An investment of $600 is made into an account that earns 6. 5% annual simple interest for 15

years. Assuming no other deposits or withdrawals are made, what will be the balance in the

account?

The best estimate of ∫(4 to 11) f(x) dx using a trapezoidal sum with 3 subintervals can be found by dividing the interval into three equal subintervals and applying the trapezoidal rule.

The trapezoidal rule is a method for approximating the definite integral of a function over an interval. It involves dividing the interval into subintervals and approximating the area under the curve by the sum of trapezoids formed between adjacent points.

In this case, we are given the interval from 4 to 11 and want to estimate the integral of f(x) over this interval using a trapezoidal sum with 3 subintervals. To do this, we divide the interval into three equal subintervals: [4, 6], [6, 8], and [8, 11]. Then, we apply the trapezoidal rule to each subinterval and sum up the results.

The trapezoidal rule states that the area under each subinterval can be approximated as (b-a) * (f(a) + f(b)) / 2, where a and b are the endpoints of the subinterval.

By applying the trapezoidal rule to each subinterval and summing the results, we obtain the best estimate of the integral.

To learn more about trapezoidal rule visit:

brainly.com/question/30401353

#SPJ11

Answer:\(g(x)=\frac{3}{7}(21(x+5))^{1/2}\)

Step-by-step explanation:

Transformation rule:

Shifting by k units left : \(f(x)\to f(x+5)\)

Dilation by a factor of h units: \(f(x)\to hf(x)\)

Let g be a horizontal shrink by a factor of 3/7, followed by a translation 5 units left  of the graph of \(f(x)=(21x)^{1/2}\)

The rule for g described by the transformations of the graph of f. : \(g(x)=\frac{3}{7}(21(x+5))^{1/2}\)

Answer:

ab+ac=a(b+c)

where a is the greatest common factor

find gcf of each

factor each

18=2*3*3

12=2*2*3

GCF=2*3=6

so

18+12=6(3)+6(2)=6(3+2)

Step-by-step explanation:

The radius of convergence and interval of convergence of the series, [infinity] xn / 9^(7n!) n = 1, is  R = ∞.

To determine the radius of convergence and interval of convergence of the series, [infinity] xn / 9^(7n!) n = 1, we shall apply the ratio test.

Firstly, let's write down the series to be tested with the general term written explicitly.

[infinity] xn / 9^(7n!) n

= 1x_n

= x_n9^(7n!)x_(n+1)

= x_(n+1)9^(7(n+1)!)

Thus, we can write out the ratio as: |x_(n+1)|9^(7(n+1)!)|x_n|9^(7n!)

The above equation is only valid when n is sufficiently large. This is because for n < N (N some positive integer), the values of the ratio test might be undefined (or meaningless) for one reason or another.

To make the calculation of the ratio easier, we shall take the absolute value of each term in the above equation.

Hence, |x_(n+1)| / |x_n| = 9^(7n! - 7(n+1)!)

Now we are able to find the radius of convergence. The ratio test tells us that a series is convergent if the ratio of successive terms approaches zero as n approaches infinity.

We can write this mathematically as: lim_(n->∞) |x_(n+1)| / |x_n| < 1

For the series given in this question, this condition is equivalent to: lim_(n->∞) 9^(7n! - 7(n+1)!) < 1

Simplifying, we get: lim_(n->∞) 9^(-7n!) / 9^(-7(n+1)!) < 1lim_(n->∞) 1 / 9^7 < 1

Since the limit is less than 1, the series is convergent.

The radius of convergence is: R = ∞

Interval of convergence can be obtained from the formula: [-R, R].

Therefore, interval of convergence of the series is (-∞, ∞).

Know more about the radius of convergence

https://brainly.com/question/17019250

#SPJ11

Answer:

y = 9

Step-by-step explanation:

\(\frac{2}{6}\) = \(\frac{y}{27}\) ( cross- multiply )

6y = 2 × 27 = 54 ( divide both sides by 6 )

y = 9

Answer:

Step-by-step explanation: From the question 2/6 = y/ 27

Cross multiply

It becomes 2 * 27 = 6 * y

54 = 6y

Make y the subject

y = 54/ 6

y = 9

The sample size needed is 103.

