What is the measure of the missing angle?

At the end of 6 years, the balance in Lee's account will be approximately $75,481.80. To calculate the balance in Lee's account at the end of 6 years, we need to consider the two deposits separately and calculate the interest earned on each deposit.

First, let's calculate the balance after the initial deposit of $15,300. The interest is compounded semiannually at a rate of 8%. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the principal amount (initial deposit)

r = annual interest rate (8% = 0.08)

n = number of compounding periods per year (semiannually = 2)

t = number of years

For the first 3 years, the balance will be:

A1 = 15,300(1 + 0.08/2)^(2*3)

A1 = 15,300(1 + 0.04)^(6)

A1 ≈ 15,300(1.04)^6

A1 ≈ 15,300(1.265319)

A1 ≈ 19,350.79

Now, let's calculate the balance after the additional deposit of $40,300 at the beginning of year 4. We'll use the same formula:

A2 = (A1 + 40,300)(1 + 0.08/2)^(2*3)

A2 ≈ (19,350.79 + 40,300)(1.04)^6

A2 ≈ 59,650.79(1.265319)

A2 ≈ 75,481.80

Note: The table mentioned in the question was not provided, so the calculations were done manually using the compound interest formula.

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To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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Step-by-step explanation:

15x²-14x+3

Product =45

Sum=-14

=(-9,-5)

15x²-9x-5x+3

3x(5x-3)-1(5x+3)

=(5x-3)(3x-1)

There is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less.

To find the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60, we can use the sampling distribution of the sample proportion and the z-score.

Given:

Sample size (n) = 100

Observed sample proportion ) = 0.48

True population proportion (p) = 0.60

To find the probability, we need to standardize the observed sample proportion using the z-score formula:

z = ( - p) / √(p * (1 - p) / n)

Substituting the values:

z = (0.48 - 0.60) / √(0.60 * (1 - 0.60) / 100)

= -0.12 / √(0.24 / 100)

= -0.12 / √0.0024

= -0.12 / 0.049

Using a standard normal distribution table or a statistical calculator, we can find the probability associated with the z-score.

The probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is the probability to the left of the z-score obtained.

P ≤ 0.48) = P(z ≤ -0.12)

Using a standard normal distribution table, we find that the probability of z ≤ -0.12 is approximately 0.4522.

Therefore, the probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is approximately 0.4522 or 45.22%.

This means that there is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less, if the true population proportion is 0.60.

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a. 0.5(x)(x + 2) = 24 can be used tο find the lengths οf the legs οf the triangle.

An equatiοn is a mathematical statement that uses an equal sign (=) tο shοw that twο expressiοns are equal.

The area οf right angled triangle is given by 1/2 × h × b

Here, h = x + 2

and b = x

The area of the right triangle shown is 24 square feet.

With that in mind:

Area = 1/2 × x × x + 2

or

0.5(x)(x + 2)

= 24

Thus, a. 0.5(x)(x + 2) = 24 can be used to find the lengths of the legs of the triangle

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Complete question:

The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle?

Select three options.

a. 0.5(x)(x + 2) = 24

b. x(x + 2) = 24

c. x² + 2x – 24 = 0

d. x² + 2x – 48 = 0

e. x² + (x + 2)² = 100

Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Answer:

V≈2143.03cm³

Step-by-step explanation:

The volume of the sphere is 2143.57 cm³.

A = 4 × π × r², where 'r' is the radius of the sphere.

V = (4/3) × π × r³

For given example,

a surface area of the sphere is 803.84 cm^2.

⇒ A = 803.84 cm²

Using the formula of the surface area of the sphere,

⇒ 4πr² = 803.84

⇒ r² = 64

⇒ r = 8 cm

Using the formula of the volume of the sphere,

⇒ V = (4/3) × π × r³

⇒ V = (4/3) × 3.14 × 8³

⇒ V = 2143.57 cm³

Therefore, the volume of the sphere is 2143.57 cm³.

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Answer: 113.4 miles

Step-by-step explanation:

I think this correct because 7.56 x 5 = 37.8   then 21 days is 3 weeks so 37.8 x 3 = 113.4

Answer:

\( \displaystyle \large \boxed{x = \frac{ - 3 \pm \sqrt{ 7}i }{2} }\)

Step-by-step explanation:

We are given the equation:

\( \displaystyle \large{ {x}^{2} + 3x + 4 = 0}\)

Since the expression is not factorable with real numbers, we use the Quadratic Formula.

Quadratic Formula

\( \displaystyle \large{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }\)

Compare the expression:

\( \displaystyle \large{a {x}^{2} + bx + c = {x}^{2} + 3x + 4 }\)

a = 1

b = 3

c = 4

Substitute a = 1, b = 3 and c = 4 in the formula.

