4 hundreds+6 hundreds=10 hundreds=

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 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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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

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.

In this case, the bounce heights form a geometric sequence with a common ratio of 2/3. , the ball reaches a height of  [tex]8[/tex] feet on the third bounce,

The definition of a geometric sequence is a set of numbers where each term is created by multiplying the preceding term by a fixed factor.

If the bounce heights form a geometric sequence with common ratio "r", we can write:

27 = initial height

[tex]18 = 27r[/tex]

[tex]12 = 18r = 27 \times r^2[/tex]

Solving for "r", we get:

[tex]r = 2/3[/tex]

So, the fourth bounce height would be:

[tex](12) \times (2/3) = 8[/tex]

Therefore, the ball reaches a height of 8 feet on the third bounce, not the fourth bounce as stated in the original statement.

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Answer:

x=52

Step-by-step explanation:

Set equal to 180

x-30+3x+2=180

solve for x

4x-28=180

4x=208

x=52

plug in to check

Answer:

Step-by-step explanation:

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

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.

The distance between these two streets on Broad St is 0.3 miles.

We can use proportions to solve the problem.

Let's assume x is the distance between Thomas St and Denny Way on Broad St.

We know that on Aurora Ave, the distance between Thomas St and Denny Way is 0.2 miles, and on Broad St, the distance between Mercer St and Denny Way is 0.7 miles.

So, we can set up the following proportion:

0.2/0.45 = x/0.7

Simplifying, we get:

x = (0.2/0.45) * 0.7

x = 0.3111 miles

Rounded to the nearest tenth, the distance between Thomas St and Denny Way on Broad St is 0.3 miles.

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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! :)

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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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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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:

14.65

Step-by-step explanation:

3.6 ft + 6.25+4.8=14.65

Answer:

Hope you have understood this sum

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:

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

The cοmplete table with the οrdered pairs is:

(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))

(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm: [tex]ax^2 + bx + c = 0.[/tex]

Tο find the sοlutiοns tο the system οf cοnics, we can use substitutiοn tο eliminate οne variable and οbtain a quadratic equatiοn in the οther variable. Then, we can sοlve this quadratic equatiοn tο find the pοssible values οf the remaining variable.

Frοm the given system οf cοnics:

[tex]y^2/4 - x^2/2 = 1 ...(1)[/tex]

[tex]y^2 = 8(x + 1) ...(2)[/tex]

We can eliminate [tex]y^2[/tex] frοm equatiοn (1) by multiplying bοth sides by 4:

[tex]y^2 - 2x^2 = 4[/tex]

Substituting the value οf [tex]y^2[/tex]  frοm equatiοn (2), we get:

[tex]8(x + 1) - 2x^2 = 4[/tex]

Simplifying and rearranging, we get:

[tex]x^2 + 2x - 2 = 0[/tex]

We can sοlve this quadratic equatiοn using the quadratic fοrmula:

[tex]x = (-2 \± \sqrt{(2^2 - 4(1)(-2))}) / (2(1))[/tex]

x = (-2 ± √12) / 2

x = -1 ± √3

Substituting these values οf x in equatiοn (2), we can find the cοrrespοnding values οf y:

When x = -1 + √3, we get:

[tex]y^2[/tex] = 8((-1 + √3) + 1) = 8√3

y = ±2√(2√3)

Therefοre, the sοlutiοns are:

(-1 + √3, 2√(2√3)) and (-1 + √3, -2√(2√3))

When x = -1 - √3, we get:

[tex]y^2[/tex] = 8((-1 - √3) + 1) = -8√3

This equatiοn has nο real sοlutiοns fοr y.

Therefοre, the cοmplete table with the οrdered pairs is:

(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))

(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))

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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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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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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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The value of x is 24

The measure of is angle 1 is 101°

The measure of angle 2 is 79°

The measure of angle 3 is 101°

The measure of angle 4 is 101°

The measure of angle 5 is 79°

The measure of angle 6 is 79°

The measure of angle 7 is 101°

The measure of angle 8 is 79°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

3x +19 = 5x-29 ( opposite angle)

collect like terms

5x-3x = 29+19

2x = 48

x = 24

angle 1 = 180-(3×24+7)

= 180- 79

= 101°

angle 2 = 3x+7 = 79°( opposite angles)

angle 3 = 101° ( opposite angles)

angle 4 = angle 1 = 101° ( corresponding angles)

angle 5 = 79° ( corresponding angles)

angle 6 = angle 5 = 79°( opposite angle)

angle 7 = angle 4 = 101 ( corresponding angles)

angle 8 = angle 7 = 79 ( opposite angle )

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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 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

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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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:

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

The probability that the mean length of the 25 items is less than 12.4 inches is approximately 0.0009

We can solve this problem by using the Central Limit Theorem (CLT), which states that the sample mean of a large enough sample size from any distribution with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is 14.7 inches, the population standard deviation is 4.8 inches, and the sample size is 25. Thus, the mean of the sample means is also 14.7 inches, and the standard deviation of the sample means is 4.8 inches / sqrt(25) = 0.96 inches.

To find the probability that the mean length of the 25 items is less than 12.4 inches, we can standardize the sample mean using the z-score formula

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean we want to find the probability of (in this case, 12.4 inches), mu is the population mean (14.7 inches), sigma is the population standard deviation (4.8 inches), and n is the sample size (25).

Substituting these values, we get

z = (12.4 - 14.7) / (4.8 / sqrt(25)) = -3.13

We can then use a standard normal distribution table or calculator to find the probability that a standard normal variable is less than -3.13, which is approximately 0.0009.

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