The cost of Jacquie's gym membership is $20 per month. Jacquie gets a 10% discount of the monthly cost in any month in which she refers a friend who also becomes a member. How much does Jacquie save in a month when one of her friends joins the gym?

False they are not congruent.

Start by looking at the Properties of congruent triangle:

1. SSS -"side, side, side" and means that we have two triangles with all three sides equal

we are only given the length of one side in this triangle so we can not use this one to determine if the triangles are congruent or not.

2.SAS -"side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

once again, we are only given the length of one side in each triangle, so this one also cant help us to determine if the triangles are congruent.

3. ASA- "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

in the triangle to the right we get: ∠62, 7, ∠60

in the triangle to the left we get : ∠58, 7, ∠62

these do not match up with each other.

with this information we can determine that the triangles are not congruent therefore the answer is B. False

Answer:

θ = 51.7

SOH-CAH-TOA

CAH: COS = ADJ/HYP   cos(θ) = 19.4/29.3

θ = 48.5

93.2 + 48.5 + x = 180

x = 38.3

90 + 38.3 + θ = 180

θ = 51.7

Step-by-step explanation:

The class boundaries and class intervals for the given distribution are shown. The mean, median, and sample standard deviation for the given numbers are 3.6, 3, and 4.61 respectively.

Distribution refers to the property or operation that combines two or more mathematical operations within an expression. It allows us to simplify or expand expressions by applying the operations to individual terms or factors.

The given temperature readings are given as 15, 23, 31, 39, and 47.

We know that the class mark is the average of the upper limit and lower limit of the class interval.

Hence, we can calculate the class interval by taking the difference between the lower and upper limits of the class.

The given data can be organized into a frequency distribution table as shown below.

Class Interval    Frequency Class Mark
14.5- 22.5   23-22  18.5
22.5- 30.5   31-23  26.5
30.5- 38.5   39-31  34.5
38.5- 46.5   47-39  42.5

Part-1: The class boundaries,
a) The class boundaries are the upper limit of a class and the lower limit of the following class.

We can calculate the class boundaries by using the following formula:

Class boundaries = upper limit of a class + 0.5 — (lower limit of a class — 0.5)

Class Interval    Class Boundaries
14.5- 22.5   14.5, 22.5
22.5- 30.5   22.5, 30.5
30.5- 38.5   30.5, 38.5
38.5- 46.5   38.5, 46.5

b) The class interval can be calculated as the difference between the upper limit of the class and the lower limit of the class.

We can calculate the class interval using the following formula:

Class interval = Upper limit – Lower limit

Class Interval    Class Boundaries Class Interval
14.5- 22.5   14.5, 22.5  8
22.5- 30.5   22.5, 30.5  8
30.5- 38.5   30.5, 38.5  8
38.5- 46.5   38.5, 46.5  8

Thus, the class boundaries and class intervals for the given distribution are as shown above.

Part 2: Mean, Median, and Sample Standard Deviation for the given numbers

The given numbers are: 10, 3, 6, -2, 1.

Now we can calculate the mean, median, and sample standard deviation as follows:

1. The mean is calculated as the sum of all the numbers divided by the total number of numbers.

Mean = (10 + 3 + 6 – 2 + 1) / 5 = 18 / 5 = 3.6

2. To find the median, we need to arrange the numbers in ascending order.

The median is the middle value in the list.

Hence, the median of the given numbers is 3.

3. The sample standard deviation is calculated using the following formula:

sample standard deviation = √(Σ(x–μ)²/n-1)

Where Σ represents the sum, x represents each number in the data set, μ represents the mean, and n represents the sample size.

First, we need to find the deviation of each number from the mean.

10-3.6 = 6.4
3-3.6 = -0.6
6-3.6 = 2.4
-2-3.6 = -5.6
1-3.6 = -2.6

Next, we need to square each deviation.

6.4² = 40.96
(-0.6)² = 0.36
2.4² = 5.76
(-5.6)² = 31.36
(-2.6)² = 6.76

Now, we add up all the squared deviations.

Σ(x–μ)² = 40.96 + 0.36 + 5.76 + 31.36 + 6.76 = 85.2

Finally, we can calculate the sample standard deviation.

sample standard deviation = √(85.2 / 4) = √21.3 ≈ 4.61

Therefore, the mean, median, and sample standard deviation for the given numbers are 3.6, 3, and 4.61 respectively.

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Answer:

I guess the answer is 5 and 8

Answer:

I think answer is 5 and 8

Answer:

Its either A or B:

The length of diagonal PS and diagonal P'S' are in the ratio 1:3.

The lengths of side PT and side R'Q' are in the ratio 1:3.

The Lagrange error bound is a method for estimating the error in approximating a function using a polynomial

Let's say you have a function f(x) and you want to approximate it using a polynomial of degree n, denoted by Pn(x). The Lagrange error bound states that the absolute error between f(x) and Pn(x) is bounded by:

|f(x) - Pn(x)| ≤ M/[(n+1)!] |x - c|^(n+1)

where M is a bound on the (n+1)th derivative of f(x) on an interval containing x and c is some constant value in that interval (typically the midpoint of the interval). Note that the bound depends on the choice of x and c.

