Answer:
The amount invested in ADB is ¢1363.[tex]\overline 3[/tex] =
The amount invested in Barclays is ¢3,427.[tex]\overline 3[/tex]
The amount invested in GCB is ¢1,713.[tex]\overline 3[/tex]
Step-by-step explanation:
The parameters of the investment Stonewall made are;
The amount in interest he receives from ADB, Barclays and GCB = ¢250
The amount of interest ADP pays = 2% per annum
The amount of interest Barclays pays = 4% per annum
The amount of interest GCB pays = 5% per annum
The amount invested in Barclays = The amount invested in ADB and GCB + ¢350
The amount invested in Barclays = 2 × The amount invested in GCB
a) Let 'x', represent the amount invested in ADB, 'y' represent the amount invested in Barclays, and 'z', represent the amount invested in GCB
We have;
y = x + z + 350
y = 2·z
0.02·x + 0.04·y + 0.05·z = 250
Therefore, we get the three linear equations as follows;
-x + y - z = 350...(1)
y - 2·z = 0...(2)
0.02·x + 0.04·y + 0.05·z = 250...(3)
Using Matrix inversion, we have;
[tex]\left[\begin{array}{ccc}-1&1&-1\\0&1&-2\\0.02&0.04&0.05\end{array}\right] \times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}350&0&250\end{array}\right][/tex]
The transpose of the 3 by 3 matrix [tex]M^T[/tex] is given as follows;
[tex]M^T = \left[\begin{array}{ccc}-1&0&0.02\\1&1&0.04\\-1&-2&0.05\end{array}\right][/tex]
The Adjugate Matrix is given as follows;
[tex]Adj = \left[\begin{array}{ccc}0.13&-0.09&-1\\-0.04&-0.03&-2\\-0.02&0.06&-1\end{array}\right][/tex]
The inverse of the matrix = Adj/Det where, Det = -0.15, is therefore;
[tex]M^{-1} = \left[\begin{array}{ccc}\dfrac{-13}{15} &\dfrac{3}{5} &\dfrac{20}{3} \\\\\dfrac{4}{15} &\dfrac{1}{5} &\dfrac{40}{3} \\\\\dfrac{2}{15} &-\dfrac{2}{5} &\dfrac{20}{3} \end{array}\right][/tex]
We therefore, get the solution as follows;
[tex]\left[\begin{array}{ccc}\dfrac{-13}{15} &\dfrac{3}{5} &\dfrac{20}{3} \\\\\dfrac{4}{15} &\dfrac{1}{5} &\dfrac{40}{3} \\\\\dfrac{2}{15} &-\dfrac{2}{5} &\dfrac{20}{3} \end{array}\right]\times \left[\begin{array}{c}350&0&250\end{array}\right] = \left[\begin{array}{c}\dfrac{4,090}{3} \\&\dfrac{10,280}{3} \\ & \dfrac{5,140}{3} \end{array}\right][/tex]
[tex]\begin{array}{c}x = \dfrac{4,090}{3} \\&y = \dfrac{10,280}{3} \\ & z = \dfrac{5,140}{3} \end{array}[/tex]
The amount invested in ADB, x = ¢4,090/3 = ¢1363.[tex]\overline 3[/tex]
The amount invested in Barclays, y = ¢10,282/3 = ¢3,427.[tex]\overline 3[/tex]
The amount invested in GCB, z = ¢5,140/3 = ¢1,713.[tex]\overline 3[/tex]
4a=32
Fill in the blank:
a=___
Answer:
a = 8Step-by-step explanation:
Divide both sides by 4.a = 32 ÷ 4
a = 8
Plz answer quick need help. are the sums of double odd?
There are 60 apples and then add 59 apples two times . How many apples and there altogether
Answer:
Step-by-step explanation:
59 apples two times = 59 x 2 = 118 apples
Total apples = 118 + 60 = 178 apples
As a preliminary helper result, show by induction that for events E1, E2,..., EM, M P(E, or E2 or ... ог Ем) < Р(Еm). m=1
By applying the principle of inclusion-exclusion, we can show that for any events E1, E2,..., EM, the inequality P(E1 or E2 or ... or EM) < P(EM) holds. This result holds true for any integer M ≥ 1.
