For each function shown:
*Name the starting point.
*Explain how y changes as x increases.

Function #1: \(y = 0.5 + 3x\)

Function #2: \(y = 3(5)^x\)

For the random sample, the test statistic is -3.88.

The hypothesis to be tested can be expressed as follows:

H0: p1 ≤ p2, or equivalently p1 - p2 ≤ 0 (null hypothesis)

HA: p1 > p2, or equivalently p1 - p2 > 0 (alternative hypothesis)

where p1 is the true proportion of vehicles exceeding the pollution standard at low altitudes, and p2 is the true proportion of vehicles exceeding the pollution standard at high altitudes.

The test statistic to test this hypothesis is given by:

z = (p1 - p2) / sqrt(p(1 - p) * (1/n1 + 1/n2))

where p1 and p2 are the sample proportions of vehicles exceeding the pollution standard at low and high altitudes, respectively, p = (x1 + x2) / (n1 + n2) is the pooled sample proportion, x1 and x2 are the numbers of vehicles exceeding the pollution standard in the two samples, and n1 and n2 are the sample sizes.

For the given data, we have:

x1 = 41, n1 = 310, p1 = 41/310 ≈ 0.1323, x2 = 21, n2 = 95, p2 = 21/95 ≈ 0.2211, p = (x1 + x2) / (n1 + n2) ≈ (41 + 21) / (310 + 95) ≈ 0.1521

Substituting the values, we get:

z = (0.1323 - 0.2211) / sqrt(0.1521 * 0.8479 * (1/310 + 1/95))≈ -3.88

The test statistic is approximately -3.88.

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Answer:

-20.5, -8, 4.5, and 17

Step-by-step explanation:

You just replace x with the given information, then solve it

Answer:

-20.5

-8

4.5

17

Step-by-step explanation:

plug in the X value

Answer:

raspberry cookie is better

The solution is correct. The solution below will explain why the answer is correct for the problem, the ways in which the 'reasons' for the various steps could be improved, and finally a demonstration that the answer is wrong.

1. The solution is correct.

Step 1: log 5x + log(x - 1) = 2

Step 2: log (5x(x - 1)) = 2

Step 3: 10log(5x(x-1)) = 10²

Step 4: Write the original equation, product property of logarithms, and exponentiating each side using base 10logx = x.

Step 5: 5x² — 5x = 100

Step 6: x² – 5x = 20

Step 7: (x - 5)(x + 4) = 0

Step 8: Factor to find solutions, hence, the solution is x = 5 or x = -4.

Step 9: Write in standard form. Therefore, the solution is x = 5 or x = -4.

2. Improving the 'reasons' for the various steps

When considering the 'reasons' for the various steps, the following points could be improved:

Step 1: Students need to understand why we are adding the logarithms.

Step 2: Explain why we are taking the log of both sides of the equation.

Step 3: Provide reasons for the use of the power property of logarithms.

3. Demonstrating that the answer is wrong:

When solving logarithmic equations, it is always a good idea to check the answer and determine if it is correct. Let us substitute the solution into the equation to see if it is valid:

Given log 5x + log(x - 1) = 2...

When x = 5, the equation becomes log 5(5) + log(5-1) = 2... log 25 + log 4 = 2... log 100 = 2...

Thus, the answer is correct.

When x = -4, the equation becomes log 5(-4) + log(-4-1) = 2... log -20 + log -5 = 2...

Thus, this solution is incorrect.

4. Explaining the step(s) in the solution that is/are incorrect and why

Step 7: (x - 5)(x + 4) = 0

The factorization of the quadratic equation is the source of the mistake.

Instead of (x - 5)(x + 4), it should have been (x - 4)(x + 5).

5. Improvement suggestion

The solution given is effective, but the reasons could be improved. This would assist in the learner's understanding of the method.

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This is the potential function for the exact equation \frac{y}{x} 6x (\ln{x}-2)y'.

The potential function for the exact equation \frac{y}{x} 6x (\ln{x}-2)y' is \frac{y^2}{2}+6x^2y-2xy.

To find the potential function, we need to integrate the first term with respect to y and the second term with respect to x. This gives us:

\int\frac{y}{x}dy = \frac{y^2}{2}+C_1

\int 6xy dx = 3x^2y+C_2

We can then combine these two integrals to get the potential function:

\frac{y^2}{2}+3x^2y+C_1+C_2

Since we are looking for a potential function, we can ignore the constants and just focus on the terms with variables. This gives us:

\frac{y^2}{2}+3x^2y

We can also simplify this by factoring out a y:

y(\frac{y}{2}+3x^2)

This is the potential function for the exact equation \frac{y}{x} 6x (\ln{x}-2)y'.

