Two-thirds of the members of Highland Church attended the International Dinner during their annual missions conference. When seven of the members were not able to attend, the total number of attendees was Seventy-one. How many members does Highland Church have?​

The number of weeks (x) when you both donate the same number of items (y) is equal to 3 weeks.

In order to write and solve a system of linear equations to describe this situation, we would assign variables to the number of weeks and number of items respectively, and then translate the word problem into algebraic equation as follows:

Since you have already donated 14 items and plan to donate 3 more each week, a linear equation which represents this situation is given by;

D = 3x + 14         ........equation 1.

Since you have already donated 8 items and plan to donate 5 more each week, a linear equation which represents this situation is given by;

D = 5x + 8         ........equation 2.

Equating equation 1 and equation 2, we have:

3x + 14 = 5x + 8

5x - 3x = 14 - 8

2x = 6

x = 6/2

x = 3 weeks.

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The requried average rate of change is given as -7 dollars per hour. Option D is correct.

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.

here,
The average rate of change for the data from the 5th hour to the 8th hour is given as,
m = (y₂ - y₁) /  (x₂ - x₁)

m = 75 - 96 / 8 - 5
m = -21/3
m = -7 dollars per hour.

Thus, the requried average rate of change is given as -7 dollars per hour. Option D is correct.

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The accelerations of each car are given as follows:

The velocities are given as follows:

The acceleration is obtained as the change in the velocity by the change in time, with the change in time having squared units, as velocity is given by change in distance divided by change in time.

A race car accelerates on a straight track from 0 to 100 km/h in 6 s, hence it's acceleration is given as follows:

a = 100/6 = 16.67 km/s².

For the second car, it accelerates from 0 to 100 km/h in 5 s, hence it's acceleration is given as follows:

a = 100/5 = 20 km/s².

The velocity equation for each car is defined as follows:

v(t) = at.

As the velocity is obtained integrating the acceleration.

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The first random sample is example of Stratified Sampling technique. The other one is an example of simple sampling technique.

Some following sampling techniques are examples of probabilistic sampling.

Stratified Sampling is defined as the partition of population into groups based on a factor that may influence/differentiate the variable that is being measured.

We have a random sample of 72% from a list of male legislators and 28% of a sample from a list of female legislators. As we see there are two different groups with different percent of people's based on gender legislators. So, it is an example of Stratified Sampling.

In other example, a friend who homeschools her children about her opinion on state education policy, then collect the other information to find more participants for this study. It is an example of simple sampling technique.

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Answer:

Step-by-step explanation: First add all the different hours of speed he made each week together.

* 15.5 + 17.75 + 20.35 = 53.6

Then divide your answer by the overall amount of weeks he traveled

* 53.6 / 3 = 17.83 recurring

Hope I answered this correctly and I hope it helps.

Answer:

The percent increase in amount of tickets sold is 90 %

Step-by-step explanation:

We need to calculate what what is the percentage of tickets sold the second weekend, in comparison to the first weekend:

[tex]\frac{15314}{8060} = 1,9[/tex]

Then we just subtract the 1 and we get 0.9 - which is 90%

Quartiles divide data sets in fourths.

The numbers that separate a sorted data set into four (almost) equal sections are known as quartiles. When the number of data values is a multiple of four, the set can be evenly partitioned into four sections.

You can divide the data into three equal groups called quartiles. The first quartile (Q1) separates the bottom 25 percent of the data. The middle point is located in the second quartile (Q2). In statistics, the top 25% of results are separated into the third quartile (Q3) as the upper quartile. In sales and survey statistics, quantiles are frequently used to divide populations into groups.

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The equation of the line is y = (1/4)x - 10 that parallel to y=(1/4)x+2 and passes through (4,-9).

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line is parallel to y=(1/4)x+2, it has the same slope, m = 1/4.

To find the y-intercept of the line that passes through (4,-9), we can substitute the point's coordinates into the equation and solve for b.

