Complete the table and use the results to find the indicated limit.

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

The correct statements regarding the quadratic function y = x² + 3x + 1 are given as follows:

The quadratic function in this problem is defined as follows:

y = x² + 3x + 1.

Hence the coefficients are given as follows:

a = 1, b = 3, c = 1.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -3/2.

The y-coordinate of the vertex is then given as follows:

y = (-3/2)² + 3(-3/2) + 1

y = 9/4 - 9/2 + 1

y = 9/4 - 18/4 + 4/4

y = -5/4.

Hence the vertex-form definition of the quadratic equation is given as follows:

y = (x + 3/2)² - 5/4.

Due to the positive leading coefficient, the vertex means that the function has a minimum of y = -5/4 at x = -3/2.

The domain of the function is all real values, as the quadratic function has no constraints such as a fraction or an even root.

The complete problem is given by the image shown at the end of the answer.

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Equation (B) "y = 3x + 10" represents the growth of the puppy.

So, the equation that represents the situation:

Then:

For example, Salomon checks the weight for the 6th time then:

So, the equation is correct.

Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.

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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}

Which equation represents the growth of the puppy? Select one:

A. y = x + 3

B. y = 3x + 10

C. y = 10x + 3

D. y = x + 10

The third vertex of the isosceles triangle is (a/2, b).

Let one vertex of the triangle lies on the base of the x-axis as 'a' which is written as (a,0)

Similarly, the other vertex of the triangle lies on the base of the y-axis as 'b' which is written as (0,b)

Let other vertex be at origin (0, 0)

An isosceles triangle is a triangle that has at least two sides of equal length.

Hence, the vertex of the triangle is (a/2, b).

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Using the normal distribution, the probabilities are given as follows:

a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.

b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.

c) Third quartile for the average of 25 eggs: 213 milligrams.

d) Less than 220 if less than 210: 0.1011 = 10.11%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the cholesterol levels are given as follows:

[tex]\mu = 215, \sigma = 15[/tex]

For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (220 - 215)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6293.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210- 215)/15

Z = -0.33

Z = -0.33 has a p-value of 0.3707.

Hence the probability is:

0.6293 - 0.3707 = 0.2586.

For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:

n = 25, s = 15/sqrt(25) = 3.

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (220 - 215)/3

Z = 1.33

Z = 1.33 has a p-value of 0.9082.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210 - 215)/15

Z = -1.33

Z = -1.33 has a p-value of 0.0918.

Then the probability is:

0.9082 - 0.0918 = 0.8164 = 81.64%.

The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.675 = (X - 215)/3

X - 215 = -0.675 x 3

X = 213.

The conditional probability in item d is calculated as follows:

P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.

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A family taking a road trip vacation travels 126 miles in 3 hours.

We can calculate the constant of proportionality as:

Then, in 5 hours they would travel:

In 5 hours they would travel 210 miles.

Answer:

1)

b = 42° (corresponding angles, parallel lines)

2)

b + 31 + 90 = 180 (sum of angles on a straight line=180)

b = 59°

3)

b + 34 = 180 (sum of angles on a straight line=180)

b = 146°

4)

b + 30 + 90 = 180 (sum of angles on a straight line=180)

b = 60°

5)

b + 35 + 90 = 180 (sum of angles on a straight line=180)

b = 55°

6)

b = 58° (alternate angles, parallel lines)

The probability of getting a green of a yellow marble can be determined like this:

Probability = (yellow marbles + green marbles) / total number of marbles

Probability = (1 + 4) / 10

Probability = 5 / 10

Probability = 1/2

By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:

Number of predictions = 150 × 1/2

Number of predictions = 75

Then, the answer is 75 times

Answer:

75 times.

Step-by-step explanation:

There are a total of 10 marbles in the bag.

Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.

In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.

Probability a yellow marble is drawn (in 1 draw) = 1/10.

In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.

So, the number of times for a green or yellow marble

= 60+15= 75.

Answer: 19

Step-by-step explanation:

[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

initial money = $8

final money = $11

percent of change = ?

Step 02:

percent of change

percent of change = ( final money - initial money ) / initial money * 100

= ( 11 - 8 ) / 8 * 100

= 3/8 * 100

= 0.375 * 100 = 37.5 %

The answer is:

The percent of change is 37.5 %

Answer:

9 + 7 + 7.2 = 23.2

23.2 x 2 = 46.4

Step-by-step explanation:

The three sigma control limits range from 0 to 8.20 for this size inspection limit and The probability of a type I error is 0.0038.

The inspection unit calculator in this case is 2

1.5 non-conformities on average per machine

Consequently, we would typically discover 2 * 1.5 = 3 non-conformities.

Here, C equals 3.

Lower Limit = C - 3 * c, which equals 3 - 3 * sqrt (3), which results in -2.19 (impossible), therefore 0

Reduced Limit = 0

Upper Limit: 8.20 when C + 3 * с + 3 + 3 * sqrt(3)

In this case, the three sigma control limits range from 0 to 8.20 for this size inspection limit.

