Find the perimeter and area of a rectangle of cardboard measuring 18.7 cm by 18.5 cm

p(x) × q(x)

= (3x² - x + 1) × (2x² + 3x - 2)

= 6x⁴ + 9x³ - 6x² - 2x³ - 3x² + 2x + 2x² + 3x - 2

= 6x⁴ + 7x³ - 7x² + 5x - 2

Answer:

400 is the answer

Step-by-step explanation:

The correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.

        \(${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}\)

       where \({\displaystyle s'_{x}}\) and \({\displaystyle s'_{y}}\) are the uncorrected sample standard deviations of         X and Y.

Given is a term as correlation coefficient.

        \($r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}\)

       where -

        \(r\) = correlation coefficient

       \(x_{i}\) = values of the x - variable in a sample

       \(\bar{x}\) =  mean of the values of the x-variable

       \(y_{i}\) = values of the y-variable in a sample

       \(\bar{y}\) = mean of the values of the y-variable

Therefore, the correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.

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Answer:

g = j - 12

Step-by-step explanation:

We know that if g is Gus' number of engine quantity, then j is Jessie's number of engine quantity, from this statement we have that Jessie made 12 more than Gus, therefore:

j = g + 12

if we solve for g:

g = j - 12

which is the same as saying that Gus made 12 number of engine less than Jessie

Answer:

g = x - 12

where x is the number of axles installed by Jessie

Step-by-step explanation:

Using a simple analogy. If a man has 7 cars while his friend has 3 cars, The statement may be written as the man has 4 cars more than his friend. The 4 cars being the difference between the number of cars he has and the number his friend has.

As such, if the number of engine blocks installed by Gus is g and Jessie installed 12 more axles than the number of engine blocks Gus installed yesterday, where Jessie must have installed x axles,

x = g + 12

Such that

g = x - 12

Answer:

B

Step-by-step explanation:

If you Divide 60 by 2 you would get 30 but if you divide by four ill be 15 so for b ill be 2 and a will be 4

To be 94% confident that the true mean IQ is within 2 points of the sample mean, you must obtain a sample of at least 199 individuals.

To determine how large a sample must be obtained to be 94% confident that the true mean IQ is within 2 points of the sample mean, we will use the following terms: confidence level, margin of error, and standard deviation. We will also need the z-score corresponding to the desired confidence level.

Step 1: Identify the confidence level, margin of error, and standard deviation
Confidence level: 94%
Margin of error: 2 points
Standard deviation (σ): Since it's not provided, we will use a common value for IQ, which is 15 points.

Step 2: Find the z-score corresponding to the 94% confidence level
A 94% confidence level has a z-score of approximately 1.88 (you can find this value in a z-score table or using a calculator).

Step 3: Use the formula for sample size
n = (z * σ / E\()^2\)
n = (1.88 * 15 / 2\()^2\)
n = (28.2 / 2\()^2\)
n = \((14.1)^2\)
n ≈ 198.81

Step 4: Round appropriately
Since we can't have a fraction of a person in a sample, round up to the nearest whole number. In this case, the sample size should be 199.

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The statement that is NOT true is option c: λ = 20 arrivals per hour.

The Poisson distribution is used to model the number of events that occur within a fixed interval of time or space, given the average rate of occurrence (λ). The key property of the Poisson distribution is that the average rate remains constant over time.

In this case, if arrivals occur according to the Poisson distribution every 20 minutes, we need to determine the average rate of arrivals per unit of time.

Option a states that λ = 72 arrivals per day. Since there are 24 hours in a day, the average rate can be calculated as λ = 72 arrivals / 24 hours = 3 arrivals per hour. This is consistent with the Poisson distribution.

Option b states that λ = 3 arrivals per hour. This is also consistent with the given information.

Option c states that λ = 20 arrivals per hour. However, this is not consistent with the given information, as the arrivals occur every 20 minutes, not every hour. The correct average rate should be λ = 60 minutes / 20 minutes = 3 arrivals per hour.

Option d states that λ = 1/20 arrivals per minute. This is consistent with the given information, as it represents the average rate of 1 arrival every 20 minutes, which can be converted to arrivals per minute.

Therefore, the statement that is NOT true is option c: λ = 20 arrivals per hour.

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The terms are matched is Exaggeration: Makes something seem too good or too bad.