\( \displaystyle \large{x = \frac{ - 3 \pm \sqrt{ {3}^{2} - 4(1)(4)} }{2(1)} } \\ \displaystyle \large{x = \frac{ - 3 \pm \sqrt{ 9 - 16} }{2} } \\ \displaystyle \large{x = \frac{ - 3 \pm \sqrt{ - 7} }{2} }\)

Imaginary Unit

\( \displaystyle \large{i = \sqrt{ - 1} }\)

Therefore,

\(\displaystyle \large{x = \frac{ - 3 \pm \sqrt{ 7} \sqrt{ - 1} }{2} } \\ \displaystyle \large{x = \frac{ - 3 \pm \sqrt{ 7}i }{2} }\)

Answer:

$6.50 per candle

Step-by-step explanation:

19.50 / 3 = 6.50

Answer:

$6.50

Step-by-step explanation:

$19.50 divided 3 is 6.50

Answer:

5:1

Step-by-step explanation:

10 the greatest common factor.

50 divided by 10 is 5

10 divided by 10 is one

5 comes first then 1.

Answer:

5:1

Step-by-step explanation:

I hope this helps!

Answer: You can buy at most, 120 bagels.

Plz mark brainliest:)

Answer:

120 bagels:) have a great day!!!!!!!!!!!!!!!

Step-by-step explanation:

The degrees of freedom for the F test in a one-way ANOVA are D. (c - n) and (n - 1).

The numerator degrees of freedom (c - n) is the number of groups (c) minus the number of observations in each group (n). The denominator degrees of freedom (n - 1) is the total number of observations (n) minus the number of groups (1). These degrees of freedom are used to calculate the F statistic, which is used to determine if there is a significant difference between the means of the groups. The degrees of freedom for the F test in a one-way ANOVA are given by two values. The first value represents the degrees of freedom between groups (DFbetween), and the second value represents the degrees of freedom within groups (DFwithin). The correct is B. (c - 1) and (n - c), where 'c' represents the number of groups (categories) and 'n' represents the total number of observations (data points) in the dataset.

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The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

The perimeter of a rectangle is P = 2(L + W) where

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

The area of the rectangle, A = LW where

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

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Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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The side triangle symbol in abstract algebra typically represents the concept of "normal subgroup."

In abstract algebra, a group is a mathematical object consisting of a set of elements and an operation that combines any two elements to form a third element. A subgroup is a subset of a group that also forms a group under the same operation. A normal subgroup is a subgroup that is invariant under conjugation by elements of the larger group.

In other words, for any element of the larger group, if you conjugate the elements of the subgroup by that element and then take the inverse of the element, the resulting set of elements is still a subgroup of the larger group. The symbol for normal subgroup is a triangle with a vertical line on one side.

Therefore, the side triangle symbol in abstract algebra represents the concept of "normal subgroup."

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If the function approaches a specific value (y = c) as x approaches infinity or negative infinity, then it has a horizontal asymptote at y = c.

To determine if a function has a horizontal asymptote, consider the behavior of the function as x approaches positive or negative infinity. The main idea is to analyze the end behavior of the function.

Degree of Polynomials:

If the degree of the numerator is less than the degree of the denominator, the function has a horizontal asymptote at y = 0 (the x-axis). If the degree of the numerator is equal to the degree of the denominator, divide the coefficients of the highest degree terms. The resulting ratio determines the horizontal asymptote. If the degrees are unequal, there is no horizontal asymptote.

Limits:

Take the limit of the function as x approaches positive or negative infinity. If the limit evaluates to a finite value, that value represents the horizontal asymptote. If the limit is infinite (∞) or does not exist, there is no horizontal asymptote.

Infinity:

If the function involves terms like exponential functions or logarithmic functions, analyze their behavior as x approaches infinity. Exponential functions with positive exponents tend to infinity, while those with negative exponents approach zero. Logarithmic functions tend to negative infinity as x approaches zero.

By considering these methods, you can determine if a function has a horizontal asymptote and find its equation or behavior as x approaches infinity or negative infinity. Remember to apply these techniques with caution and consider the specific characteristics of the function being analyzed.

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Using translation concepts, the function whose graph is plotted is given by:

y = 0.5cos(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the y-intercept is different of zero, hence it is a cosine function. The amplitude is of 0.5, hence the function is multiplied by 0.5, that is, y = 0.5cos(x), which means that option C is correct.

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The probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

The expression that represents the probability of getting exactly 3 heads when a penny is flipped 9 times is:

p(3 successes) = (9 C 3) * (0.5)^3 * (0.5)^(9-3)

Where:

"p(3 successes)" represents the probability of getting 3 heads.

"9 C 3" represents the number of ways to choose 3 flips out of 9 flips (also known as the binomial coefficient). This is calculated as 9! / (3! * (9-3)!), which simplifies to 84.

"0.5" represents the probability of getting heads on a single flip of a fair penny.

"(0.5)^(9-3)" represents the probability of getting tails on the remaining 6 flips, since the probability of getting either heads or tails on a single flip is 0.5.

Simplifying the expression, we get:

p(3 successes) = (9 C 3) * (0.5)^9

p(3 successes) = (84) * (0.5)^9

p(3 successes) ≈ 0.1641

Therefore, the probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

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Answer:

Part 1

1. The amount of money that the jury will award the defendant is $39,405.80.

2. The sale price of the dress is $24.

3. John will keep $71.75 of his check.

4. The population of the town in 1980 was 4,560.

5. 203 students voted for Mary.