(b) Type I errors happen when non confirmations go above the acceptable range.

This is a POISSON (3)

P(c > 8.20) = -1 POISSON (8, 3, true)

=1 - 0.9962

= 0.0038

In this case, the probability of a type I error is 0.0038.

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Answer:

[tex]-2\sqrt{} 6x^{8}[/tex]

Step-by-step explanation:

The result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20

The equation is

(-2/3)w - 4/5 = -3/2

Here we have to rearrange the terms and combine the like terms.

Mover 4/5 to the right hand side of the equation

(-2/3)w = -3/2 + 4/5

(-2/3)w = -7/10

Move the number (-2/3) to the right hand side of the equation

x = -7/10 ÷ (-2/3)

To make it multiplication, take the reciprocal of the the second number

x = -7/10 × (-3/2)

Multiply the numbers

x = 21/20

Hence, the result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20

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Answer:

a₉₀ = 168

Step-by-step explanation:

there is a common difference between consecutive terms, that is

- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 10 and d = 2 , then

a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168

Let's begin by listing out the information given to us:

216^(-2n) = (1/6)^(3n+2)

6 is a factor of 216: 216 = 6³

1/6 = 6^(-1)

⇒ 6^(-2*3n) = 6^[(-1*(3n+2)]

⇒ 6^(-6n) = 6^(-3n-2)

Since both sides are in the same base, we equate the exponents. We have:

-6n = -3n - 2

Add "6n" from both sides, we have:

-6n + 6n = -3n + 6n - 2 ⇒ 0 = 3n - 2

⇒ 3n = 2

No, the given relation is not a function. An association between items of two sets—the domain and the codomain—is known as a binary relation.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A binary connection in mathematics links elements of one set, referred to as the domain, with elements of another set, referred to as the codomain. A new set of ordered pairs made up of elements from sets X and Y and x in X is known as a binary relation across these sets.

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, functions represented the idealised relationship between two changing quantities.

Consider the given relation

{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}

We need to check whether the given relation is function or not.

A relation is a function if there exist a unique value of y for each value of x.

In the given relation, for x=0.3 there exist more than one value of y.

y=0.6 at x=0.3

y=0.7 at x=0.3

For one input there exist more than one output. Therefore, the given relation is not a function.

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Vector a = (3, 2), then;

Also, vector b = (-5, 6), then;

Then, -3a + 2b = (-9, -6) + (-10, 12)

The answer is (-19,6)

For a 44° elevation angle, the grade will be 96%.

Given that,

if the angle of elevation of the road is 44 degrees,

The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)

A tangent ?

One of the six basic trigonometric functions is tangent, denoted as tan().

The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.

[tex]tan \alpha = sin\alpha /cos \alpha[/tex]

The tangent of the angle is the ratio of rise to run.

tan(angle) = grade

tan(44°) ≈ 0.96 = 96%

Therefore, The grade will be 96% for an angle of elevation of 44°.

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Answer:

A

Step-by-step explanation:

It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).

These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.

a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]

without given any restriction x is all the numbers greater than 0.

NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

Answer:

F (false)

Step-by-step explanation:

i hope this helps! Have a good day! c:

The researcher draws a random sample using a Multistage cluster sample

At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.

In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.

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Answer: A.

Step-by-step explanation:

1. The function is even (symmetric about the y-axis)

2. The function F(x) is positive

[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]

5.

The sum of three consecutive integers is 228. You can write this situation, in an algebraic way, as follow:

x + (x + 1) + (x + 2) = 228

where the lower number is x, and the largest number is (x + 2).

You solve the previous equation for x:

x + (x + 1) + (x + 2) = 228 eliminate prenthesis

x + x + 1 + x + 2 = 228 sum similar terms

3x + 3 = 228 rest 3 both sides

3x = 228 - 3

3x = 225 divide by 3

x = 225/3

x = 75

Then, the lower number is 75, and the largest one is (75+2) = 77

The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².

In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.

Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:

F = μkN = μk(mg)

Where:

Substituting the given parameters into the formula, we have;

F = 0.20 × 2.0 × 9.81

F = 3.924 Newton.

By applying Newton's second law of motion, the net force is given by:

∑Fx = Applied force - kinetic frictional force = ma

Acceleration, a = [Applied force - kinetic frictional force]/m

Acceleration, a = [25 - 3.924]/2

Acceleration, a = 21.076/2

Acceleration, a = 10.538 ≈ 11 m/s²

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The two linear equations are perpendicular.

Here we have the two linear equations:

12y - 4x = 84

y = -3x + 8

If we write both of them in the slope-intercept form (as the second one) we will get:

12y - 4x = 84

12y = 4x + 84

y = (4x + 84)/12

y = (1/3)*x + 7

Now, if we take the product of the slopes of the two lines, we get:

p = -3*(1/3) = -1

when this product is -1, the lines are perpendicular, so that is the relation between our lines.

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Answer:

a = 0 , a = 9

Step-by-step explanation:

a(a - 9) = 0

equate each factor to zero and solve for a

a = 0

a - 9 = 0 ⇒ a = 9