So the equation would be:

y = (1/4)x + b  ....(i)

Substitute the point (4,-9) in it

-9 = (1/4) × 4 + b

Solving it

b = -9 - (1/4) × 4 = -9 - 1 = -10

Substitute the value of b = -10 in equation (i),

y = (1/4)x - 10

Therefore, the required equation of the line is y = (1/4)x - 10.

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Answer:

1, 2 and 5

Step-by-step explanation:

angle 10 = 180 - angle 9 = angle 4 + angle 6

angle 7 = 180 - angle 6 = angle 4 + angle 9

angle 3 = 180 - angle 4 = angle 6 + angle 9

The gradient vector field of f(x, y) = tan(3x − 5y) is (3sec^2(3x - 5y), -5sec^2(3x - 5y))

A gradient vector is a mathematical object that describes the direction of the steepest increase of a scalar function. In other words, it is a vector that points in the direction of the greatest rate of change of a scalar field.

To find the gradient vector field of f(x, y) = tan(3x − 5y), we first need to find the partial derivatives of f with respect to x and y.

The partial derivative of f with respect to x is:

df/dx = 3sec^2(3x - 5y)

The partial derivative of f with respect to y is:

df/dy = -5sec^2(3x - 5y)

The gradient vector field of f is then given by the vector function:

Grad f(x,y) = <df/dx, df/dy> = <3sec^2(3x - 5y), -5sec^2(3x - 5y)>

So the gradient vector field of f(x, y) = tan(3x − 5y) is (3sec^2(3x - 5y), -5sec^2(3x - 5y)).

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Answer:

Step-by-step explanation:

the answer is 64 because 126-62 is 64

The amount Niko earns than Miley in one week is estimated to be $210

the exact amount is $209.85

The estimated amount is solved using subtraction operation.

The weekly amounts of Niko and Miley will be compared and the difference is the amount that Niko earn more than Miley.

From the chart Niko's weekly earning is $650.35 and Miley's weekly earning is $44.50

difference of the two earnings

= Niko's weekly earning - Miley's weekly earning

= 650.35 - 440.50

= 209.85

Niko earns $209.85 more than Miley this could be estimated to be $210

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The circumference of the circle is 44 unit.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

radius=r=7

i.e. circumference

=2πr

=2*22/7*7

=44

hence,  The circumference of the circle is 44 unit.

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The property for ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C is c. transitive property.

The transitive property is when the property of A is congruent to the property of B and the property of B is congruent to the property of C, so the property of A also congruent to the property of C.

In mathematics, the transitive property can be written as below,

[tex]{\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc.}[/tex]

Option a is wrong because reflexive property is only congruent to itself.

Option b is wrong because symmetric property is only congruent to two property.

Option d is wrong because addition property is not for angle.

Thus, the correct option si c. transitive property.

Your question is incomplete, but most probably your full question was

What property is illustrated in: If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C.

a. Reflexive Property

b. Symmetric Property

c. Transitive Property

d. Addition Property

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Answer:

y = 0.25x + 1

Step-by-step explanation:

so, the coordinates are (0, 1) and (4, 2)

The slope formula is: change in y over change in x

which is: (2 - 1) / (4 - 0) = 0.25

the y-intercept formula is: the y value when x is equal to 0

which is: 1

So we group them together:

the slope-intercept form is y = mx + b

m = slope

b = y-intercept

which is: y = 0.25x + 1

SSS - Side - Side - Side

SAS - Side - Angle - Side

ASA - Angle - Side - Angle

AAS - Angle - Angle - Side

The above theorems can be used to compare two triangles.

SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.

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SSS, SAS, ASA, and AAS are four types of triangle congruence.

SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.

SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.

ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.

AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.

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The first number or term that appears in both sequences is equals to the sixteen.

We have two sequences, for first sequence rule is subtract 8 starting from 72. The second sequence rule is subtract 6 starting from 58. We can see that both are arithmetic sequence, which defined as a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms. Now, First number in sequence 1ˢᵗ , a₁

= 72

common difference, d₁ = 8

Similarly, for 2ⁿᵈ sequence, aₙ = 58 - 6n

First number in sequence, b₁ = 58

common difference, d₂ = 6

We have to locate the number which appears in both sequences.