6. Mrs Eversole will pay $17.50.

7. 180 tickets have been sold.

8. The trip will cost $280 next month.

Part 2

9. The actual height of the chimney is 28 ft.

10. The number of books that are usually checked out in a day is 717.

11. Manuel's baseball cards' total collection will be 336.

12. The chalk will be as big as 5.31 ounces.

13. Wanda shoots are 25.

14. From Newmark to Briton will be about 188 miles.

15. There were 30 questions on the test.

Part 3

16. Anfernee Hardaway missed 19%.

17. The percentage of students that liked turkey the best is 16%.

18. The percentage of the time, Barry reached the base is 53%.

19. The percentage of the class that passed the test is 92%.

Step-by-step explanation:

a. 5% of $788,116 = $39,405.80

b. 75% of $32 = $24

c. John's earnings = $6.25 * 14 = $87.50

Taxes = 18%; therefore, take home = 82% (100 - 18)

He will keep 82% of $87.50 = $71.75

d. Population in 1980 = 95% of 4,800 = 4,560

e. 45% of 452 = 203

f. Mrs Eversole will pay $250 * 0.07 = $17.50

g. 36% of 500 = 180

h. 80% of $350 = $280

i. Actual height = 37.8/135 * 100 = 28 ft

j. If 41% = 294, then 100% = 294/41 * 100 = 717

k. Manuel's total collection = 42/12.5% * 100% = 336

l. If 32% = 1.7 ounces, then the chalk will be 1.7/32% * 100 = 5.31 ounces.

m. If 56% = 14, then Wanda shot 14/56% * 100% = 25

n. Newmark to Briton will be 160/85% * 100 = 188 miles

o. If 80% = 24, then the number of questions = 24/80% * 100 = 30

p. Anfernee missed 36 shots = 19% (36/191 * 100)

q. 36/225 * 100 = 16%

r. The percentage of the time, Barry reached the base is 342/644 * 100 = 53%

s. 23/25 * 100 = 92%

Answer:

x = 5

Step-by-step explanation:

12x + 5 = 65

subtract 5 from both sides

12x + 5 - 5 = 65 - 5

12x = 60

divide by 12

x = 5

Coressponding angles in parallel lines are equal and for u and v to be parallel,

So we have,

\(12x + 5 = 65\)

\(12x = 65 - 5\)

\(12x = 60\)

\(x = \frac{60}{12} \)

\(x = 5\)

Hence the value of x must be 5° to make the lines u and v parallel

The factors indicated, are classified according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

Movement along the aggregate demand curve

Shift of the aggregate demand curve

An aggregate demand curve depicts the total domestic expenditure on goods and services at each price level.

The AD curve is trending higher due to rising economic prosperity. People's spending grows as their income rises, leading to an increase in AD and vice versa. As a result of the positive link between income and AD, the AD curve slopes higher.

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Full Question:

Classify each factor according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

The probability of picking a card less than 7 from a standard deck of cards is 2/13.

To find the probability (P) of picking a card less than 7, we need to determine the number of favorable outcomes (cards less than 7) and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are the cards with values less than 7, which are 5 and 6. The total number of possible outcomes is the total number of cards in the deck, which depends on the specific deck being used.

Assuming a standard deck of 52 cards, there are four 5s and four 6s, making a total of eight favorable outcomes.

Therefore, P(less than 7) = favorable outcomes / total outcomes = 8 / 52.

Simplifying the fraction, we find that P(less than 7) = 2 / 13.

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Answer: image 4

Step-by-step explanation: did it on edge and was correct

The final image after composition ry-axis ◦ T3, -1 is Figure 4.

Thus, figure 4 is correct figure.

Given transformation rule, ry-axis ◦ T3, -1.

First, reflect the coordinates of LMNP across y axis by the rule

(x, y) -> (-x, y)

Then, translation 3 units to the right and 1 unit down

So, if the original point was (x, y), after the translation it becomes (x + 3, y -1 ).

Now, the coordinates of LMNP are:

L (-5, 1), M (-5, 4), N(-3, 4) and P(-3, 1).

Then, after reflection from y axis

L' (5, 1), M' (5, 4), N'(3, 4) and P'(3, 1).

and, after Transformation T (3, -1) the coordinates are:

L' (5+3, 1-1)  - L"(8, 0),

M' (5 +3, 4-1) = M"(8, 3),

N'(3+3, 4-1) = N"(6, 3),

P'(3+3, 1-1) = P"(6, 0)

Therefore, the required transformed figure is (4).

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a = -1/2

Hope this helps :)

Answer:

a = -1/2

Step-by-step explanation:

-1/4a - 4 = 7/4a - 3

-a/2^2 - 4 = 7/ 2^2 a - 3

(-a) - ( 2^2) 4 / 2^2 = 7a/ 2^2 - 3

a = -1/2

I know this confusing but this how I got the answer.

I hope this helps

Answer:

x = 2.5 or 5/2.

Step-by-step explanation:

They're congruent angle, so set them equal to each other

5x + 13 = x + 23

Solve for x:

4x = 10

x = 10/4 = 5/2 = 2.5