Convert the following equation to Slope-Intercept Form
HINT: Slope-Intercept Form is y = mx + b
y+1 = -5(x – 3)

Answer:

Step-by-step explanation:

10 to the 3rd power is the same as 10x10x10

(6 x 5) x 10*3

(30) x 1000

30000

Answer:

This function returns a zero value when x is equal to negative one or negative two.

Step-by-step explanation:

We can solve this by factoring the function:

f(x) = x² + 3x + 2

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

= (x + 1)(x + 2)

So function equals zero when x = -1 or -2

The ordered pair of C'' after the sequence of transformation is (-14, -5)

Here we have know that  ABC can be plotted at A (-14, 14), B (-8, 11) & C (-14, 5).

Here we all know that the y-axis reflection rule is written as,

=> (x, y) → (-x, y)

And the value of x coordinate flips in sign from positive to negative, or vice versa. Then the value of y coordinate stays the same.

Then the point is look like C(-14,5) will then reflect based on the following rule,

=> (x, y) → (x, y)

The transformed coordinates are look like,

=> (-14,5) ((-14),5)

=> (-14,5)→ (14,5)

Therefore, here we have point C' located at (14,5) after applying the y-axis reflection rule on point C.

Now, the next operation to do is is the 180 degree rotation.

And this can be clockwise or counterclockwise.

Then the rotation rule is written as

=> (x, y) → (-x,y)

Now, for this time both coordinates flip in sign.

Here we have know that this rule only works if the center of rotation is the origin.

Now, let us apply that rotation rule to C' to find where C" is located.

Then the rule can be written as,  (x, y) → (-x,y)

=> (14,5)→ (-14, -5)

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The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

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

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

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Complete question

What is √(2 + 2x) - 6 = 2

Answer:

(-5, 7)

Step-by-step explanation:

(x,y) over y= -x = (-y, -x)

(-7, 5) is turned to (-5, 7)

The angle by which the sprinkler should rotate is 0.89 Radians or 50.93°.

The space inside the section of the circle formed by two radii and an arc is the sector's area. It is a small portion of the circle's total surface area.

Area of sector of circle (A) = \(\frac{1}{2} r^{2}x\)

where, A= 100 square yards,

r = 15 yards,

x = central angle in Radians

substituting in equation

\(100 = \frac{1}{2}15^{2}x\)

\(x = \frac{200}{225} \\\)

x = 0.888889 Radians or x ≈ 50.929588°

thus, x = 0.89 Radians or 50.93° (rounded off to 2 decimals)

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Answer:

Step-by-step explanation:

Sally's hypothesis can be shown as:

From the data in the table we can see that:

As we see there is a difference, Sally can pick up one paper clip for each 4 coils.

Correct answer choice is D.

Answer:

Greatest common factor (GCF) of 60: 223

Greatest common factor (GCF) of 108: 22333

The Greatest Common Factor (GCF) is:   2 x 2 x 3 = 12

Step-by-step explanation:

To get the Greatest Common Factor (GCF) of 60 and 108 we need to factor each value first and then we choose all the copies of factors and multiply them.

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Substituting the given values into the formula, we get logistic growth as

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

A pattern of population expansion known as logistic growth sees population growth begin slowly, pick up speed, then slow to a stop as resources run out. It can be shown as an S-shaped curve or a logistic function.

The formula for logistic growth can be expressed as:

\(P(t) = K / (1 + A * e^{(-r * t)})\)

where:

P(t) is the population at time t,

K is the carrying capacity,

A = (K - P₀) / P₀,

P₀ is the initial population,

r is the growth rate per unit of time, and

e is the base of the natural logarithm (approximately 2.71828).

Given the information you provided:

r = 0.013 (per year)

K = 2392

P₀ = 127

First, let's calculate the value of A:

A = (K - P₀) / P₀ = (2392 - 127) / 127 = 18.748

Now, substituting the given values into the formula, we get:

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

Remember to round the parameters to three decimal places when performing calculations.

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The probability that exactly 10 customers will arrive at the vendor in the next 30 minutes is approximately 0.0656 or about 6.56%.

The number of customers arriving at the vendor in a 10-minute interval follows a Poisson distribution with a mean of λ = 3.