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Answer:

The total distance of the round trip was 4 miles

Step-by-step explanation:

1. Let's check all the information given to answer the question correctly:

Speed of Dave walking to his friend's house = 4 mph

Speed of Dave biking from his friend's house = 10 mph

Time walking is 18 minutes longer than time biking

2. What was the total distance of the round trip?

Time walking = x

Time biking = x - 18

For solving x, we will use the following equation:

4x = 10 * (x - 18)

4x = 10x - 180

-6x = - 180

x = -180/-6 (Dividing by - 6)

x = 30

Dave walked 30 minutes and biked 12 minutes, now we can calculate the total distance, this way:

30 minutes = 0.5 hours and 12 minutes = 0.2 hours

Total distance = 4 *0.5 + 10 * 0.2

Total distance = 2 + 2

Total distance = 4 miles.

Answer:

4 miles is the answer

By applying Algebraic fractions simplifying concept, it can conclude that the simplified expression is - (9p + 3) / q.

Algebraic fractions simplifying can be done by factoring the quantifier and denominator, then dividing by the common factors of the quantifier and denominator.

We have the following algebraic fraction:

((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)

To simplify this expression, we will do the following steps:

First, we apply the division rule: (a/b) / (c/d) = ad / bc:

    ((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)

⇔ ((9p² - 1) (3p - 6)) / ((pq - 2q) (1 - 3p))

Then we find the factors of (9p² - 1), that are (3p - 1) (3p + 1):

⇔ ((3p - 1) (3p + 1) (3p - 6)) / ((pq - 2q) (1 - 3p))

Factor other expressions that are not already factored in:

⇔ ((3p - 1) (3p + 1) 3 (p - 2)) / (q (p - 2) (1 - 3p))

Now we cancel the common factor (p - 2), so we have:

⇔ (3 (3p - 1) (3p + 1)) / (-q (3p - 1))

Then we cancel the common factor (3p -1), so we have:

⇔ (3 (3p + 1)) / -q

Finally, we expand the expression:

⇔ - (9p + 3) / q

Thus the simplified expression is - (9p + 3) / q.

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Answer:

yoooo how you guys doing?

Answer:

y=-x+4

Step-by-step explanation:

Answer: y= x+4

Step-by-step explanation:

The distance between the hunter and the bird is 5.39

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below.

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

The hunter is at (0, 0) and shoots at (2, 5), so we can plug those values ​​into the formula for the distance:

distance = √( (2 - 9)² + (5 - 0)²)

distance = √( (2 )² + (5 )²)

distance = √( 4 + 25) = 5.39

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Answer:

Solution,

Onions less than 60 grams = 2 --> Pickling

Onions greater than 120 grams = 5 + 3 = 8 --> Market

Onions between 60 and 120 = 13---> Processing

Total frequency = 2 + 8 + 13 = 23

Now,

\(x = \frac{13}{23} \times 360\)

\(x = 203.48\)

\(x = 203.5\)

Hope this helps ..

Good luck on your assignment...

Answer:

x=190°

Step-by-step explanation:

find the frequency of the given numbers dividing by their numbers

onions less than 60g=(2+2/2)=²/9

onions greater than 120g=(5+3/2)= 4 (4+3/2). =3.5/9

To convert into degrees so that they can fit in the bar graph multiply the frequencies by 360 that is:

picking=²/9×360=80°

market=3.5/9×360=90°

x=360°-90°-80°

x=190°

confirmation

pie chart° add up to 360°

picking=80°

market=90°

x=190°

190°+80°+90°=360°

Answer:

C) 13

Step-by-step explanation:

f(x) = 5x -2

f(3) = 5(3) -2

f(3) = 15 - 2

f(3l) = 13

Step-by-step explanation:

BCD = 180- 100 = 80

the opposite angles of a parallelogram are of equal measure

SO DAB = X = 80

The sum of all parallelogram angles = 360

360 - 160 = 200

200 equals the measure of angle ADC + ABC

ABC = ADC

200 = 2ABC

ABC = 100

ADB = DBC = 30

Y = 100 - 30 = 70

another way to find y is using the rule that says that the sum of the triangle ADB angles = 180

180 = 80 + 30 + y

y = 70

Answer:

-8<8

1,3>-1,2

-5<0

0<4

0>-0,1

3<5

3,2>3,12

zero es mas grande que los numeros negativos

Answer:

First don't forget the [ tex ] [ /tex ] in order to execute the latex code.

Step-by-step explanation:

\( \sin A=\frac{5}{\sqrt{89}}sinA= 89 \)

\( \cos AcosA \) = \( \cos \)

The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Given that:

\(\sin A=\dfrac{5}{\sqrt{89}}\)

So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.

There must be existing a right triangle with same measure of angle A such that:

Perpendicular's length = P = 5 units

and Hypotenuse' length = H = \(\sqrt{89}\) units.

Using Pythagoras theorem, we get:

Base' length = B as:

\(P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8\)

(took positive root as B is representing length, a non-negative quantity).

Thus, Base is of 8 units length.

Thus, we get:

\(\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}\)

Rationalizing, we get:

\(\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}\)

Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is \(\dfrac{8\sqrt{89}}{89}\)

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Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

To find Piper's total balance in one year, she should multiply her current balance by a factor of 1.06. This factor represents the 6% annual interest rate applied to the initial investment without any additional deposits or withdrawals.

When calculating simple interest, the total balance after one year can be found by multiplying the current balance by the sum of 1 and the interest rate expressed as a decimal. In this case, the interest rate is 6%, which is equivalent to 0.06 as a decimal.

To find the total balance, Piper would multiply her current balance by 1 + 0.06, which simplifies to 1.06. This factor of 1.06 accounts for the initial investment and the 6% interest earned over the course of one year. It assumes that no additional funds are added or removed from the investment during that time.

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Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

-----------------------------------------------------------------------------------------------

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

Answer:

\( {3}^{10} \)

Step-by-step explanation:

\( {( {3}^{5}) }^{2} . \: {3}^{0} \\ {3}^{5 \times 2} . \: 1 \\ {3}^{10} . \: 1 \\ {3}^{10} \\ \)

The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Answer:

5.7

Step-by-step explanation:

They give you the value of a. Take that value and plug it into the equation.

2a + 3.1

a = 1.3

2(1.3) + 3.1

2.6 + 3.1

5.7

Hope this helped!

There are 36 cards in the box.  In this scenario, we are given that the probability of choosing a red card from a box is one-third. We also know that there are 24 blue cards in the box. Our goal is to find the total number of cards in the box.

Let's use the concept of probability to solve this problem. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability of choosing a red card is given as 1/3, and the favorable outcome is selecting a red card. Let R be the number of red cards, and T be the total number of cards in the box. The probability formula can be represented as:

Probability of choosing a red card = R / T

We are given that the probability of choosing a red card is 1/3:

1/3 = R / T

Since there are 24 blue cards in the box, we can represent the total number of cards as the sum of red and blue cards:

T = R + 24

Now, we can solve the system of equations to find the values of R and T:

1. 1/3 = R / T
2. T = R + 24

From equation 1, we can express R as:

R = (1/3) * T

Substitute this expression for R in equation 2:

T = (1/3) * T + 24

Multiplying both sides by 3 to eliminate the fraction, we get:

3T = T + 72

Subtracting T from both sides:

2T = 72

Now, divide by 2 to find the total number of cards, T:

T = 36

So, there are 36 cards in the box.

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um you need to be more specific on the question bud

Answer: The prime factorization is 3*11*11.

Answer:

Step-by-step explanation:

y = -2x - 7

-y = 2x - 13  

y = -2x + 13

parallel

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Tree diagram

Heads - 1

           - 2

           - 3

           - 4

           - 5

           - 6

Tails    - 1

           - 2

           - 3

           - 4

           - 5

           - 6

Count all the possibilities, and boom- 12 :)

Sorry if its wrong tho-

Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.

Answer:

81

Step-by-step explanation:

2. substitute values

(2+3+4)²

2. solve brackets first

(9)²

3. evaluate

9² = 81

The length of Rocky Mountain Juniper tree will be 1.269 feet.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

Now,

Let the height of Rocky Mountain Juniper tree = x feet

And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as;

⇒ 5.1 / 81.6 = x / 20.3

Solve for x as;

⇒ 5.1 × 20.3 / 81.6 = x

⇒ 103.53 / 81.6 = x

⇒ x = 1.269 feet

Thus, The length of Rocky Mountain Juniper tree will be 1.269 feet.

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