To prove the statement by induction, we will assume that for M = 1, the inequality holds true. Then we will show that if the statement holds for M, it also holds for M + 1.
Base case (M = 1):
For M = 1, we have P(E1) ≤ P(E1), which is true.
Inductive step:
Assuming that the inequality holds for M, we need to show that it holds for M + 1. That is, we need to prove P(E1 or E2 or ... or EM or EM+1) < P(EM+1).
Using the principle of inclusion-exclusion, we can express the probability of the union of events as follows: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1) - P((E1 or E2 or ... or EM) and EM+1). Since events E1, E2, ..., EM, and EM+1 are mutually exclusive, the last term on the right-hand side becomes zero: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1)
Since we assumed that P(E1 or E2 or ... or EM) < P(EM), we can rewrite the inequality as: P(E1 or E2 or ... or EM or EM+1) < P(EM) + P(EM+1)
Now we need to show that P(EM) + P(EM+1) < P(EM+1) for the inequality to hold. Simplifying the expression, we have: P(EM) + P(EM+1) < P(EM+1)
Since P(EM+1) is a probability and is always non-negative, this inequality holds true. Therefore, by the principle of mathematical induction, we have shown that for any integer M ≥ 1, the inequality P(E1 or E2 or ... or EM) < P(EM) holds.
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In a publication of a renowned magazine, it is stated that cars travel in
average at least 20,000 kilometers per year, but do you think the average actually
is minor. To test this claim, a sample of 100 car owners is asked
randomly selected to keep a record of the kilometers they travel. It would
If you agree with this statement, if the random sample indicates an average of 19,000
kilometers and a standard deviation of 3900 kilometers? Use a significance level of
0.05 and for its engineering conclusion use:
a) The classical method.
b) The P-value method as an auxiliary.
Both the classical method and the p-value method lead to the conclusion that the average distance cars travel per year is less than 20,000 kilometers,
a) t = -2.564
b) t = -2.564
How to thest the claim?To test the claim that the average distance cars travel per year is less than 20,000 kilometers, we can conduct a hypothesis test using the classical method and the p-value method.
a) The steps we need to follow are:
Step 1: Formulate the null and alternative hypotheses:
Null hypothesis (H₀): The average distance cars travel per year is 20,000 kilometers.
Alternative hypothesis (H₁): The average distance cars travel per year is less than 20,000 kilometers.
Step 2: Determine the test statistic:
Since we know the sample size (n = 100), the sample mean (x = 19,000 kilometers), and the sample standard deviation (s = 3900 kilometers), we can use the t-test statistic.
t = (x - μ₀) / (s / √n)
where μ₀ is the assumed population mean under the null hypothesis.
Step 3: Set the significance level:
The significance level is given as 0.05, which means we want to be 95% confident in our conclusion.
Step 4: Calculate the critical value:
Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value corresponding to a 0.05 significance level and degrees of freedom (df) = n - 1 = 99. From the t-distribution table or calculator, the critical t-value is approximately -1.660.
Step 5: Calculate the test statistic:
t = (19,000 - 20,000) / (3900 / √100)
t = -10 / (3900 / 10)
t ≈ -2.564
Step 6: Compare the test statistic with the critical value:
Since -2.564 is less than -1.660, the test statistic falls in the rejection region. We reject the null hypothesis.
Step 7: Make a conclusion:
Based on the classical method, since the test statistic falls in the rejection region, we conclude that the average distance cars travel per year is significantly less than 20,000 kilometers.
b) The P-value method:
Using the same test statistic t = -2.564 and the degrees of freedom (df) = 99, we can calculate the p-value. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
From a t-distribution table or calculator, the p-value corresponding to t = -2.564 and df = 99 is approximately 0.0075 (or 0.75% if multiplied by 100).
Since the p-value (0.0075) is less than the significance level (0.05), we reject the null hypothesis. This suggests strong evidence that the average distance cars travel per year is significantly less than 20,000 kilometers.