Therefore, the sample size needed to construct a 96% confidence interval with a margin of error of no more than 7% to estimate the proportion, without any knowledge of the population proportion, to estimate the proportion of tips that exceed 18% of its dinner bills is 103.

To know more about simple random sampling, visit the link : https://brainly.com/question/13219833

#SPJ11

Answer:

63.6

Step-by-step explanation:

diameter = 9

radius = 9/2= 4.5

Area of circle = 22/7 × radius²

so,

22/7×4.5×4.5 = 63.6428571

if we round off it to nearest tenth it will be = 63.6

Answer:

The root of    x = -2 + √2

Step-by-step explanation:

Step(i):-

Given \(\sqrt{2x^{2} } + x +\sqrt{2} = 0\)

      ⇒    \(\sqrt{2} } ( x^2 ) ^{\frac{1}{2} } + x +\sqrt{2} = 0\)

      ⇒   \(\sqrt{2}x + x +\sqrt{2} = 0\)

     ⇒      \((\sqrt{2} + 1) x = - \sqrt{2}\)

           \(x = \frac{-\sqrt{2} }{(\sqrt{2} + 1)}\)

Step(ii):-

Rationalizing

     \(x = \frac{-\sqrt{2} }{(\sqrt{2} + 1)} X \frac{(\sqrt{2} - 1)}{(\sqrt{2} - 1)}\)

Apply ( a-b ) ( a+b) = a²-b²

    \(x = \frac{-\sqrt{2}(\sqrt{2} -1) }{(\sqrt{2})^{2} - 1^{2} )} = \frac{-(2-\sqrt{2} }{2-1}\)

The root of    x = -2 + √2

The angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

We know that the rectangle has sides of length 4 ft and 5.5 ft, so we can use the Pythagorean Theorem to find the length of the diagonal \($BD$\):

\($$ BD^2 = 4^2 + 5.5^2 $$\)

\($$ BD^2 = 16 + 30.25 $$\)

\($$ BD^2 = 46.25 $$\)

\($$ BD = \sqrt{46.25} $$\)

\($$ BD = 6.8 \text{ ft (rounded to one decimal place)} $$\)

Now, we can use the Law of Cosines to find the angle between sides \($AB$\)and \($AD$\) in triangle \($ABD$\):

\($$ \cos(A) = \frac{BD^2 + AB^2 - AD^2}{2 \cdot BD \cdot AB} $$\)

\($$ \cos(A) = \frac{6.8^2 + 4^2 - 5.5^2}{2 \cdot 6.8 \cdot 4} $$\)

\($$ \cos(A) = 0.5471 $$\)

\($$ A = \cos^{-1}(0.5471) $$\)

\($$ A = 56.1^\circ \text{ (rounded to one decimal place)} $$\)

Similarly, we can use the Law of Cosines to find the angle between sides \($BC$\) and \($CD$\) in triangle:

\($$ \cos(B) = \frac{BD^2 + BC^2 - CD^2}{2 \cdot BD \cdot BC} $$\)

\($$ \cos(B) = \frac{6.8^2 + 5.5^2 - 4^2}{2 \cdot 6.8 \cdot 5.5} $$\)

\($$ \cos(B) = 0.7416 $$\)

\($$ B = \cos^{-1}(0.7416) $$\)

\($$ B = 42.5^\circ \text{ (rounded to one decimal place)} $$\)

Therefore, the angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

To learn more about Angles refer here:

https://brainly.com/question/7116550

#SPJ11

Answer:

Step-by-step explanation:

Essentially, we can use the pythagorean rule that:

a^2+b^2=c^2

c^2 resembles the hypotenuse, which is almost always the largest number. therefore, we simply have to find two which equal the largest side:

9^2+40^2=41^2

81+1600=1681

1681=1681

Based on this math, A is our right angle!

