Money Magic
Enzo’s goal was to save $50,000 to make his way to Vegas. How did having a fixed, predetermined goal impact your gameplay?

Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9."

Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment. Here is the loan amortization table for the $210,000, 15-year mortgage with an APR of 3.8%, assuming the borrower pays an extra $100 towards the principal each month:

Month Payment Interest Paid Principal Paid Extra Principal Paid Remaining Balance

1 $1,529 $662 $297 $100 $209,703

2 $1,529 $657 $301 $100 $209,402

3 $1,529 $652 $306 $100 $209,096

4 $1,529 $647 $311 $100 $208,783

5 $1,529 $642 $316 $100 $208,463

6 $1,529 $637 $321 $100 $208,137

7 $1,529 $632 $326 $100 $207,803

8 $1,529 $627 $331 $100 $207,463

9 $1,529 $622 $336 $100 $207,116

10 $1,529 $617 $341 $100 $206,762

11 $1,529 $611 $347 $100 $206,411

12 $1,529 $606 $352 $100 $206,052

13 $1,529 $601 $357 $100 $205,686

14 $1,529 $596 $362 $100 $205,322

15 $1,529 $590 $368 $100 $204,950

16 $1,529 $585 $373 $100 $204,570

17 $1,529 $580 $378 $100 $204,182

18 $1,529 $574 $384 $100 $203,787

19 $1,529 $569 $389 $100 $203,383

20 $1,529 $563 $395 $100 $202,972

21 $1,529 $558 $400 $100 $202,552

22 $1,529 $552 $406 $100 $202,125

23 $1,529 $547 $411  

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Answer:

x^2-11x+28=0

Step-by-step explanation:

(x-7)(x-4)=0

= x^2-7x-4x+28=0

= x^2-11x+28=0

Step-by-step explanation:

The third one is not      all of the others are

a. The critical value(s) is/are z = -1.645, 1.64

b. Fail to reject H0.

There is not sufficient evidence to warrant rejection of the claim that p = 1/2. The test statistic of z = -1.91 is obtained when testing the claim that p = 1/2.

We want to know whether to reject H0 or fail to reject H0 using a significance level of α = 0.10.

Using the standard normal distribution table, the critical value(s) are z = ± 1.645 (rounded to two decimal places).

Since -1.91 is less than -1.645, we fail to reject H0.

In other words, there is not sufficient evidence to warrant rejection of the claim that p = 1/2.

Therefore, the correct conclusion is "Fail to reject H0.

There is not sufficient evidence to warrant rejection of the claim that p = 1/2."

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Since this bakery can make 3 cheesecakes for every 4 blocks of cream cheese, a table that represent the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses is: B. table B.

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

In order to have a proportional relationship, the variables representing the number of blocks of cream cheese and the number of cheesecakes must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3 = 8/6 = 12/9 = 16/12

Constant of proportionality, k = 4/3.

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The height of the parallelogram is 3 cm.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and have the same length. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure). Some common properties of parallelograms include:

The opposite sides of a parallelogram are equal in length.

The opposite angles of a parallelogram are equal in measure.

The consecutive angles of a parallelogram are supplementary (i.e., they add up to 180 degrees).

The diagonals of a parallelogram bisect each other (i.e., they intersect at their midpoint).

Here the given ,

Area of the parallelogram = 18 square centimeters.

Base b = 6 cm

Area of parallelogram = bh square unit

=> 18=6*h

=> h= 18/6 = 3 cm

Hence the height of the parallelogram is 3 cm.

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The exact answer on Edge is

"Use the product of powers property to simplify the numerator by removing the parentheses.  Follow the order of operations by removing the innermost parentheses first.  Cube the quantity to get the product of 2 to the third power, r to the 6th power, and t to the third power, or 2^3r^6t^3 in the numerator. "

Wendy's conclusion is invalid as she cannot generalize her findings as sample size is too small to represent the entire school population accurately.

Wendy's assessment is incorrect. This is due to the fact that she is unable to extrapolate from a sample of just 40 students who play football for the school. The sample size is insufficient to provide an accurate representation of the student body as a whole. Also, the football players might be more prone to injuries than those who don't participate in sports, which could further skew the results.

Moreover, Wendy did not choose the football team members using a random sample approach. Instead, she restricted her questions to those students who were already on the football team, thereby introducing sample bias. She might have unintentionally left out pupils who don't participate in athletics but may nonetheless have hurt themselves while doing other physical activities.