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An adult pass is 3 times as much as a child's pass. What is the cost of the adults pass? Write an expression for the situation
Answer:
however much the Child's pass is x 3 = Adult Pass cost
Step-by-step explanation:
Find the total area.
Answer:
area = 164.52 cm²
Step-by-step explanation:
area = (12x6) + (12x3x0.5x2) + (3.14)(0.5)(6²) = 164.52 cm²
Peter makes 15 dollars an hour and he spends 25 dollars a day on transportation and food. Write an expression to describe his spendings and earnings in a day, where h is the number of hours that Peter works that day
15h - 25 dollars is an expression to describe his spendings and earnings in a day.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Peter makes 15 dollars an hour, so if he works for h hours, he earns:
15h dollars
Peter spends 25 dollars a day on transportation and food, so his total spending can be expressed as:
25 dollars
Therefore, his total earnings minus his total spending can be expressed as:
15h - 25 dollars
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The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first 12 terms of the corresponding series? A. 2,125,760 B. 6,377,288 C. 236,192 D. 708,584
Answer:
2,125,760
Step-by-step explanation:
The first term (a) is 8
The fourth term is 216
Hence the sum of the first 12 term can be calculated as follows
= 8-8(3)^12/1-3
= 8-24^12/-2
= 2,125,760
The sum of first 12 terms is 2,125,760
Sum of the first 12 term = 2,125,760
For geometric sequence,
aₙ = arⁿ⁻¹
where
a = first term
r = common ratio
n = number of terms
Therefore,
a = 8
a₄ = 216
let's find the common ratio
216 = 8 × r⁴⁻¹
216 = 8 × r³
r³ = 216 / 8
r³ = 27
r = [tex]\sqrt[3]{27}[/tex]
r = 3
Let's find sum of the first 12 terms.
Sₙ = a (rⁿ - 1) / r - 1
S₁₂ = 8(3¹² - 1) / 3 - 1
S₁₂ = 8(531440) / 2
S₁₂ = 4251520 / 2
S₁₂ = 2,125,760
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Suppose you have two similar trapezoids with a scale factor of 4. If the angle measures of trapezoid ABCD are 70,110,110,70, what is the answer?
Answer: 140, 220, 220, 140
Step-by-step explanation:
All you have to do is double the numbers.
Social Networking sites A recent survey of 10 social networking sites has a mean of 12.67 million visitors for a specific month. The standard deviation was 4 million. Find the 99% confidence interval of the true mean. Assume the variable is normally distributed. Round your answers to at least two decimal places.
______million <μ< _____million
The 99% confidence interval of the true mean is given as follows:
8.56 million < μ < 16.78 million.
What is a t-distribution confidence interval?
The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[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.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 10 - 1 = 9 df, is t = 3.2498.
The parameter values for this problem are given as follows:
[tex]\overline{x} = 12.67, s = 4, n = 10[/tex]
The lower bound of the interval is then given as follows:
[tex]12.67 - 3.2498 \times \frac{4}{\sqrt{10}} = 8.56[/tex]
The upper bound of the interval is then given as follows:
[tex]12.67 + 3.2498 \times \frac{4}{\sqrt{10}} = 16.78[/tex]
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write 3^3 in expanded form and evaluate. can someone help me??
Answer:
27.
Step-by-step explanation:
3^3 = 3 * 3 * 3
= 9 * 3
= 27.