The probability of exactly x customers arriving in a 10-minute interval is given by:

P(X = x) = \((e^{(-\lambda)} \times \lambda^x) / x!\)

e is the base of the natural logarithm (approximately equal to 2.71828).

The probability of exactly 10 customers arriving in the next 30 minutes we need to consider three consecutive 10-minute intervals.

The total number of customers arriving in 30 minutes follows a Poisson distribution with a mean of λ = 9 (3 customers per 10-minute interval × 3 intervals

= 9 customers in 30 minutes).

The Poisson probability formula to calculate the probability of exactly 10 customers arriving in 30 minutes:

P(X = 10) = (e⁽⁻⁹⁾ × 9¹⁰) / 10!

X is the random variable representing the number of customers arriving in 30 minutes.

Using a calculator or a computer program can evaluate this expression to get:

P(X = 10) ≈ 0.0656

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Answer:

i. 5(x + 0.2x) yards

ii. 6x yards

Step-by-step explanation:

Since the requested quilts are 20% larger than the normal pattern, then;

20% of x = 0.2 x

Thus,the yards of material to make each of the requested quilts increased by 0.2x yards.

So that;

To make one of the requested quilt, the yards required = x + 0.2x

For 5 requested quilts, the total yards required = 5(x + 0.2x)

Total yards of material for the requested quilts is 5(x + 0.2x).

Also,

5(x + 0.2x) = 5x + 5(0.2x)

                  = 5x + x

                  = 6x

Thus, the total yards required is 5(x + 0.2x) or 6x.

Statistic shows that 70 percentage of jeep customers are considered as dreamers. The 3rd Option is correct.

Some Jeep customers are considered "dreamers" because the Jeep brand has long been associated with adventure, freedom, and a sense of rugged individualism. Jeep vehicles are often seen as being able to take their drivers off the beaten path, to explore new places and experiences.

Jeep has also marketed their vehicles as a symbol of the American spirit and a connection to the country's history. For many, owning a Jeep is seen as an aspirational goal, representing a lifestyle that is free, adventurous, and independent.

In this sense, Jeep customers can be considered "dreamers" because they are buying into the idea of what the Jeep brand represents, and they may see owning a Jeep as a way to fulfill their dreams of adventure, exploration, and freedom.

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Answer:

x = 10

Step-by-step explanation:

In similar polygons, the lengths of the sides are proportional.

(3x + 5)/42 = 30/36

(3x + 5)/42 = 5/6

6(3x + 5) = 5 × 42

18x + 30 = 210

18x = 180

x = 10

Answer:

x=10

Step-by-step explanation:

7.

\(\frac{3x+5}{42} =\frac{30}{36} \\3x+5=\frac{30}{36} \times 42\\3x+5=35\\3x=35-5=30\\x=\frac{30}{3} =10\)

To find P(Q and R), we can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P(R) = 0.24P(Q and R) = P(Q) × P(R) = 0.37 × 0.24 = 0.0888.

Therefore, the probability of both Q and R occurring together is 0.0888. Long Answer:Independent events:In probability theory, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Two events A and B are independent if the probability of A and B occurring together is equal to the product of the probabilities of A and B occurring separately. Mathematically,P(A and B) = P(A) × P(B) Suppose Q and R are independent events. Find P(Q and R).

We can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P

(R) = 0.24

P(Q and R) = P(Q) × P(R)

= 0.37 × 0.24

= 0.0888

Therefore, the probability of both Q and R occurring together is 0.0888. Hence, P(Q and R) = 0.0888. In probability theory, independent events are the events that are not dependent on each other. It means the probability of one event occurring does not affect the probability of the other event occurring.

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Therefore , it verifies the statement that over 29 year period her heart rate will decrease by 8% percentage .

In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, if you correctly answered 75 out of 100 expression questions on a test (75/100), you would have received a 75%.

Here,

given :  20 year old : 193 beat per minute.

forty year old : 178 beat per minute.

Thus ,

193 * 8 /100 = 15.44

=> 15(approx)

Thus , if we subtract the 8 % of bpm from 193

=> 193 - 15= 178

Therefore , it verifies the statement that over 29 year period her heart rate will decrease by 8% .