Wendy's assertion that 375 of the school's 1,000 kids have sustained sports-related injuries is therefore unfounded. Wendy would need to employ a more representative and random sampling technique that includes students from various sports teams as well as those who do not play sports in order to draw a reliable conclusion. She would also require a larger sample size to obtain a more accurate representative of the total student body.

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Complete Question: Wendy questioned the 40 members of the varsity football team about their experiences with sports-related injuries. "Sure," fifteen football players answered. Wendy came to the conclusion that 375 of the 1,000 pupils at her school had had sports-related injuries. Decide if Wendy's conclusion is true or not.

Answer:

14.65

Step-by-step explanation:

3.6 ft + 6.25+4.8=14.65

Given that AB is a diameter. |BC| = |CD| and AÔD = 64°, The angles  of the quadrilateral ABCD is 90 degrees

Since |BC| = |CD|, we know that triangle BCD is an isosceles triangle.

Since triangle BCD is isosceles, angles BDC and CBD are equal. Let's call each of these angles x.

180 - 64

= 116 degrees

angle BCD = 180 - 116

= opposite angles in a cyclic quadrilateral are supplementary

116 + 64 + 2 OBC = 360

2 obc = 360 - 116 - 64

0bc = 180 / 2

= 90 degrees

Hence the angles  of the quadrilateral ABCD is 90 degrees

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Answer:

Step-by-step explanation:

To obtain the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule, we can take the derivative of each term separately and then add or subtract the resulting derivatives.

The derivative of 5x^10 is:

(5x^10)' = 50x^9

The derivative of -2x^2 is:

(-2x^2)' = -4x

The derivative of x is:

(x)' = 1

The derivative of -1 is:

(-1)' = 0

Putting these derivatives together using the addition and subtraction rule, we get:

F'(x) = (50x^9) - (4x) + (1) + (0)

Simplifying this expression, we get:

F'(x) = 50x^9 - 4x + 1

Therefore, the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule is F'(x) = 50x^9 - 4x + 1.

Answer:

20 : 50

Step-by-step explanation:

sum the parts of the ratio , 2 + 5 = 7 parts

divide 70 by 7 to find the value of one part of the ratio

70 ÷ 7 = 10 ← value of 1 part of the ratio , then

2 parts = 2 × 10 = 20

5 parts = 5 × 10 = 50

then

50 divided in the ratio 2 : 5 is 20 : 50

Answer: Alexis is 1.4224 meters tall.

Step-by-step explanation:

If you want your answer rounded, it's 1.4 meters. I hope this helped you! Brainilist is highly appreciated and helpful! <3

Answer:

Step-by-step explanation:

-145c is lower because it’s further left on a numberline

Are angles C and D supplementary angles: B. No.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees. Mathematically, a supplementary angle can be calculated by using this mathematical equation:

C + D = 180

Where:

C and D are measure of the angles subtended.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are not supplementary angles:

58 + 102 = 160° ≠ 180°

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Answer:

2a + 3b - 6bc + c

Step-by-step explanation:

For our terms, we will use a, b, c, and bc terms.

Now, here is what I came up with.

[tex]2a+3b-6bc+c[/tex]

Answer:

13.5pi inches^3

Step-by-step explanation:

the jar is a cylinder.

the volume of a cylinder is the height * base area, and the base area is a circle. the area of a circle is pi*r^2.

the radius is half the diameter, so it is 1.5.

the area of the circle is pi * 1.5^2 = 2.25pi.

multiply this by the height, and we get 13.5pi. the units is cubic inches, or inches^3.

If f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.

We can follow these steps:

Step 1: Approach (0,0) along the x-axis (y = 0)
Evaluate the limit of f(x,0) as x approaches 0. If the limit exists and is equal to L, proceed to step 2.

Step 2: Approach (0,0) along the y-axis (x = 0)
Evaluate the limit of f(0,y) as y approaches 0. If the limit exists and is equal to L, proceed to step 3.

Step 3: Conclude the limit
If both the limits in steps 1 and 2 exist and are equal to L, then the limit of f(x,y) as (x,y) approaches (0,0) is L. Otherwise, the limit does not exist.

So, if f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.

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The null hypothesis is that the proportion of computer chips that do not fail in the first 1000 hours of use is equal to 50%. The alternative hypothesis is that the proportion is greater than 50%.