Hope this helps!

The sign of the x-component and y-component of the vector will be negative and positive, respectively. The magnitude of vector A is approximately 8.944m, and the angle it makes with the positive x-axis is approximately 63.43 degrees.

(a) To calculate the magnitude of vector A with x-component 4m and y-component 8m, we can use the Pythagorean theorem. The magnitude (|A|) is given by the square root of the sum of the squares of the components: |A| = √(4^2 + 8^2) = √(16 + 64) = √80 ≈ 8.944m.

(b) To calculate the angle that vector A makes with the positive x-axis, we can use the inverse tangent function. The angle (θ) is given by the arctangent of the ratio of the y-component to the x-component: θ = tan^(-1)(8/4) ≈ 63.43 degrees.

In summary, the magnitude of vector A is approximately 8.944m, and the angle it makes with the positive x-axis is approximately 63.43 degrees.

Learn more about vector here:

https://brainly.com/question/24256726

#SPJ11

Answer:

Speed of Jennifer on Sunday \(=45\) mi/hr

Step-by-step explanation:

Let speed of Jennifer on Saturday be x mi/hr

On Saturday morning, it took Jennifer 3.6 hours to drive to her mother's house for the weekend.

Distance travelled by Jennifer on Saturday = Speed × Time \(=3.6x\) miles

Speed of Jennifer on Sunday = \((x-5)\) mi/hr

On Sunday evening, due to  heavy traffic, it took Jennifer 4 hours to return home.

Distance travelled by Jennifer on Sunday = Speed × Time \(=4(x-5)\) miles

As distance is obviously same on both Saturday and Sunday,

\(3.6x=4(x-5)\\3.6x=4x-20\\20=4x-3.6x\\20=0.4x\\x=\frac{20}{0.4}\\ x=50\)

Therefore,

Speed of Jennifer on Sunday = \((50-5)=45\)  mi/hr

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), \(\sqrt{35}\) is the side length of the pink square and \(\sqrt{50}\) is the side length of the green square.

That means a = \(\sqrt{35}\) and b = \(\sqrt{50}\) , so...

\((\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}\)

35 + 50 = c^2

85 = c^2

\(\sqrt{85} = c\)

Now we need to square the square root of 85 to find the area of the blue square.

\((\sqrt{85})^{2} = Area of blue square\)

85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

\(x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5\)

x = 5 units

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

To know more about measure, visit:

https://brainly.com/question/28913275

#SPJ11

The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

Learn more about probability here

brainly.com/question/28326750

#SPJ4

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example'

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that \(X\) is less than or equal to is 0.1,

the probability that \(X\) is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that \(X\) is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that \(X\) is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

To learn more about cumulative distribution, visit

brainly.com/question/19884447

#SPJ4

Using the z table, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

\(\alpha\)=1−0.82

\(\alpha\)=0.18

Now finding the value of \(\alpha\)/2

\(\alpha\)/2=0.18/2

\(\alpha\)/2=0.09

Now finding the value of \(z_{a/2}\).

\(z_{0.82}\) = 1.34

Hence, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

To learn more about standard normal random variable link is here

brainly.com/question/14782203

#SPJ4

The pattern for the sequence 8, 17, 26, 35, 44, … is 9n - 1

The pattern in the question is given as

8, 17, 26, 35, 44, …

In the above expressions and pattern, we can see that

The current term is added to 9 to get the next term

From the above, we have the following

This means that the pattern is an arithmetic sequence with the following features

a = 8

d = 9

An arithmetic sequence is represented as

f(n) = a + (n - 1)d

When the values of "a" and "d" are substituted in the above equation, we have the pattern to be

f(n) = 8 + (n - 1)9

So, we have

f(n) = 8 + 9n - 9

Evaluate

f(n) = 9n - 1

Hence, the pattern for the sequence is 9n - 1

Read more about sequence at

brainly.com/question/6561461

#SPJ1

Answer:

2. a & c

3. a, b & c

Step-by-step explanation:

Substitute each solutions to the question to see if you get the answer

a. 5(2)-0=10 -- so (2,0) is the solution

b. 5(3)-0=15 -- (3,0) is not the solution

c. 5(0)-(-10)=10 -- (0,-10) is the solution

d. 5(1)-(1)=4 -- (1,1) is not the solution

a. -(-4)+ 6(1) = 10 -- so (-4,1) is the solution

b. -(-22)+ 6(-2) = 10 -- so (-22,-2) is the solution

c. -(2)+ 6(2) = 10 -- so (2,2) is the solution

d. -(10)+ 6(0) = - 10 -- so (10,0) is not the solution

The chi-square statistic is used to determine whether there are differences between two nominally scaled variables. Chi-Square is a statistical test used to compare two nominal variables to determine whether they differ.

The Chi-Square test is used to test for differences between two groups. When you want to compare groups or examine the relationship between two variables, this test is useful. The chi-square test is a method of statistical inference that can be used to compare observed frequencies with expected frequencies, allowing us to determine whether there is a meaningful difference between them. When the p-value obtained from a chi-square test is less than 0.05, it is generally considered statistically significant.

Learn more about Chi-Square

https://brainly.com/question/32595988

#SPJ11

The final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.

Considering the triangle formed by the ship ∆ABC where A, B and C are the points for; the port, where the ship changes its course, and its final bearing. The final distance "a" of the port from the ship is calculated with cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

a² = 40² + 70² - 2(40)(70)cos82°

a² = 1600 + 4900 - 5600cos82°

a² = 5720.63 {take square root of both sides}

a = 75.63

For the triangle ABC, by sine rule;

a/sinA = b/sinB = c/sinC

75.63/sin82° = 70/sinC

C = sin⁻¹(70 × sin82°/75.63) {by cross multiplication}

C = 66.43

angle C = 60 + 6.43 {60° is an alternate angle with angle 30° at the point B where the ship chenged course and 6.43° is a complementary angle at the 3rd quadrant of point C}

The final bearing of the port from the ship is calculated as;

180° + (90 - 6.43)° = 263.57°

Therefore, the final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.

Know more about bearing here:https://brainly.com/question/22518031

#SPJ1

The area of triangle ABC = (40/3) sq.cm.

Given that triangle ABC with midpoints M and N for AB and AC respectively, Bn intersects CM at O and area of triangle MON is 4 square centimeters. To find the area of ABC, we need to use the concept of the midpoint theorem and apply the Area of Triangle Rule.

Solution: By midpoint theorem, we know that MO || BN and NO || BM Also, CM and BN intersect at point O. Therefore, triangles BOC and MON are similar (AA similarity).We know that the area of MON is 4 sq.cm. Then, the ratio of the area of triangle BOC to the area of triangle MON will be in the ratio of the square of their corresponding sides. Let's say BO = x and OC = y, then the area of triangle BOC will be (1/2) * x * y. The ratio of area of triangle BOC to the area of triangle MON is in the ratio of the square of the corresponding sides. Hence,(1/2)xy/4 = (BO/MO)^2   or   (BO/MO)^2 = xy/8Also, BM = MC = MA and CN = NA = AN Thus, by the area of triangle rule, area of triangle BOC/area of triangle MON = CO/ON = BO/MO = x/(2/3)MO  => CO/ON = x/(2/3)MO Also, BO/MO = (x/(2/3))MO  => BO = (2/3)xNow, substitute the value of BO in (BO/MO)^2 = xy/8 equation, we get:(2/3)^2 x^2/MO^2 = xy/8   =>  MO^2 = (16/9)x^2/ySo, MO/ON = 2/3  =>  MO = (2/5)CO, then(2/5)CO/ON = 2/3   =>  CO/ON = 3/5Also, since BM = MC = MA and CN = NA = AN, BO = (2/3)x, CO = (3/5)y and MO = (2/5)x, NO = (3/5)y Now, area of triangle BOC = (1/2) * BO * CO = (1/2) * (2/3)x * (3/5)y = (2/5)xy Similarly, area of triangle MON = (1/2) * MO * NO = (1/2) * (2/5)x * (3/5)y = (3/25)xy Hence, area of triangle BOC/area of triangle MON = (2/5)xy / (3/25)xy = 10/3Now, we know the ratio of area of triangle BOC to the area of triangle MON, which is 10/3, and also we know that the area of triangle MON is 4 sq.cm. Substituting these values in the formula, we get, area of triangle BOC = (10/3)*4 = 40/3 sq.cm. Now, we need to find the area of triangle ABC. We know that the triangles ABC and BOC have the same base BC and also have the same height.

Know more about triangle here:

https://brainly.com/question/29083884

#SPJ11

Answer:

Step-by-step explanation:

I don’t know why they bother teaching recursive formulas as the explicit is almost always used :)

For 2,9,16,23...

Recursive is a(n+1)=an+7

Explicit is an=2+7(n-1)

(or more neatly an=7n-5)

For 2,14,98,686...

Recursive is a(n+1)=7an

Explicit is an=2(7^(n-1))

(or (2/7)7^n )

Answer: Yes, they are similar

Step-by-step explanation:

Angle A is congruent to angle D

Angle B is congruent to angle E

Angle C is congruent to angle F

Therefore, the triangles are similar by the AAA (angle-angle-angle) similarity theorem.

The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

To learn more about Null Hypothesis visit :

brainly.com/question/16261813

#SPJ4

Answer:

It might be weird but i is the answer and I don't know why exactly.

Step-by-step explanation:

I think it's because there is no real number when having a negative square.

Answer:

answer D is correct maybe that help

Answer:5.86 9.26

Step-by-step explanation:

Answer:

For the first one it's 53 small cubes can fit in the right rectangle prism. For the second one the answer is A=120

The probability that their first child will be a phenotypically normal girl is 3/8 or 37.5%.

Lou Gehrig's disease, also known as amyotrophic lateral sclerosis (ALS), is typically considered as an autosomal recessive disease. This means that both copies of the gene responsible for the disease need to be inherited, one from each parent, in order for an individual to be affected by the disease.

Given that the woman and her husband are both carriers of the disease, they each have one copy of the mutated gene and one normal gene. The probability of passing on the mutated gene to their child is 1/2 for each parent since they are carriers.

To determine the probability of their first child being a phenotypically normal girl, we need to consider the inheritance pattern. Let's break it down:

Gender: The probability of having a girl is 1/2, as gender is determined by the combination of the father's sperm (containing either an X or a Y chromosome) and the mother's egg (containing an X chromosome).

Phenotypically normal: For the child to be phenotypically normal, they should inherit at least one normal gene from either parent. The probability of inheriting a normal gene from the mother is 1/2, and the same probability applies for inheriting a normal gene from the father.

Independence: The probability of having a girl and inheriting a normal gene are independent events, so we can multiply their individual probabilities to calculate the combined probability.

Therefore, the probability of having a phenotypically normal girl is:

Probability of being a girl × Probability of inheriting a normal gene

= (1/2) × (1/2)

= 1/4

However, we also need to consider the possibility of having a boy. The probability of having a phenotypically normal boy is also 1/4.

Adding the probabilities of having a phenotypically normal girl and a phenotypically normal boy, we get:

1/4 + 1/4 = 2/4 = 1/2        

Since the question specifically asks for the probability of having a phenotypically normal girl, we divide the probability of a phenotypically normal girl by the total probability of having a child:

(1/4) / (1/2) = 1/4 * 2/1 = 1/2 = 2/4 = 1/2

Therefore, the probability that their first child will be a phenotypically normal girl is 1/2 or 50%.

Visit here to learn more about probability:

brainly.com/question/32117953

#SPJ11