The nᵗʰ term of the 1ˢᵗ sequence,aₙ = a₁+ (n-1)d₁

The nᵗʰ term of 2ⁿᵈ sequence, bₙ = b₁ +(n−1)d₂

For the same number to appear on both sequence, the nᵗʰ term must be equal, so

a₁ + (n-1)d₁ = b₁ +(n−1)d₂

=> 72 + (n-1)8 = 58 +(n-1)6

=> 8n - 8 + 72 = 58 + 6n - 6

=> 8n - 6n = 52 - 64 = - 12

=> n = -6

plugging the value of n ,

72 + (-6- 1)8 = 72 - 56 = 16

58 +(-7)6 = 58 - 42 = 16

Therefore, 16 is the first common term/ number appears in both sequences.

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The value of x given as x + 2 > 3x - 8 in the inequality is x < 5.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Here, they are denoted by the symbols ≥ < > ≤.

It was given that we should solve the inequality using the algebraic approach: x + 2 greater-than 3 x minus 8.

From the information, the inequality is given as:

x + 2 > 3x - 8

In this case, it is important to collect the like terms

Collect the like terms

x - 3x > - 8 - 2

-2x > -10

Then we have to divide through by 2 in order to get the value of x.

Divide

x < 10 / 2

x < 5

Therefore, the calculation shows that x is less than 5.

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Answer:angles of 720˚ has 1+5=6 sides.

Step-by-step explanation:

7 dollar because I don't know

Systematic Sampling is the probability sampling method involves selecting large, broad groups rather than individuals.

Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population according to random starting points, but with regular periodic intervals. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.

Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population at regular periodic intervals according to random starting points. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. Systematic sampling is considered random if the regular intervals are predetermined and the starting point is random, even though it preselects the sample population.

Systematic sampling, when performed correctly on large populations of a defined size, allows researchers, including marketing and sales professionals, to obtain representative results on large groups of people. without having to contact each individual. Example, if we select a random group of 1,000 people from a population of 50,000 by systematic sampling, we should list all potential participants and choose a starting point. When the list is created, every 50th of her on the list (starting counting from the starting point you chose) will be selected as participants because 50,000 ÷ 1,000 = 50.

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The 98% confidence interval for the mean repair cost for the stereos is; (83.653, 99.987)

A confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate.

For this population, the confidence interval is given by the formula;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is z-score at confidence level

We are given;

x' = 91.82

s = 16.84

n = 23

Confidence level = 98%

The z-score at 98% confidence level is 2.326. Thus;

CI = 91.82 ± 2.326(16.84/√23)

CI = 91.82 ± 8.167

CI = 83.653, 99.987

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The number of terms for the following sequence:

90, 98, 86,....16, 14 is 39

Sequence is defined as defined as an array of numbers in a particular order of arrangment.  It can be AP or GP.

But the sequence given in this question is an AP with the following

Last term = 14,

First term = 90,

Common difference = -2

The nth term of a sequence (AP) when the last term is given is denoted by

L=a + (n-1)d

14= 90 + (n-1)*-2

14=90-2n+2

Rearrange the equation to have

14-90-2=-2n

122=-2n

Making n the subject to get

Therefore number of terms is =61

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Answer:hard how did you find this??

Step-by-step explanation:

It will take 5 months for Eduardo and Peta to weigh the same.

Eduardo weighs 120 pounds and is gaining 5 pounds each month, so after 1 month he will weigh 120 + 5 = 125 pounds.

After 2 months he will weigh 125 + 5 = 130 pounds.

This pattern continues, so after n months he will weigh 120 + 5n pounds.

Peta weighs 160 pounds and is losing 3 pounds each month, so after 1 month she will weigh 160 - 3 = 157 pounds.

After 2 months she will weigh 157 - 3 = 154 pounds.

This pattern continues, so after n months she will weigh 160 - 3n pounds.

We want to find the number of months it will take for Eduardo and Peta to weigh the same, so we set the expressions for their weights equal to each other and solve for n:

120 + 5n = 160 - 3n

8n = 40

n = 5

It will take 5 months for Eduardo and Peta to weigh the same.