Answer:
IMAO YOU GAVE UP, PSY
Step-by-step explanation:
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME I ALREADY DID NUMBER 2 BTW SO NO NEED JUST PLS HELP IN THE BOTTOM :(
Answer:
3. The equivalent fractions are presented as follows;
[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]
4. The equivalent fractions are presented as follows;
[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]
5. The reason why it works is because [tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]
Step-by-step explanation:
3. Based on the shaded region of the given figures, the two fractions are equivalent
Mathematically, we can show the equivalency of the two fractions as follows;
[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]
Therefore;
[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]
4. From the shaded region of the given figure, the fractions are equivalent
Mathematically, we have;
[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]
Therefore;
[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]
5. The amount of salt required by the recipe = 1/4 teaspoon of salt
The measure of the spoon Jonas has = 1/8 teaspoon
When Jonas adds two 1/8 teaspoons, he gets;
[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}[/tex]
Therefore;
[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]
Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.
yo i really need help please in order to pass this i’ll give a brainliest to anyway who knows the correct answer please no links
all i know is that it would not be 13.9
Answer:
12in
Step-by-step explanation:
this is the only subject i'm good at in math XDDD.
round 3.060 to the nearest whole number.
Answer:
3
Step-by-step explanation:
dude kinda obv that its 3
Answer:
answer would be 3
Step-by-step explanation:
solve the system of substitution y=-2x y=5x-21
Answer:
x = 3 is the answerStep-by-step explanation:
1. Write the equation.
y = -2x
y = 5x - 21
2. Substitute the values.
(-2x) = 5x - 21
3. Solve the equation.
-2x = 5x - 21
-5x - 5x
-7x = -21
4. Both negatives cancel
7x = 21
5. Divide both sides by 7
7x = 21
/7 /7
6. x = 3
7. Check the answer.
-2(3) = 5(3) - 21
-6 = 15 - 21
-6 = -6
x = 3 is the answerHope this helped,
Kavitha
P.S Sorry for taking so long.
Help!! Please!!!!!!!
Answer:
E
Step-by-step explanation:
What is the solution to the system of
equations graphed below?
a.(-13,-20)
b.(-15,-22)
c.(-1,-8)
d.(-10,-15)
Answer:
(-13,-20)
Step-by-step explanation:
We know that the graph with x-intercept at (7,0) and y-intercept at (0,-7) is y = x-7
and the second equation is y = 2x+6
Therefore, we have two equations.
[tex] \large{ \begin{cases} y = x - 7 \\ y = 2x + 6 \end{cases}}[/tex]
Because both equations are equal (y=y)
x-7=2x+6
-7-6=2x-x
-13=x
We know the value of x, but not y-value. We substitute the value of x to get the value of y.
Substitute in any given equations which I will be substituting in the first equation.
y=-13-7
y = -20
Therefore when x = -13, y = -20
In coordinate form, we can write as (-13,-20).
If you have any questions, feel free to ask.
Plzzz help me!!!!!!!!
A person pushes a car with a force of 50 pounds. The car moves 5 feet into his garage. How much work was done?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
plllllzzz helppppppp
Answer:
5. B
6. A
7. C
Step-by-step explanation:
Answer:
5.) b. 12 - 2x
6.) a. 8x
7.) c. 5d + 3c = 66
Step-by-step explanation:
uhm, I don't really have proof, i've just been doing this for a long time, you're just gonna have to trust me on this one
i really need help so can you plz help meeee
Answer:
5/11 is 0.4555555555555555555555555
so basically the first option out of the two.
U do know you can just calculate this with the calculator right?
dentify all the steps necessary for graphing parametric equations? select all answers that apply. select one or more: a. draw arrows on the curve to show the direction the curve follows b. plot the points c. create a table d. solve the equations for t and plot that point e. connect the points with a dashed line f. connect the points with a smooth curve g. combine both equations into one equation in terms of t h. setup your coordinate plane with t on the horizontal axis
The steps necessary for graphing parametric equations include creating a table, solving the equations for t and plotting those points, connecting the points with a smooth curve, and setting up the coordinate plane with t on the horizontal axis (c, d, f, h).
Create a table: Choose a range of values for t and calculate the corresponding values for x and y using the parametric equations. List these values in a table.
Solve the equations for t and plot those points: Solve the parametric equations separately for t to obtain the x and y coordinates. Plot these points on the coordinate plane.
Connect the points with a smooth curve: Once all the points are plotted, connect them with a smooth curve. This curve represents the graph of the parametric equations.
Set up the coordinate plane with t on the horizontal axis: Label the horizontal axis as t and the vertical axis as either x or y. This allows you to visualize how the x and y values change with respect to the parameter t.