Literary terminology refers to the techniques, styles, and formats used by writers and speakers to skillfully emphasize, decorate, or enhance their composition.

Reversal: Changes circumstances suddenly

Exaggeration: Makes something seem too good or too bad

Parody:  Mimics a subject directly

Ridicule: Makes a subject appear to be silly

Satire: Exposes human weakness

Hence, the sentences are matched above according to Literary terminology. It can refer to the playful techniques that comedians use to make us laugh, or the witty tricks that Wordsmith uses to shape new words and phrases in their composition.

Therefore, the terms are matched is Exaggeration: Makes something seem too good or too bad.

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The Y intercept is (0,275) and the X intercept is (125,0). the intercepts should be the point of when the line hits the axis'

Answer:

each would be 2

Step-by-step explanation:

because the hambuer would be 2 dollars

Answer:

$12.00

Step-by-step explanation:

16-12=4

Answer:

-16 + x = -4

-16 - -4 = -12

I pay $12

The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.857 or 85.7%.

The random variable X represents the outcome of the first test, where it takes on a value of 1 if the student passes and 0 if the student fails.

Similarly, the random variable Y represents the outcome of the second test, taking on a value of 1 if the student passes and 0 if the student fails. Given that the joint probability of passing both tests is 0.6, we can interpret this as the probability of X=1 and Y=1.

The marginal probability of failing the first test is 0.3, which can be represented as P(X=0). To find the conditional probability of passing the second test, given that the student passed the first test, we use the formula \(P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1).\)

Since we know that \(P(X=1 and Y=1) = 0.6, and P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7\), we can substitute these values into the formula:
\(P(Y=1 | X=1) = 0.6 / 0.7\)

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.8571 or 85.71%.

The conditional probability of passing the second test, given that the student passed the first test, can be calculated using the formula for conditional probability:

P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1)

We are given that the joint probability of passing both tests is 0.6, which means P(X=1 and Y=1) = 0.6.

To find P(X=1), we need to use the marginal probability of failing the first test, which is given as 0.3. Since the marginal probability of passing the first test is the complement of failing the first test (i.e., 1 - 0.3 = 0.7), we can say P(X=1) = 0.7.

Now we can substitute these values into the conditional probability formula:

P(Y=1 | X=1) = 0.6 / 0.7

Simplifying this expression, we have:

P(Y=1 | X=1) = 0.8571

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The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035

We want to find the option that is equal to the repeating decimal 0.353535.

Option A; 35 + 0.35 + 0.0035

When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.

Option B; 0.0035+ 0.000035 + 0.00000035

When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.

Option C; 0.35 + 0.0035 + 0.000035

When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.

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Answer:

1.) C - 0.35+0.0035+0.000035+...

2.) The first term of the geometric series is 0.35.

3.) The common ratio of the geometric series is 0.01

4.) The simplified fractional representation of 0.353535... is 35 / 99

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

-1

Answer:

-11

Step-by-step explanation:

Equation:

5+x=-6

Answer:

Step-by-step explanation:

(-4 - 4)/(3 - 1)= -8/2= -4

y - 4 = -4(x - 1)

y - 4 = -4x + 4

y = -4x + 8

answer is option 1

The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The body mass index (BMI) is given by:

BMI = [mass in pounds / (height in inches)²] * 703

Given mass = 175 pounds, height = 65 in, hence:

BMI = [175/65²] * 703 = 29.12

BMI = 29.12

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Answer:

\(a_n = 2+6(n-1)\)

Step-by-step explanation:

Explicit Arithmetic Formula: \(a_n=a_1 + d(n-1)\)

a₁ is 1st term in sequence

d is common difference

n is term number

Step 1: Find d

d = 8 - 2 = 6

Step 2: Plug in variables into formula

\(a_n = 2+6(n-1)\)

By dilation, the image of the vertex M of the quadrilateral is M'(x, y) = (6, 5).