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Yes, the point (5, 6) a vertex of the triangle.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, the sides of a triangle are formed by the x-axis, the line 3x-2y=3, and the line 5y+6x=60.

Here, 3x-2y=3 -------(I) and 6x+5y=60 -------(II)

Multiply equation (I) by 2, we get

6x-4y=6 -------(III)

Subtract equation (III) from equation (II), we get

6x+5y-6x+4y=60-6

9y=54

y=6

Substitute y=6 in equation (I), we get

3x-2(6)=3

3x=15

x=5

So, the vertex is (5, 6)

Yes, the point (5, 6) a vertex of the triangle.

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From the equation A = 1 + prt. solving for r will result to (A - 1) / pt

Using the expression A = 1 + prt solving for r involves making r the subject of the formula this is achieved by taking r to be at one side of the equation

The side is usually at the left hand side of the equation, making r the subject of the formula in the question is done as follows

A = 1 + prt

subtract  to both sides of the equation

A - 1 = 1 + prt - 1

A - 1 = prt

divide both sides of the equation by pt

(A - 1) / pt = prt / pt

(A - 1) / pt = r

rearranging the equation

(A - 1) / pt = r

r = (A - 1) / pt

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9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is  53 when x is between 0 and 9.

What is integration ?

Integration is a fundamental concept in calculus, which is used to find the area under a curve and the total change of a function. It is the reverse process of differentiation and can be used to find the original function, given its derivative.

For f(x) = 5 for x < 5, we have

∫(5dx) from 0 to 5 = 5*(5-0) = 25

For f(x) = x for x ≥ 5, we have

∫(x dx) from 5 to 9 = (1/2)x^2 from 5 to 9 = (1/2)(9^2 - 5^2) = (1/2)(81 - 25) = (1/2)(56) = 28

So the definite integral of the piecewise function is

∫(9 f(x) dx) from 0 to 9 = ∫(5dx) from 0 to 5 + ∫(x dx) from 5 to 9 = 25 + 28 = 53,

Therefore , 9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is  53 when x is between 0 and 9.

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The value of x is 36 degrees which states that two angles are supplementary.

The given problem can be solved using the formula for supplementary angles,  (that is, their sum is 180 degrees) if their measures add to 180 degrees.

In this case, we are given two angles: (x + 35) degrees and (3x + 1) degrees. We know that the sum of these two angles must be 180 degrees, so:

x + 35 + 3x + 1 = 180

4x + 36 = 180

4x = 144

x = 36

Therefore, the value of x is 36 degrees.

To calculate this, we first added the two angles together to get 4x + 36 = 180. We then subtracted 36 from both sides of the equation to get 4x = 144. Finally, we divided each side of the equation by 4 to get x = 36.

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The value of x is 17

In this question we ahve been given that two lines intersects each other at one point, making an angle of measure (x+35) degrees whose opposite angle measures (3x+1) degrees.

We need to find the value of x.

We know that opposite angles are the angles that are opposite each other when two lines intersect each other at one point.

Also the opposite angles are congruent means they have the same measurement.

So, x + 35 = 3x + 1

We solve above equation to find x.

x + 35 = 3x + 1

x + 35 - 1 = 3x + 1 - 1

x + 34 -x = 3x - x

34 = 2x

2x/2 = 34/2

x = 17

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An extraneous solution is a solution that is obtained when solving an equation, but is not a valid solution to the original equation. This can happen when solving certain types of equations, such as rational equations, where taking the square root or other inverse operations can produce solutions that are not valid for the original equation.

For example, if you have the equation (x+3)/(x-2) = 2, and you solve for x, you will find that x = 5 is a solution. However, if you substitute x = 5 back into the original equation, you will find that it is not a valid solution. This is because the denominator (x-2) would be zero, which is not allowed in a fraction. So, x = 5 is an extraneous solution.

Generally when solving an equation we need to check our solution back in original equation. in rational equation checking the solution back in original is necessary step as it can have multiple solution or extraneous solution.

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Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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