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A method of assigning probabilities based upon personal judgment is referred to as the:
a. subjective method b. classical method c, Crelative frequency method
d, . non-probabilistic method.
A method of assigning probabilities based upon personal judgment is referred to as the subjective method. The correct answer is a.
The subjective method of assigning probabilities is based on personal judgment or subjective beliefs about the likelihood of events occurring. It involves incorporating individual knowledge, experience, and intuition to estimate the probabilities of different outcomes.
Unlike the classical method, which assigns probabilities based on equally likely outcomes, or the relative frequency method, which uses observed frequencies to determine probabilities, the subjective method relies on individual opinions and subjective assessments of probabilities.
In the subjective method, probabilities are not determined through mathematical calculations or empirical data. Instead, they are based on an individual's expertise, opinions, and subjective reasoning.
This method is commonly used in situations where objective data or historical information is limited or unavailable, such as in decision-making under uncertainty or when dealing with complex and uncertain scenarios.
The correct answer is a.
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Write the integer that represents the opposite of each situation
100 feet above sea level
evaluate sum in closed form
f(x) = sin x + 1/3 sin 2x + 1/5 sin 3x + ....
The sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).
What is sum of series?
A series' sum is the sum of the words or list of numbers that make up the series. If a series has a sum, it will be one integer (or fraction), such as 0, 1/2, or 99.
As given series is,
f(x) = sinx + sin(2x)/3 + sin(3x)/5+.....
The series function is trigonometric function such as sinx, sin(2x), sin(3x).
The nth term of series is sin(nx).
The coefficient of series is 1, 1/3, 1/5.
The coefficient of nth terms is 1/(2n - 1).
Sum of series is,
= infinity ∑(n = 1) sin(nx)/(2n - 1).
Hence, the sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).
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A box contains 12 cereal bars. The empty box weighs 1.75 oz. The box and cereal bars together weighs 18.55 oz. How much does each cereal bar weigh?
Answer:
Each cereal bar weighs 16.8 oz
Step-by-step explanation:
Multiply 12 times 1.4 to get 16.8
Add 16.8 and 1.75 to get 18.55
Hope this helps! Pls mark brainliest
Can I get help with number 15 am stuck
Find the equation of the line for the following
Find the equation of the line for the following: -) passing through (3, 2) with slope 4. 8) passing through (4, -2) and (5,6). - passing through (3,-1) and parallel to the line 6x +2y +4.
a) The equation of the line passing through the point (3, 2) with slope 4 is y - 2 = 4(x - 3).
b. The equation of the line passing through (4, -2) and (5,6) is y + 2 = 8(x - 4).
c) The slope of the line 6x +2y +4 is -3.
a. To derive the equation, we use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m represents the slope.
Substituting the given values into the equation, we have:
y - 2 = 4(x - 3)
This equation can be further simplified if required.
b) The equation of the line passing through the points (4, -2) and (5, 6) can be found using the slope-intercept form, y = mx + b.
First, we calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁).
m = (6 - (-2)) / (5 - 4) = 8.
Next, we substitute one of the given points and the calculated slope into the slope-intercept form:
y - y₁ = m(x - x₁).
y - (-2) = 8(x - 4).
Simplifying the equation:
y + 2 = 8(x - 4).
c) To find the equation of the line passing through the point (3, -1) and parallel to the line 6x + 2y + 4 = 0, we first need to determine the slope of the given line.
Rearranging the equation 6x + 2y + 4 = 0, we have:
2y = -6x - 4,
y = -3x - 2.
The given line has a slope of -3.
Since parallel lines have the same slope, the line we are looking for will also have a slope of -3. Using the point-slope form with the given point (3, -1), the equation becomes:
y - (-1) = -3(x - 3).
Simplifying:
y + 1 = -3(x - 3).
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Graph y = -x^2 – 2. Identify the vertex of the graph. Tell whether it is a minimum or maximum.
Answer:
Maximum, and (0, -2)
Step-by-step explanation: