Answer:
a) Simple interest paid = $360
b) Total repayment amount = $6360
Step-by-step explanation:
It is given that:
Principal, P = $6000
Rate of interest, R = 2%
Time, T = 3 years
(a) Total interest paid:
Formula for Simple Interest is given as:
[tex]S.I. = \dfrac{P \times R \times T}{100}[/tex]
Putting the values of P, R and T to find out Simple Interest:[tex]\\\Rightarrow S.I. = \dfrac{6000 \times 2 \times 3}{100}\\\Rightarrow S.I. = \$360[/tex]
(b) Total repayment amount:
We know that formula for total amount is given as:
Amount = Principal + Simple Interest
Amount = 6000 + 360 = $6360
So, total repayment amount = $6360
So, the answers are:
a) Simple interest paid = $360
b) Total repayment amount = $6360
can someone help please, it wont give me the last mark
Answer:
The explanation is:
All interior angles in an equilateral triangle are congruent, making them all 60° by the sum of angles in a triangle. Because alternate interior angles of parallel lines are congruent, x = 60°.
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level. Dates 6th 13th 1990, July 139246 138548 1990, July 134012 132908 1991, September 137055 136018 1991, September 133732 131843 1991, December 123552 121641 1991, December 121139 118723 1992, March 128293 125532 1992, March 124631 120249 1992, November 124609 122770 1992, November 117584 117263
Answer: The mean difference is between 799586.3 and 803257.9.
Step-by-step explanation: To estimate the mean difference for confidence interval:
Find the statistic sample:
d = value of 6th - value of 13th;Sample mean of difference: mean = ∑d / nSample standard deviation: s = ∑(d - mean)² / n - 1;For the traffic count, mean = 1835.8 and s = 1382607.3
The confidence interval is 90%, so:
α = [tex]\frac{1-0.9}{2}[/tex]
α = 0.05
The degrees of dreedom are:
df = n - 1
df = 10 - 1
df = 9
Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.
Error will be:
E = [tex]t.\frac{s}{\sqrt{n} }[/tex]
E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])
E = 801422.1
The interval is: mean - E < μ < E + mean
1835.8 - 801422.1 < μ < 1835.8+801422.1
-799586.3 < μ < 803257.9
The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.
9/8+7/40= and does the answer simplify
Answer:
1 3/10
Step-by-step explanation:
9/8 +7/40
Get a common denominator of 40
9/8 *5/5 + 7/40
45/40 + 7/40
52/40
Rewriting as
40/40 +12/40
1 + 3/10
1 3/10
Answer:
1 3/10
Step-by-step explanation:
First, you need to get a common denominator:
8x5=40 <-- common denominator
45/40+7/40= 52/40
yes you can simplify it.
your final answer will be: 1 3/10
Use the fundamental identities to simply the expression.
Answer:
[tex]\cos (\theta)[/tex]
Step-by-step explanation:
[tex]\dfrac{\tan (\theta) \cot (\theta)}{\sec (\theta)}= \\\\\\\dfrac{\dfrac{\sin (\theta)}{\cos (\theta)}\cdot \dfrac{\cos (\theta)}{\sin (\theta)}}{\dfrac{1}{\cos (\theta)}}= \\\\\\1\cdot \cos (\theta)=\\\\\\\boxed{\cos (\theta)}[/tex]
Hope this helps!
Tickets for a raffle cost $19. There were 798 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)
Answer:
-17.32
Step-by-step explanation:
(1319- 19*797)/798 = -17.3233
Find the work done in emptying a cylindrical tank filled with water. The water is being pumped out from the 6 top. The tank has a diameter of 4 feet and is 6 feet tall. The tank is on ground level. Water is 62.4 lbs/ft
Answer:
908360.67 lb-ft
Step-by-step explanation:
height of tank= 6 ft
diameter of the tank = 4 ft
density of water p = 62.4 lbs/ft
A is the cross sectional area of the tank
A = [tex]\pi r^{2}[/tex]
where r = diameter/2 = 4/2 = 2 ft
A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2
work done = force x distance through which force is moved
work = F x d
Force due to the water = pgAh
where g = acceleration due to gravity = 32.174 ft/s^2
Force = 62.4 x 32.174 x 12.568 x 6 = 151393.44 lb
work done = force x distance moved
work = 151393.44 x 6 = 908360.67 lb-ft
Question 5(Multiple Choice Worth 1 points)
(02.05 MC)
Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater value when x = 3?
Answer:
g(x) is greater
Step-by-step explanation:
The graph of Fx), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answer:
Correct answer is:
C. [tex]F(x) =-x^{2} -3[/tex]
Step-by-step explanation:
We are given a function:
[tex]G(x) = x^{2}[/tex]
The graph of [tex]G(x)[/tex] is also shown in the given question figure.
It is a parabola with vertex at (0,0).
Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.
General equation of parabola is given as:
[tex]y = a(x-h)^2+k[/tex]
Here, in G(x), a = 1
Vertex (h,k) is (0,0).
As seen from the question figure,
The graph of F(x) opens down that is why it will have:
Sign of [tex]x^{2}[/tex] as negative. i.e. [tex]a = -1[/tex]
And vertex is at (0,-3)
Putting the values of a and vertex coordinates,
Hence, the equation of parabola will become:
[tex]y = -1(x-0)^2+(-3)\\y = -x^2-3[/tex]
The correct answer is:
C. [tex]F(x) =-x^{2} -3[/tex]
The required equation of graph f(x) is [tex]y = -x^{2} -3[/tex]
Given that,
The graph of f(x), resembles the graph of G(x) = [tex]x^{2}[/tex].
We have to find,
Which of the following could be the equation of f(x).
According to the question,
Function, [tex]G(x) = x^{2}[/tex],
The graph in the given question figure. It is a parabola with vertex at (0,0).
By the graph predict that Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.
General equation of parabola is given by,
[tex]y = a(x-h)^{2} +k[/tex]
Where, a = 1, and vertex (h, k) is (0,0).
The graph of F(x) unknown function opens down ,
Sign of [tex]x^{2}[/tex] as negative. and the vertex is at (0,-3)
To find the equation of function f(x),
Putting the values of a and vertex coordinates,
[tex]y = a(x-h)^{2} +k[/tex]
The equation of parabola become:
[tex]y = -1(x-0)^{2} +(-3)\\\\y = -x^{2} -3[/tex]
Hence, The required equation of f(x) is [tex]y = -x^{2} -3[/tex].
For more information about Parabola click the link given below.
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The SAT exam is used in admissions decisions by many four-year colleges and universities. In 2006, The College Board carried out a study of 6,498 SAT essays that were selected at random from the more than 1.4 million SAT exams taken in the 2005 - 2006 academic year. For this sample of essays, 15% were written in cursive and 85% were printed in block letters. The results showed that the average score for essays written in cursive was higher than the average score for essays that were printed.
A. is this study an observational study or an experiment? Explain your answer.
B. is it reasonable to conclude that writing the essay in cursive was the cause of the higher scores? Explain your answer?
Answer:
Step-by-step explanation:
A. This study is an observation study as there is manipulative to the data on the part of the researcher. They only collected information based on what was seen and observed. There were no treatment conditions.
B. It is not reasonable to conclude that writing the essay in cursive is the cause for higher scores as the causation factor inducing higher scores here in this case might not be on how the essays are put down. So an experiment will be needed to be carried out to find this out.
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?
Answer:
The probability is 1
Step-by-step explanation:
P ( Jamaal winning) = Jamaal / number of people running
= 1/1
= 1
Answer:
1
Step-by-step explanation: :-)
Write a system of linear equations for the graph below
Answer:
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
Step-by-step explanation:
Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,
Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
If these points are (0, 3) and (3, -6),
Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)
Equation of the line which passes through (0, 3) and slope = (-3),
y - y' = m(x - x')
y - 3 = (-3)(x- 0)
y - 3 = -3x
y = -3x + 3
Now slope of another line that passes through (3, -6) and (0, -7),
m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]
m' = [tex]\frac{1}{3}[/tex]
Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]
y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]
y + 7 = [tex]\frac{1}{3}x[/tex]
y = [tex]\frac{1}{3}x-7[/tex]
Therefore, system of linear equations are,
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
A grocery store owner claims that the mean amount spent per checkout is more than $74. A test is made of H0: μ = 74 versus H1: μ > 74. The null hypothesis is rejected. State the appropriate conclusion. Group of answer choices
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A grocery store owner claims that the mean amount spent per checkout is more than $74. A test is made of H0: μ = 74 versus H1: μ > 74. The null hypothesis is rejected. State the appropriate conclusion. A) There is not enough evidence to conclude that the mean checkout price is greater than $74. B) The mean checkout amount is less than or equal to $74 C) The mean checkout amount is greater than $74. D) There is not enough evidence to conclude that the mean checkout price is less than or equal to $74
Solution:
The alternative hypothesis is the opposite of the null hypothesis. It is the hypothesis that is true if the null hypothesis is false.
Since the null hypothesis is rejected, it means that there was enough evidence to make us accept the alternative hypothesis. Considering the given scenario, the correct option would be
B)The mean checkout amount is greater than $74
Check all of the points that are solutions to the system of inequalities.
'X + y 2 2 +4
y< 4
Answer:
C. (5, 3)
D. (7, -1)
Step-by-step explanation:
The requirement that y < 4 eliminates points A, E, F. None of 7, 4, 5 are less than 4.
The requirement that x+y ≥ 6 eliminates point B. 1-1 = 0 is not at least 6.
Points C and D satisfy both inequalities.
What are the x-intercepts of the graph of the function below?
y = x^2 – 3x - 28
A. (-7,0) and (-4,0)
B. (7,0) and (-4,0)
C. (7,0) and (4,0)
D. (-7,0) and (4.0)
Answer:
The x intercepts are (7,0) and (-4,0)
Step-by-step explanation:
y = x^2 – 3x - 28
Set y=0
0 = x^2 – 3x - 28
Factor. What 2 numbers multiply to -28 and add to -3
-7*4 = -28
-7+4 = -3
0 = (x-7)(x+4)
Using the zero product property
0 = (x-7) 0 = x+4
x=7 x = -4
The x intercepts are (7,0) and (-4,0)
URGENT!!!! WILL GIVE BRANLIEST PLS HELP OR AT LEAST TAKE A LOOK!! I HAVE LESS THEN 10 MINUTES LEFT PLS!!!! IM LOOSING HOPE! SHARE YO SMARTNESS!!!! PLEASSEEEEE!!!!
I ASKED 2 QUESTIONS, THEY ARE IN THESE LINK
https://brainly.com/question/16901202?answeringSource=feedPersonal%2FquestionPage%2F1
https://brainly.com/question/16900998
Answer:
Ok
Step-by-step explanation:
:DDD
What is (14x2 + 19x - 3) = (2x+3)?
Answer:
Dear User
Answer to your query is provided below
X = 2/7 or X = -3/2
Step-by-step explanation:
Explanation for the same is attached in image
The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 5 inches Which calculation will give the total surface area of the solid figure? 5 × 6 × 6 square inches 6 × 5 × 5 square inches 6 × 5 × 5 × 5 square inches 5 × 6 × 6 × 6 square inchesv
Answer:
6 × 5 × 5 square inches
Step-by-step explanation:
The area of one of the figure's 6 squares is the product of its side length, so is ...
5 × 5 square inches
The area of all 6 of those squares is 6 times this, or ...
6 × 5 × 5 square inches
Can someone help me with this?
Answer:
poop
Step-by-step explanation:
poop
Find the slope through each pair of two points. Report answers in simplest form.
(-3,6) and (-5,9)
m =
Answer: m=-3/2
Step-by-step explanation:
To find the slope, we use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. With our given points, we can directly plug them into the formula.
[tex]m=\frac{9-6}{-5-(-3)} =\frac{3}{-2}[/tex]
Our slope is m=-3/2.
What is the sum of (4x2 – 10x + 3) and (-6x2 + 10x + 12)
Answer:
-2x² + 15
Step-by-step explanation:
Step 1: Add like terms
4x² - 6x² = -2x²
-10x + 10x = 0
12 + 3 = 15
Step 2: Rewrite
-2x² + 15
[tex](8 - 10x + 3) + ( - 12 + 10x + 12)[/tex]
[tex](11 - 10x) + (10x)[/tex]
[tex] 11 - 10x + 10x[/tex]
[tex] = 11[/tex]
Which scenario is the best example of a deus ex machina?
Answer:
D.
Step-by-step explanation:
Deus ex machina is the plot device of using something very improbable to resolve a situation.
if 25% or the person'so salary is $135.75 then what is the amount of his full salary?
Answer:
543
Step-by-step explanation:
let x= total salary
0.25x=135.75
x=543
Answer:
[tex]\$ \: 543.00[/tex]
Step-by-step explanation:
[tex]25\% \times x =135.75[/tex]
[tex]1/4 \times x =135.75[/tex]
[tex]0.25 \times x =135.75[/tex]
[tex]x=135.75 \times 4[/tex]
[tex]x=543[/tex]
What number should be in the blank in the sequence? 7; 17; 37; 77; ___ ; 317
Answer:
the answer is 157
Step-by-step explanation:
7 +10= 17
17+20=37
37+40=77
77+80=157
157+160=317
At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...
Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (3, 4) and (5, 0).
Answer:
A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero
Step-by-step explanation:
Answer:
The answer would be C because the y-intercept is when x is equal to 0
please mark me brainliest
answer please anybody ???
Step-by-step explanation:
a) 2x = 8 x 3
2x = 24
x = 12
b) 3x = 12
x = 4
Algebra 1
Function Notation Worksheet Alternate
Name
For #I-8: Evaluate the following expressions given the functions below:
f(x) = x2 – 7
g(x) = -3x - 1
j(x)=2x-9
h(x) = 1
X=
1. g(10) =
2. What is the value of x if g(x) = 16
3. f(3) =
4. What is the value of x if f(x) = 23
X
5. h(-2) =
6. What is the value of x if h(x) = -2
X =
7. |(7) =
8. h(a) =
For #9-12: Translate the following statements into coordinate points:
9. S(-1) = 3
10. g(4) = -1
11. h(2) = 8
12. k(2) = 9
Answer:
None
Step-by-step explanation:
The answers are:
1. g(10) -31
2. x= -17/3
3. f(3)= 2
4.x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = x² – 7
g(x) = -3x - 1
j(x)= 2x-9
h(x) = 1
1. g(10)= -3(10) -1 = -30 - 1= -31
2. g(x) = 16
-3x- 1= 16
-3x = 17
x= -17/3
3. f(3)= (3)² – 7 = 9- 7= 2
4. f(x)= 23
x² – 7= 23
x² = 30
x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
8. S(-1) = 3
The value of function s(a) at a=-1 is 3.
10. g(4) = -1
The value of function g(a) at a=4 is -1.
11. h(2) = 8
The value of function h(a) at a=2 is 8.
12. k(2) = 9
The value of function k(a) at a= 2 is 9.
Learn more about function here:
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Which of the following expressions is equal to -1?
sec90°
sin180°
csc270°
Answer:
csc 270° is the answer.
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X>1), n=4, p=0.6.
Answer:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X >1)[/tex]
And for this case we can use the complement rule and we got:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Use the Central Limit Theorem to find a mean given a probability Question A video game company sells an average of 132 games a month, with a standard deviation of 9 games. The company is looking to reward stores that are selling in the top 7%. How many video games must a store sell in order to be eligible for a reward if the company is only looking at 36 of their stores. Use the 2-table below: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883 1.2 0.885 0.887 0.889 0.891 0.893 0.894 0.896 0.898 0.900 0.901 1.3 0.9030.905 0.9070.908 0.910 0.911 0.913 0.915 0.9160.918 1.4 0.919 0.921 0.922 0.924 0.925 0.926 0.928 0.929 0.931 0.932 1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954
Round the z.score and a to two decimal places. Round up to the nearest whole number.
Answer:
The number of games must a store sell in order to be eligible for a reward is 135.
Step-by-step explanation:
Let the random variable X represent the number of video games sold in a month by the sores.
The random variable X has a mean of, μ = 132 and a standard deviation of, σ = 9.
It is provided that the company is looking to reward stores that are selling in the top 7%.
That is, [tex]P (\bar X > \bar x) = 0.07[/tex].
The z-score related to this probability is, z = 1.48.
Compute the number of games must a store sell in order to be eligible for a reward as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]\bar x=\mu+z\cdot \sigma/\sqrt{n}[/tex]
[tex]=132+1.48\times (9/\sqrt{36})\\\\=132+2.22\\\\=134.22\\\\\approx 135[/tex]
Thus, the number of games must a store sell in order to be eligible for a reward is 135.
Answer:
1.48
1.5
135
Step-by-step explanation:
66 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.8397
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the cards are chosen is not important. Also, they are drawn without replacement. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that at least one of the cards drawn is a spade?
Either none is a spade, or at least one is a spade. The sum of the probabilities of these outcomes is 1.
The standard deck has 52 cards, of which 13 are spades. So
Probability that none are spades:
Desired outcomes:
6 cards from a set of 52 - 13 = 39. So
[tex]D = C_{39,6} = \frac{39!}{6!33!} = 3262623[/tex]
Total outcomes:
6 cards from a set of 52. So
[tex]T = C_{52,6} = \frac{52!}{6!46!} = 20358520[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{3262623}{20358520} = 0.1603[/tex]
Probability that at least one is a spade:
1 - 0.1603 = 0.8397
The answer is 0.8397