At the 0.10 level of significance, we will reject the null hypothesis if the test statistic is greater than 1.28. The test statistic can be calculated using the formula:

[tex]z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$[/tex]

where [tex]\hat{p}$[/tex] is the sample proportion, [tex]p_0$[/tex] is the hypothesized proportion under the null hypothesis, and $n$ is the sample size.

In this case, we have [tex]\hat{p} = 0.53$, $p_0 = 0.50$, and $n = 1200$.[/tex] Substituting these values into the formula, we get:

[tex]z = \frac{0.53 - 0.50}{\sqrt{\frac{0.50(1-0.50)}{1200}}} = 2.77$[/tex]

Since the test statistic is greater than 1.28, we reject the null hypothesis and conclude that there is sufficient evidence at the 0.10 level to support the company's claim that more than 50% of computer chips do not fail in the first 1000 hours of their use.

Therefore, the null hypothesis is equal to 50%, and the alternative hypothesis is 50%. The test statistic is 2.77, which is greater than the critical value of 1.28 at the 0.10 level of significance, so we reject the null hypothesis and conclude that there is sufficient evidence to support the company's claim.

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Answer:

2145

Step-by-step explanation:

Given: Sum of three consecutive odd integers = 39

Calculation:Let x, x + 2, x + 4 be the three consecutive odd integers.

Sum of three consecutive odd integers = 39

⇒ x + (x + 2) + (x + 4) = 39

⇒ 3x + 6 = 39

⇒ 3x = 33

⇒ x = 11

∴ The integers are 11, 13 and 15.

∴ Their product = 11 × 13 × 15 = 2145

You're welcome! :)

Answer:

[tex]4a^{2} + 4ab[/tex]

Step-by-step explanation:

as I can see in the image posted by you,

current length = a + b

current width = a

according to the condition, original paper length and width was twice of their current values,

original length = 2(a+b)

original width = 2a

therefore,

original area = 2(a+b) * 2a

original area = 4(a+b)a

original area = [tex]4a^{2} + 4ab[/tex]

Hopefully you found the answer helpful

The method that is most appropriate when calculating margin-of-error for population mean is (b) Student's t-distribution.

When calculating the margin of error for the population mean, the most appropriate method depends on the sample size.

If the sample size is large (n > 30) and the population standard deviation is known, then a normal z-distribution can be used to calculate the margin of error.

If the sample size is small (n < 30) or the population standard deviation is unknown, then Student’s t-distribution should be used to calculate the margin of error.

In this case, we are told that the information was obtained from 14 strands of this particular virus. Since n < 30, we should use Student’s t-distribution to calculate the margin of error.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Considering the following scenario, which method would be most appropriate when calculating the margin of error for the population mean?

A research scientist wants to know how many times per hour a certain strand of virus reproduces. she obtains information from 14 strands of this particular virus and finds the mean to be 7.4 . the population is assumed to be normally distributed.

(a) Normal z-distribution

(b) Student's t-distribution

(c) More advanced statistical techniques

Step-by-step explanation:

VOLUME of pyramid =   1/3  base area  * height

 Base area is a square = 3 x 3

                                   = 1/3 ( 3x3) * 16 = 48 in^3

The exact value of the cosine of angle A + B is equal to - 1239 / 1961.

In this problem we need to determine the exact value of a trigonometric function, this can be done by using definitions of trigonometric functions, Pythagorean theorem and trigonometric formulas:

Trigonometric function

sin θ = y / r

cos θ = x / r

tan θ = y / x

Pythagorean theorem

r² = x² + y²

Trigonometric formula

cos (A + B) = cos A · cos B - sin A · sin B

First, determine the exact values of sines and cosines:

Angle A

r = √(28² + 45²)

r = 53

sin A = 45 / 53

cos A = 28 / 53

Angle B

y = √(37² - 12²)

y = 35

sin B = 35 / 37

Second, calculate the exact value of the trigonometric function by trigonometric formula:

cos (A + B) = (28 / 53) · (12 / 37) - (45 / 53) · (35 / 37)

cos (A + B) = - 1239 / 1961

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Answer:

Hope you have understood this sum

Answer:

The coordinates of (-3,0) after a translation of 2 units up is the third one. (-3,2)

The expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

We can begin by factoring the denominators of both fractions as follows:

[tex]x^{2}[/tex]- x - 12 = (x - 4)(x + 3)

[tex]x^{2}[/tex]- + 6x - 5 = (x - 1)(x + 5)

Substituting these expressions, the given expression becomes:

[(x - 1)(x-1)  [tex]x^{2}[/tex]-+ (-6)]/[(x - 4)(x + 3)] * [(x + 5)/(x - 1)(x + 5x - 5)]

Simplifying, we can cancel out the (x - 1) and (x + 5) terms in the numerator and denominator:

[(x - 1) *  [tex]x^{2}[/tex]- + (-6)]/[(x - 4)(x + 3)] * [1/(x - 5)]

Expanding the numerator:

( [tex]x^{3}[/tex]-  [tex]x^{2}[/tex]- - 6)/( [tex]x^{2}[/tex]- - x - 12) * [1/(x - 5)]

Factoring the numerator:

( [tex]x^{2}[/tex]- + x - 6)(x - 5)/( [tex]x^{2}[/tex]- - x - 12)

Factoring again:

(x + 3)(x - 2)(x - 5)/(x - 4)(x + 3)(x - 1)

Canceling out the (x + 3) terms:

(x - 2)(x - 5)/(x - 4)(x - 1)

Therefore, the expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.

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1. sin ² x goes in the numerator. 2. sin x (sin x) is the numerator expanded. 3. Separate the two factors sin x / cos x and sin x / cos x. 4. Replace sin x / cos x with tan x. Use the trigonometric identity.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle. The three basic categories of trigonometric functions are sine, cosine, and tangent. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently. For an explanation of these three main roles, use the diagram below as a guide. The sin-cos-tan triangle is the name for this illustration. Often, the right-angled triangle is used to define trigonometry.

The given trigonometric function is 1 / cos x csc² x.

Now, the csc²x can be written as:

sin²x / cos x. Thus, sin ² x goes in the numerator.

Now, sin x (sin x) is the numerator expanded.

Separate the two factors sin x / cos x and sin x / cos x

Replace sin x / cos x with tan x.

Use the trigonometric identity to complete the proof.

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The probability that less than 9 but more than 7 bulbs from the sample are defective is 0.8944.

The formula to find the probability of x number of defective bulbs in a sample of n bulbs is as follows:

P(x) = [[tex]n \choose x[/tex] * p^x * (1-p)^(n-x)], where [tex]n \choose x[/tex] is the combination of n and x.

So, The probability of x < 9 defective bulbs in a sample of 14 bulbs is given as follows:

P(x<9) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)

Therefore, the probability that less than 9 bulbs from the sample are defective is

P(x<9) = [[tex]14 \choose0[/tex] * (0.2)^0 * (0.8)^14] + [[tex]14 \choose1[/tex] * (0.2)^1 * (0.8)^13] + [[tex]14 \choose2[/tex] * (0.2)^2 * (0.8)^12] + [[tex]14 \choose3[/tex] * (0.2)^3 * (0.8)^11] + [[tex]14 \choose4[/tex] * (0.2)^4 * (0.8)^10] + [[tex]14 \choose5[/tex] * (0.2)^5 * (0.8)^9] + [[tex]14 \choose6[/tex] * (0.2)^6 * (0.8)^8] + [[tex]14 \choose7[/tex] * (0.2)^7 * (0.8)^7]= 0.8962

Similarly, the probability that more than 7 bulbs from the sample are defective is:

P(x>7) = P(x=8) + P(x=9) + P(x=10) + P(x=11) + P(x=12) + P(x=13) + P(x=14)

Therefore, the probability that more than 7 bulbs from the sample are defective is

P(x>7) = [[tex]14 \choose8[/tex] * (0.2)^8 * (0.8)^6] + [[tex]14 \choose9[/tex] * (0.2)^9 * (0.8)^5] + [[tex]14 \choose10[/tex] * (0.2)^10 * (0.8)^4] + [[tex]14 \choose11[/tex] * (0.2)^11 * (0.8)^3] + [[tex]14 \choose12[/tex] * (0.2)^12 * (0.8)^2] + [[tex]14 \choose13[/tex] * (0.2)^13 * (0.8)^1] + [[tex]14 \choose14[/tex] * (0.2)^14 * (0.8)^0]= 0.0005

Therefore, the probability that less than 9 but more than 7 bulbs from the sample are defective is:

P(8≤x≤7) = P(x<9) - P(x≤7)

P(8≤x≤7) = P(x<9) - [P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)]= 0.8962 - 0.0018= 0.8944 (rounded to four decimal places)

Therefore, more than 7 out of the sample have a probability of failure, but less than 9 out of the sample probably have a failure.

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