In practice, the Lagrange error bound can be used to estimate the error in polynomial approximations. You can choose a value of x and a degree n for the polynomial, then use the bound to find an upper bound on the absolute error. If the error is too large, you may need to increase the degree of the polynomial or choose a different value of x.

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The given question is complete, the complete question is:

What is Lagrange error bound ?

Answer:

I think its 7/3 or 6/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) Because there are 7 red and 4 blue marbles, there are 7+4=11  marbles in the bag.

So the ratio of all marbles to blue marbles is 11 to 4.

We write this as follows. 11:4

(b)There are 7 red marbles and 4 blue marbles in the bag.

So the ratio of red marbles to blue marbles is 7 to 4.

We write this as follows. 7:4

The bias that is taken care of here is that; Some of the population may not have access to other types of phones. Option A

When we talk about a bias in research we mean the kind of scenario that is able to cause the result of a research to become lobe sided. In other words, it is that which introduces inaccuracy to a research.

A lot of people if not everyone has access to a mobile phone and this would help more people to be able to participate in the interview. Some of these people may not have any of the other kinds of phone.

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Answer:

A

Step-by-step explanation:

took the test

Answer:

  28

Step-by-step explanation:

  1² +3³ = 1 +27 = 28

The sum is 28.

the percent of .125 is 100%

If we look at the tree diagram, we can see that we have 12 numbers, they are:

{12, 13, 16, 21, 23, 26, 31, 32, 36, 61, 62, 63}

That's our sample space, if we look at each tree we can count how many numbers has 1 or 6, on the first tree we have 2 numbers: 21 and 26. On the second tree we have three numbers: 12, 13 and 16, that's expected because the first digit is 1. For the second tree we have just two, 31 and 36. For the last tree we have three again because of the digit 6.

Therefore the probability will be how many numbers that has 1 or 6 divided by the sample space, then

The probability is

Answer:

514,400 plants.

Step-by-step Explanation:

From the attached diagram given below which shows the coordinate grid, we can say the shape of the farm is that of a trapezium.

Number of plants to be planted by the farmer at 40,000 plants per acre = area of land in acres * 40,000.

Let's find the area of the land(trapezium):

Area of trapezium = ½(a+b)*h

From the coordinate grid, from point E to H on the y-axis, we have 900 units = 900 ft (Given that 1 unit = 1 foot).

Also, from F to G, we have 500 units = 500ft; and the height of the trapezium is represented by the number of units the trapezium covers on the x-axis = 800units = 800ft.

a = 900ft, b = 500ft, c= 800ft

==> Area of Land/trapezium = ½(a+b)*h

= ½(900+500)*800

= ½(1400)*800

= 700*800 = 560,000ft²

Given that 1acre = 43,560ft²

x acre = 560,000ft²

x = 560,000*1 /43,560

x = 12.86 acres

Therefore, number of plants to be planted = 12.86 acres * 40,000 plants = 514,400 plants.

Answer:

a) 2 galones y 1500 litros

Step-by-step explanation:

La fórmula para el área de la superficie lateral de una pirámide hexagonal regular =

A = 3a × √ (h² + 3a² / 4)

Donde a = longitud lateral o borde de la base de la pirámide hexagonal = 10 cm

h = altura de la pirámide hexagonal = 30cm.

Resolviendo para 1 molde

A = 3 × 10 × √ (30² + 3 × 10² / 4)

A = 936,7497 cm²

Esto significa que Fabricio tiene que cubrir 936.7497cm² de 1 molde con barniz.

En la pregunta se nos dice que:

1 galón de barniz rinde o cubre 45m²

Por lo tanto, convertimos el área de la superficie de 1 molde a m²

1 cm² = 0,0001m²

936.7497cm² =

936.7497cm² × 0.0001m² / 1 cm²

= 0.09367497m²

Por tanto, si

45m² = 1 galón de barniz

0.09367497m² = x galón

x galón = 0.09367497m² / 45 m²

= 0.002081666 galones

Esto significa que 0,002081666 galones barnizarán 1 molde.

Recuerda, en la pregunta, nos dicen que Fabricio está barnizando 1000 moldes

Si. 1 molde = 0.002081666 galón de barniz

1000 moldes

1000 × 0,002081666

= 2.081666 galones de barniz

Aproximadamente = 2 galones de barniz.

De ahí la capacidad en litros de cada molde = 1500 litros.

The relation ((2, 1), (3, 2), (-1, 1), (0, -2)) is also a function.In conclusion, both the relations y = 2x + 8 and ((2, 1), (3, 2), (-1, 1), (0, -2)) are functions since every input (x-value) has a unique output (y-value).

A function is a collection of pairs of input-output values where each input corresponds to a single output. In other words, for a relation to be a function, every x-value (input) must correspond to a unique y-value (output). Therefore, to determine whether each of the following relations is a function we need to find whether every x-value corresponds to a unique y-value or not.