In this problem we find the representation of a quadrilateral whose image by dilation must be found. The dilation formula is introduced below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that O(x, y) = (4, 6), k = 1 / 3 and M(x, y) = (10, 9), then image of point M is:

M'(x, y) = (4, 6) + (1 / 3) · [(10, 9) - (4, 6)]

M'(x, y) = (4, 6) + (1 / 3) · (6, 3)

M'(x, y) = (4, 6) + (2, 1)

M'(x, y) = (6, 5)

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Answer:

greater part = Rs.81

smaller part = Rs.59

Step-by-step explanation:

Solution:

Let the greater part be x and smaller part be (140 - x)

Acccording to question,

or, 2x+15 = 3(140 - x)

or, 2x+15 = 420-3x

or, 2x+3x = 420-15

or, 5x = 405

or, x = 405÷5

x = 81

Therefore, the greater part = x = 81

the smaller part = (140-x) =(140-81) = 59

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The function that models the population of foxes in the Arctic circle at time t (in months) since the beginning of Alyssa's study is P(t) = 185,000 * (17/18)^(t/2).

To model the population of foxes in the Arctic circle over time, we can use exponential decay since the population loses 1/18 (start fraction, 1, divided by, 18, end fraction) of its size every 2/22 months.

Let P(t) represent the population of foxes at time t (in months) since the beginning of Alyssa's study. The initial population is given as 185,000 (185,000185, comma, 000 foxes).

The exponential decay function can be written as:

P(t) = P₀ * (1 - r)^n

Where:

P₀ is the initial population (185,000 in this case).

r is the decay rate per time period (1/18 in this case).

n is the number of time periods elapsed (t/2).

Plugging in the values, the function that models the population of foxes over time becomes:

P(t) = 185,000 * (1 - 1/18)^(t/2)

Simplifying further:

P(t) = 185,000 * (17/18)^(t/2).

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Answer:

g = 1/2

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

9 + 3.5g = 11 - 0.5g

Step 2: Solve for g

Step 3: Check

Plug in g into the original equation to verify it's a solution.

Here we see that 10.75 does indeed equal 10.75.

∴ g = 1/2 is a solution of the equation.

Answer: g= 0.5

Step-by-step explanation:

Add

3.5g and 0.5g. to get

9+4g=11

then subtract 9 from the 11 and you should get 4g=2.

then divide 4 from 2 and you should get the answer of 2/4.

simplify it and you should get the answer g=0.5

Answer:

24,831.28

Step-by-step explanation:

Brainliest pls

Answer:

t = 16.6

Step-by-step explanation:

In the formula:

\(a = p(1 + r )^{t} \)

A is the final amount, in this case is 11500 people. P is the initial amount, in this case is 6500 people. r is the growth rate, which in this case is 0.035 - we have to express it s a decimal, not a percent. And finally t is the time, which is the variable we want to find.

Let's clear t first and replace all these values at the end. To clear t we have to leave only the factor which exponent is t on one side of the equation. To do this we have to divide both sides by P:

\( \frac{a}{p} = \frac{p}{p} (1 + r) ^{t} \\ \frac{a}{p} = (1 + r)^{t} \)

Now we have to use the following rule for the exponents and logarithms:

\( {a}^{x} = b\)

Apply logarithms on both sides:

\(log( {a}^{x}) = log(b)\)

By the exponents rule of logarithms

\(x \: log(a) = log(b)\)

For this problem we have:

\(log \frac{a}{p} = log(1 + r)^{t} \\ log \frac{a}{p} =t \: . \: log(1 + r)\)

Now we have to divide both sides by log(1+r) to clear t:

\(log \frac{a}{p} = t \: . \: \frac{log(1 + r)}{log(1 + r)} \\ t = \frac{log \: \frac{a}{p} }{log(1 + r)} \)

And finally we just have to replace the values into this equation we found: A = 11500, P = 6500 and r = 0.035:

\(t = log \: \frac{11500}{6500} \\ log(1 + 0.035) \\ log \: \frac{23}{13} \\ t = log \: 1.035 \\ t = 16.6\)

Answer:

729x^3 + 729x^2 + 243x + 27

Step-by-step explanation:

(9x+3)^3

(9x+3)(9x+3)(9x+3)

(81x^2 + 54x + 9)(9x+3)

(729x^3 + 486x^2 + 81x + 243x^2 + 162x + 27)

729x^3 + 729x^2 + 243x + 27

Answer:

\(\frac{11}{45}\)

Step-by-step explanation:

\(\frac{55}{225}\) ( divide numerator and denominator by 5 )

= \(\frac{11}{45}\) ← in simplest form

a fraction is in simplest form when no other number but 1 divides into the numerator and denominator.