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Answer:

The correct sequence of licenses that allow you to receive a full provisional license is C: limited provisional license, full provisional license, limited learner permit.

Answer:

-(1/4)^4

Step-by-step explanation:

Hope it helped!!!

Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

The expected number of juniors in the committee is 1.3

The question is incomplete, the complete question is given below:

A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the​ committee?

The expected number of juniors in the committee is computed here as:

Juniors in the committee=13

Seniors in the committee=17

Total number of members=(13+17)=30

Fraction of juniors in total members=13/30

So expected number of juniors in the committee:

=Fraction of juniors in total members*Total number of members to be selected

=(13/30)*3

=1.3

Therefore 1.30 is the expected number of juniors in the committee

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The trigonometric function plot in Cartesian plane is shown below.

In this question we must create a graph of a trigonometric function, tangent function. The complete procedure is summarized below:

Step 1:

x = 0

tan 0 = 0

tan (π / 4) = 1

tan (π / 2) = NaN

tan (3π / 4) = - 1

tan π = 0

tan (5π / 4) = 1

tan (3π / 2) = NaN

tan (7π / 4) = - 1

tan 2π = 0

Step 2 & 3 - The result is shown in the image attached below.

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The speed of the faster cyclist is 14\ miles/hr.

What is speed?

It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.

Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,

\(2s+s=42\\3s=42\\s=14\)

Now, distance coverd by the first cyclist is \(2s=2\times 14\\=28 \ $miles\).

Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.

\(Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr\)

Hence, the speed of the faster cyclist is 14\ miles/hr.

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Answer:

the answer is 18 or number 8 on your list

Step-by-step explanation:

The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.

For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:

10 - 12|2

5 - 6|2

5 - 3|3

5- 1|5

1 - 1

Hence:

lcm(10, 12) = 2² x 3 x 5 = 60.

Hence:

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The probability that the next card Scarlett selects will have an anglerfish on it is 2/15, or approximately 0.1333.

To find the probability of selecting an anglerfish on the next card, we need to calculate the ratio of the number of anglerfish cards to the total number of cards in the deck.

From the given information, Scarlett selected 2 anglerfish cards during her previous selections.

The total number of cards she selected is 2 + 3 + 1 + 4 + 5 = 15.

Therefore, the probability of selecting an anglerfish card on the next draw is 2/15.

Calculate the total number of cards Scarlett selected.

2 + 3 + 1 + 4 + 5 = 1

Calculate the number of anglerfish cards Scarlett selected.

Scarlett selected 2 anglerfish cards.

Calculate the probability of selecting an anglerfish card on the next draw.

Probability = Number of anglerfish cards / Total number of cards

Probability = 2 / 15

Probability ≈ 0.1333

Thus, the probability that the next card Scarlett selects will have an anglerfish on it is 2/15, or approximately 0.1333.

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Answer:99904.

Step-by-step explanation:

Find the LCM of

5

10 = 2x5

15 = 3x5

20 = 2x2x5

25 = 5x5

LCM = 2x2x3x5x5 = 300

Take the smallest 5-digit number: 10000 and divide it by 300 to get 33.33. Round it off to 34 and multiply it by 300 to get 10200. Finally add 4 to 10200 to get 10204 which is the smallest final 5-digit number.

Check: 10204/5 = 2040 as quotient and a remainder of 4. Correct.

10204/10 = 1020 as quotient and a remainder of 4. Correct.

10204/15 = 680 as quotient and a remainder of 4. Correct.

10204/20 = 510 as quotient and a remainder of 4. Correct.

10204/25 = 408 as quotient and a remainder of 4. Correct.

Answer: 10204.

To get the greatest 5-digit number take 99999 and divide it by 300 to get 333.33. Round it off to 333 and multiply it by 300 to get 99900. Finally add 4 to 99900 to get 99904 which is the final greatest 5-digit number.

Check: 99904/5 = 19980 as quotient and a remainder of 4. Correct.

99904/10 = 9990 as quotient and a remainder of 4. Correct.

99904/15 = 6660 as quotient and a remainder of 4. Correct.

99904/20 = 4995 as quotient and a remainder of 4. Correct.

99904/25 = 3996 as quotient and a remainder of 4. Correct.

Answer: 99904.