Triangle JKL has the following measures :m∠J=97degree, m∠L=31degree, and j=44. What is the length of side k?
46.3
52.0
22.8
34.9

The domain and the range of the function are (-∝, ∝) and (-1, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is a polynomial function

The rule of this function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (-1, ∝)

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Answer:

Step-by-step explanation:

Suppose that you have a set of points, where the x-coordinates represent the number of months since you purchased a computer and the y-coordinates represent how much the computer is worth. Would you know how to plot these points on a Cartesian plane? How about if the situation were reversed and you had the plotted points? Could you come up with the coordinates of the points and the function rule that would generate these points?

Functions on a Cartesian Plane

Once a table has been created for a function, the next step is to visualize the relationship by graphing the coordinates of each data point. Data points are formatted as (x,y), where the first coordinate represents the horizontal distance from the origin (remember that the origin is the point where the axes intersect). The second coordinate represents the vertical distance from the origin.

Figure 4.1.5.1

To graph a coordinate point such as (4, 2), we start at the origin.

Because the first coordinate is positive four, we move 4 units to the right.

From this location, since the second coordinate is positive two, we move 2 units up.

Figure 4.1.5.2

Plot the following coordinate points on the Cartesian plane:

(5, 3)

(-2, 6)

(3, -4)

(-5, -7)

We show all the coordinate points on the same plot.

Step-by-step explanation:

To calculate the number of different license plates that can be made if the first character is a letter followed by 3 numbers, followed by 2 letters, we can use the multiplication principle.

There are 26 letters in the alphabet and 10 digits (0-9). Therefore, there are 26 choices for the first letter, 10 choices for each of the next three digits, and 26 choices for each of the last two letters.

Using the multiplication principle, we can multiply these numbers together to get the total number of possible license plates:

26 × 10 × 10 × 10 × 26 × 26 = **45,697,600**.

Therefore, there are **45,697,600** different license plates that can be made if the first character is a letter followed by 3 numbers, followed by 2 letters.

The recursive equation is aₙ = aₙ₋₁ + (2n - 1), and the explicit equation is aₙ = 2n² - 2n + 1, based on the given table.

To find the recursive and explicit equations for the given table:

1|2

2|6

3|12

4|20

We can observe that the values in the second column are obtained by multiplying the corresponding value in the first column by a constant and then adding a specific value.

Recursive equation:

Let's denote the first column as "n" and the second column as "aₙ".

Based on the given table, we can observe that the recursive equation is:

aₙ = aₙ₋₁ + (2n - 1)

Here, aₙ₋₁ represents the previous term in the sequence.

Explicit equation:

To find the explicit equation, we need to analyze the pattern in the second column.

aₙ = 2n² - 2n + 1

Here, 2n² represents the term obtained by squaring the value in the first column, -2n represents the term obtained by multiplying the value in the first column by -2, and +1 is a constant term.

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a. The null  hypotheses  H0: u = 150

The  alternative hypotheses for this situation : H1: u ≠ 150

b. We reject null hypothesis at 1% level of significance

c. We reject the null hypothesis at the 10% level  at X<= 146.03

X>=153.97

a.

H0: u = 150

H1: u ≠ 150

b.

Total sum = 15933.24

N = 100

Mean = 15933.24/100

= 159.3324

σ² = 25954.03 - (159.3324)²/100

σ² = 556.213

σ = √556.213

σ = 23.8162

Testing hypothesis

t = (bar x - u)/ σ/√n

= 159.3324-150/23.8162/√100

= 3.91

We will have a p value of 0.02

0.0002 < 0.01

Therefore, we reject null hypothesis at 1% level of significance

C.

Mean = 159.3324

Se= 2.3936

Df = 100-1 = 99

The Critical value at 0.01 = +-2.626

T = x-u/s.e

= -2.626 =( x -150)/2.3936

When we cross multiply and solve this

X = 143.714 for the lower tail

2.626 = (x-159)/2.3936

= 156.286 for upper tail.

We therefore reject H0 at

Bar X <= 143.71

Bar X >= 156.286

At 10%, Critical t = 1.660

-1.660 = (x - 150)/2.3936

X =146.02 at the lower tail

1.660 = (x-150)/2.3936

X = 153.97

We reject H0 at

X<= 146.03

X>=153.97

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Answer:

x = 22

Step-by-step explanation:

[tex]\sqrt{x-6}+2=6\\\sqrt{x-6}=4\\x-6=16\\x=22[/tex]

The statement "Each invitation costs $1.50 to print" is not true based on the given function. The cost depends on the number of invitations printed, as represented by c = 2.50(n – 2) + 1.50.

Among the given statements, the one that is not true is: "One can not print just one invitation."

The given function states that the cost of printing n invitations is represented by c = 2.50(n - 2) + 1.50. This function suggests that for each additional invitation beyond two, it costs an extra $2.50 to print. However, the function does not impose any restriction on the minimum number of invitations that can be printed.

Therefore, it is indeed possible to print just one invitation. The cost for one invitation would be c = 2.50(1 - 2) + 1.50 = 2.50(-1) + 1.50 = -2.50 + 1.50 = -1.00 dollars. Although printing a negative cost may not make practical sense, the statement that one cannot print just one invitation is not true based on the given function.

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Question

The function c = 2.50(n – 2) + 1.50 represents the cost c in dollars of printing n invitations. Which of the following is not true? One can not print just one invitation. Each invitation costs $1.50 to print For each additional invitation, it costs an extra $2.50 to print. The cost depends on the number of invitations printed.

Answer:

Standard form = 6x^2 - 5x + 1

Step-by-step explanation:

Currently, (2x - 1)(3x - 1) is in factored, whose general equation is given by:

f(x) = a(x - r)(x - s), where

The general equation of the standard form is given by:

f(x) = ax^2 + bx + c.

Thus, we can convert from factored to standard form using the FOIL method where:

We multiply the first, outer, inner, and last terms and simplify at the end:

(2x * 3x) + (2x * -1) + (-1 * 3x) + (-1 * -1)

6x^2 - 2x - 3x + 1

6x^2 - 5x + 1

Thus, the standard form of the quadratic expression (2x - 1)(3x - 1) is 6x^2 - 5x + 1.

Answer:

6X^2-5X+1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

y = 60

Step-by-step explanation:

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

to find k use the condition when y = 30 , x = 6

30 = 6k ( divide both sides by 6 )

5 = k

y = 5x ← equation of proportion

when x = 12 , then

y = 5 × 12 = 60

Answer:

Step-by-step explanation:

To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.

Given:

Average daily balance for November = $700

Unpaid balance at the end of November = $1,400

Annual percentage rate (APR) = 15.6%

Step 1: Calculate the interest charged for the month of November.

Interest = (Average daily balance * APR * Number of days in the month) / 365

Number of days in November = 30

Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)

Step 2: Add the interest to the unpaid balance to get the total balance on December 1.

Total balance = Unpaid balance + Interest

Total balance = $1,400 + $36.44 = $1,436.44

Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).

The total balance on the next billing date December 1 is $1,509.20.

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).

Given,

Then, the percentage rate for November = [tex]\sf\frac{15.6}{100}[/tex] × 700

[tex]\sf = \$109.20[/tex]

Balance on 1st December = unpaid balance at the end of November + percentage rate

[tex]\sf = $1400 +$109.20[/tex]

[tex]\sf =\$1509.20[/tex]

Therefore, the total balance on the next billing date December 1 is $1,509.20.

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In this scenario, we can use the binomial distribution to calculate the probability of getting 2 frozen rain drops after defeating 20 Frigid Elements. The binomial distribution has four parameters: n, p, q, and x.

- n is the number of trials or attempts, which is 20 in this case.

- p is the probability of success on each trial, which is 0.019 (1.9%) in this case.

- q is the probability of failure on each trial, which is 1 - p = 0.981.

- x is the number of successes we are interested in, which is 2 in this case.

Using the formula for the binomial distribution, we can calculate the probability of getting exactly 2 frozen rain drops:

P(X = 2) = (20 choose 2) * (0.019)^2 * (0.981)^(20-2)

where (20 choose 2) = 20! / (2! * (20-2)!) = 190 is the number of ways to choose 2 Frigid Elements out of 20.

Simplifying the formula, we get:

P(X = 2) = 190 * 0.019^2 * 0.981^18 = 0.261

Therefore, the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated is approximately 0.261.

Answer:

(4, 0 )

Step-by-step explanation:

2x + y = 8 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

2x + 4 - x = 8

x + 4 = 8 ( subtract 4 from both sides )

x = 4

substitute x = 4 into (2)

y = x - 4 = 4 - 4 = 0

solution is (4, 0 )

Answer: the second option.

Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

The length of a side of the square-shaped table is 1.5 meters.

To find the length of a side of the square-shaped table, we need to calculate the square root of the given area.

The area of a square is given by the formula:

Area = side length * side length

In this case, we have:

Area = 144/64 square meters

To find the side length, we take the square root of the area:

√(144/64) square meters

To simplify the calculation, we can express 144 and 64 as the square of their factors:

√((12^2)/(8^2)) square meters

Taking the square root of the numerator and the denominator separately, we have:

(√12^2) / (√8^2) square meters

Simplifying further, we get:

12/8 square meters

The fraction 12/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(12 ÷ 4) / (8 ÷ 4) square meters

3/2 square meters

Therefore, the length of a side of the table is 3/2 square meters or 1.5 meters.

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Answer:

2 groups of 7 children and

1 group of 2

Step-by-step explanation:

if you want to find out how many times it would take? divide 16 by 7

= 2

and 2 left

because 7 * 2 = 14

16-14 = 2

Hope you understand

Given sec 0= radical 10/2, cos(0) is equal to √10/5.

To find the value of cosine (cos) given the value of secant (sec), we can use the reciprocal identity between these two trigonometric functions.

The reciprocal identity states that:

sec(x) = 1/cos(x)

In this case, we are given sec(0) = √10/2.

We can rewrite this as:

1/cos(0) = √10/2

Multiplying both sides by cos(0), we get:

cos(0) * (1/cos(0)) = cos(0) * (√10/2)

The cos(0) terms cancel out on the left side, giving us:

1 = (√10/2) * cos(0)

Now, to isolate cos(0), we divide both sides by (√10/2):

1 / (√10/2) = cos(0)

To simplify the expression on the left side, we rationalize the denominator:

(1 * 2) / √10 = cos(0)

2/√10 = cos(0)

To express cos(0) in simplified radical form, we multiply the numerator and denominator by √10:

(2 * √10) / (√10 * √10) = cos(0)

(2√10) / 10 = cos(0)

Simplifying further, we get:

√10 / 5 = cos(0)

Therefore, cos(0) is equal to √10/5.

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A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

We need to find the ratio between the two capacities.

Given that there are [tex]10^9[/tex] bytes in a gigabyte and[tex]10^6[/tex] bytes in a megabyte, we can calculate the ratio as follows:

Ratio = (1 GB) / (1 MB)

= [tex](10^9 bytes) / (10^6 bytes)[/tex]

= [tex]10^(9 - 6)[/tex]

=[tex]10^3[/tex]

= 1000

Therefore, A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

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The correct answer is a.) P(X=7) ≈ 0.1735b.) P(X<4) ≈ 0.0687c.) P(X>6) ≈ 0.6786

To determine the probabilities for the given binomial experiment, we can use the binomial probability formula:

[tex]P(X=k) = C(n, k) * p^k * (1-p)^(n-k)[/tex]

Where:

P(X=k) represents the probability of getting exactly k successes,

n represents the number of trials (10 in this case),

p represents the probability of success (0.43 in this case),

k represents the number of successes.

a.) P(X=7):

P(X=7) = C(10, 7) * 0.43^7 * (1-0.43)^(10-7)

P(X=7) = 120 * 0.43^7 * 0.57^3

b.) P(X<4):

P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

[tex]= C(10, 0) * 0.43^0 * (1-0.43)^10 + C(10, 1) * 0.43^1 * (1-0.43)^9 + C(10, 2) * 0.43^2 * (1-0.43)^8 + C(10, 3) * 0.43^3 * (1-0.43)^7c.) P(X > 6):[/tex]

P(X>6) = 1 - P(X<=6)

= 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6))

By substituting the values and calculating the binomial probabilities using the formula, you can find the values for P(X=7), P(X<4), and P(X>6).Calculating this:

P(X < 4) ≈ 0.9619

Therefore, P(X < 4) is approximately 0.9619.

c.) P(X > 6)

To calculate P(X > 6), we need to sum the probabilities from X = 7 to X = 10.

P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Using the binomial probability formula for each term:

P(X > 6) = (10 C 7) * 0.43^7 * 0.57^3 + (10 C 8) * 0.43^8 * 0.57^2 + (10 C 9) * 0.43^9 * 0.57^1 + (10 C 10) * 0.43^10 * 0.57^0

Calculating this:

P(X > 6) ≈ 0.3672

Therefore, P(X > 6) is approximately 0.3672.

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Answer:

(a) therefore the equation is

a(t) = -1000t + 32800

Step-by-step explanation:

(a) a(t) = mt + b

(8, 24800). ( 20, 12800)

(t, a). ( t¹ , a¹)

slope or gradient, m = a¹ - t¹

a - t

m = 12800 - 24800

20 - 8

m = -12000

12

m = -1000

The slope is -1000

let's use (8, 24800) to find b.

24800 = -1000 (8) + b

24800 = -8000 + b

b= 24800 + 8000

b = 32800

therefore the equation is

a(t) = -1000t + 32800

(b) Since the slope is negative (-1000), it means that the altitude is decreasing at a constant rate of 1000 feet per minute. The negative sign indicates the descent, as the altitude is decreasing over time.

Therefore, the slope tells us that the plane is descending at a constant rate of 1000 feet per minute.

(c) The value 32800 tells us the initial altitude of the plane before descending. It indicates the starting point or the initial position of the aircraft above the ground level.

Therefore, the value 32800 represents the initial altitude of the plane before it began descending.

If LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK

To find the length of LN in parallelogram JKLM, we can utilize the properties of parallelograms, particularly the diagonals.

In a parallelogram, the diagonals bisect each other. This means that the diagonal LN divides the parallelogram into two congruent triangles, JLN and KLN.

Given that LJ is 46 units, we know that LK, the other half of the diagonal, is also 46 units.

Now, we have a triangle JLN, in which we know LJ (46 units) and LK (46 units). Since JL and LK are congruent sides of a triangle, we can conclude that JLKN is an isosceles trapezoid.

In an isosceles trapezoid, the diagonals are also congruent. Therefore, LN is equal in length to JK.

Hence, LN = JK.

Since we don't have any specific information about the length of JK provided in the question, we cannot determine the exact length of LN without additional information. However, we can say that LN is equal in length to JK based on the properties of parallelograms and isosceles trapezoids.

In summary, if LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK. However, without knowing the length of JK specifically, we cannot determine the exact length of LN.

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Given, the angle of elevation of the object from the observer's eye is 16° and the height of the object is 220 ft. So, the required answer is 697.44 ft (Approx).

What is the distance to the base of the object? Let AB be the height of the object, A be the position of the observer, and C be the position of the base of the object.

As per the diagram, we get; In right ΔABC, the Angle of elevation of the object = Angle BAC = 16°

We need to find the distance BC.So, we have; tan 16° = AB/BC  [∵ tan 16° = Perpendicular/Base = AB/BC]

tan 16° × BC = AB   [By cross-multiplication]

BC = AB/tan 16° [Dividing both sides by tan 16°]

BC = 220 ft/tan 16°

BC = 697.44 ft (Approx). Therefore, the distance to the base of the object is 697.44 ft (Approx). Hence, the required answer is 697.44 ft (Approx).

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The resulting vector matrix is [ -21 3 ]. Therefore, a = -21, and b = 3.

To find the resulting vector matrix of the given matrix multiplication, we need to multiply the first matrix, which is a 1x4 matrix, by the second matrix, which is a 4x1 matrix. The resulting matrix will be a 1x1 matrix (a scalar).

The calculation would be as follows:

[ 6 -5 -3 4 ] × [ -1 ] = [ (6 * -1) + (-5 * 3) + (-3 * 0) + (4 * 0) ]

[ 3 ]

Calculating the values:

[ (6 * -1) + (-5 * 3) + (-3 * 0) + (4 * 0) ]

[ 3 ]

= [ -6 - 15 + 0 + 0 ]

[ 3 ]

= [ -21 ]

[ 3 ]

So, the resulting vector matrix is [ -21 3 ]. Therefore, a = -21, and b = 3.

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The graph that correctly depicts Josiah's earnings, where the amount he earns and the number of chores completed is a proportional relationship, is the option;

On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (5, 15), and (6, 18) are plotted.

A proportional relationship is one in which the ratio of the terms in the ordered pairs in the relation are the same.

The table in the question can be presented as follows;

[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-5} & Week 1& Week 2 & Week 3 & Week 4 \\ \cline{1-5}Chores Completed & 4 & 6 & 4 & 5 \\\cline{1-5}Money Earned & \$12 & \$18 & \$12 & \multicolumn{1}{|c|}{} \\\cline{1-5}\cline{1-5}\end{tabular}[/tex]

The data in the above table indicates that when Josiah completes 4 chores, he earns $12, and when he completes 6 chres he earns $18

The amount Josiah earns and the number of chores Josiah completes is a proportional relationship, which indicates;

The amount Josiah earns per chore is therefore; $12/4 = $18/6 = $3 per chore

The amount Josiah earns per chore, indicates that in week 5, the amount Josiah earns, when he completes 5 chores is; Amount earned = 5 × $3 = $15

The points on the graph are therefore; (4, 12), (6, 18), (5, 15)

The correct option is therefore; (4, 12), (5, 15), (6, 18)

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Answer:

a

Step-by-step explanation:

...

The exponential equation to model this scenario is given  by y = 200(0.85)ˣ

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

A linear inequality has the form of a linear equation, showing the non equal comparison between numbers and variables.

The linear inequality y ≤ (1/3)x - 5 passes through the point (0, -5) and (15, 0)

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First, we can set up a proportion to find the ratio of the width to length for the photograph:

We can then use this ratio to find the width of the photograph with a length of 24 inches:

To solve for the width, we can cross-multiply:

Then divide by 4:

[tex]\therefore[/tex] The width of the photograph is 18 inches.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

Using the Linear Pair Postulate, the measure of the angle marked R is calculated as: D. 129°.

The Linear Pair Postulate states that if two angles form a linear pair, their measures add up to 180 degrees. Usually, two adjacent angles on a straight line are a linear  pair, which means they would add up to 180 degrees.

In the image given, we see that angle marked R and 51 degrees are on a straight line, therefore:

m<R = 180 - 51

m<R = 129°

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The total cost for the business trip considering the given information would be $7750.

To calculate the total cost for a business trip, you need to consider various expenses such as labor hours, training costs, and travel expenses.

First, let's break down the given information:

Labor hours: 80 hours

Hourly rate: $75 per hour

Training cost: $1000

Travel cost: $750

To calculate the cost for the business trip, you need to consider the following components:

Labor Cost:

Multiply the number of labor hours (80) by the hourly rate ($75) to determine the labor cost:

Labor Cost = 80 hours * $75/hour

Training Cost:

The training cost is given as $1000 and is not dependent on labor hours or hourly rates. Therefore, you can add this directly to the total cost.

Travel Cost:

The travel cost is given as $750 and is also not dependent on labor hours or hourly rates. This can be added directly to the total cost.

Now, let's calculate the total cost for the business trip:

Labor Cost = 80 hours * $75/hour = $6000

Training Cost = $1000

Travel Cost = $750

Total Cost = Labor Cost + Training Cost + Travel Cost

Total Cost = $6000 + $1000 + $750

Therefore, the total cost for the business trip would be:

Total Cost = $7750

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