1. y = 2x + 8To check if the relation is a function or not, we need to verify that every value of x has a unique value of y.If we notice that every x-value (input) corresponds to a unique y-value (output), it implies that the relation is a function. Therefore, the relation y = 2x + 8 is a function.2. ((2, 1), (3, 2), (-1, 1), (0, -2))

To verify whether a relation is a function or not, we need to check that each x-value in the relation has only one y-value associated with it. In this relation, we have four pairs of values, and each x-value corresponds to a single y-value, implying that the relation is a function.

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To evaluate which of a set of curves fits the data best, you can use the option "c. R2", also known as the coefficient of determination.

R2 is a statistical measure that helps determine the proportion of variance in the dependent variable explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the curve to the data.

To evaluate which of a set of curves fits the data best, we can use the R2 (coefficient of determination) metric. R2 is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.

                                         A higher R2 value indicates a better fit of the curve to the data. APE (absolute percentage error), MAPE (mean absolute percentage error), and NPV (net present value) are not appropriate metrics for evaluating the fit of a curve to data. APE and MAPE are typically used to measure forecasting accuracy, while NPV is a financial metric used to determine the present value of future cash flows.

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ANSWER :

EXPLANATION :

Copying a given segment is the process in which a given line segment is drawn following the required steps so that both object and image have the same length. Therefore,

i. PQ = 12 cm

ii. MN = 12 cm

Thus, PQ = MN

Construction is a process that requires the use of materials and instruments to produce a required image. This involves following stated or required steps.

A given line segment can be copied by following appropriate steps. Such that both lines would have the same length, and would be parallel to each other or as required.

The given question requires following the stated steps to produce the required construction. Such that line segment NM is the image of PQ, and both have equal length.

The required construction for the question is attached to this answer.

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Answer: Once the Acadians refused to sign an oath of allegiance to Britain, which would make them loyal to the crown, the British Lieutenant Governor, Charles Lawrence, as well as the Nova Scotia Council on July 28, 1755 made the decision to deport the Acadians. The Expulsion (1755–1764) occurred during the French and Indian War (the North American theatre of the Seven Years' War) and was part of the British military campaign against New France. The British first deported Acadians to the Thirteen Colonies, and after 1758 transported additional Acadians to France. When the French and Indian War began in 1754, the British government, doubting the neutrality of the Acadians, demanded that they take an oath of allegiance to the Crown. ... British Governor Charles Lawrence decided to deport the Acadians from Nova Scotia without giving his colleagues any notice. They migrated to Louisiana because they had better fishing grounds, its territory controlled the gulf of St. Lawrence, and shipping routes and British colonies along the Atlantic coast.

Step-by-step explanation:

The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

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Answer:

\(-\frac{15}{7}\)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

it should be -\(\frac{15}{7}\)

Step-by-step explanation:

The total sum of the squares is the sum of residual sum of squares and the explained sum of squares.

Simple regression analysis means that there is 1 dependent variable and 1 independent variable.

In this, there is 3 types of sum of squares:

They are related to each other as:

TSS = RSS + ESS

That is the total sum of the squares will be equal to the residual sum of squares plus the explained sum of squares.

Therefore, we get that, the total sum of the squares is the sum of residual sum of squares and the explained sum of squares.

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The source of bias that is most relevant to the situation described above is the perceived lack of anonymity.

When individuals are asked personal questions about their behaviors or beliefs, they may feel uncomfortable sharing truthful information due to concerns about being judged or having their privacy violated. This can lead to respondents providing socially desirable responses or withholding information altogether, which can bias the results of the study.

In the situation described, both members of a couple are being asked about their sexual behavior, which can be a sensitive topic. If they do not feel that their responses will be kept confidential or if they fear that their partner may judge them based on their answers, they may not provide accurate information. This can lead to biased results, as the researchers may not have a complete understanding of the participants' behavior.

To minimize the impact of perceived lack of anonymity, researchers can ensure that participants are informed about the confidentiality of their responses and that their answers will not be shared with anyone else. They can also use anonymous surveys or other methods to protect the privacy of participants.

Therefore,the source of bias that is most relevant to the situation described above is the perceived lack of anonymity.

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Answer:

7.8 rupees

Step-by-step explanation:

The domain of a function are its possible input values

The domain of the function is (b) all real numbers greater than or equal to 0.

From the graph, we have the following observations

The above observations imply that; the domain starts from 0

Hence, the domain of the function is the set of all real numbers greater than or equal to 0.

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The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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I hope these are legible. Follow them from left to right and up to down.

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

The compound interest formula is given by the formula

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

For the second year

P=26500+25000=51500

For the third year

P=54590 + 25000=79590

For the fourth year

P=84365.4 + 25000=109365.4

For the fifth year

P= 115927.324 + 25000 =140927.324

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

Answer:

90°

Step-by-step explanation:

40+50+x=180

x=90