]l= \frac{20}{4+3\pi }[/tex].
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. "Composite figures" or "composite shapes" are shapes created by combining two or more simple shapes. To determine the area of a composite form, we must add up the areas of all the shapes that make up the figure.In the given question,
Let the length and breadth of the rectangular part of the window be 2l and 2b respectively. So the radius of the semicircular arc will be l.
The total perimeter of the window will be 1 length of the rectangle, 2 breadths of the rectangle, and the length of the semicircular arc.
l+2b+πl = 10
(1+π)l+2b = 10
[tex]b = \frac{1}{2} [10-(1+\pi )l][/tex]
To admit maximum light through the window implies that the area of the window is maximized.
The area of the window will be:
[tex]A = (2l)(2b)+\frac{\pi l^{2} }{2}[/tex]
[tex]= 4lb+\frac{\pi l^{2} }{2} \\= 2l[10-(1+\pi )l] +\frac{1}{2} \pi l^{2}[/tex]
[tex]= 20l-2l^{2} -2\pi l^{2} +\frac{1}{2} \pi l^{2}[/tex]
[tex]= 20l-2l^{2} - \frac{3}{2} \pi l^{2}[/tex]
For the area to be maximum,
[tex]\frac{dA}{dl} =0\\20 -4l -3\pi l = 0\\l= \frac{20}{4+3\pi }[/tex]
[tex]b = \frac{1}{2} [10-(1+\pi )\frac{20}{4+3\pi }\\b = \frac{10+5\pi }{4+3\pi }[/tex]
Therefore, the breadth of the rectangular window is [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is [tex]l= \frac{20}{4+3\pi }[/tex].
To learn more about the Area visit:
https://brainly.com/question/29851793
#SPJ4
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!QUICK
How do you graph an inequality. Explain in 2 or more sentences
Answer:
can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2
Linear Inequality
A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...
... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.
Answer and explaining
Answer:
a
Step-by-step explanation:
i just took it
