Kai correctly used the different laws of logarithms to rewrite log27 - log(3/5) -log 5 as one logarithm.



His work is shown here



Step one: Log27-(log3- log5) -log 5


Step two: log (3^3) -log 3+ log 5- log 5


Step three: log (3^3) - log3


Step 4: 3 log3- log 3


Step 5: 2 log 3


Step 6: log (3^2)


Step 7: log 9



In which step(s) did kai apply the difference law for logarithms


A- step 3


B- step 5


C- step 4


D- step 1

In the equation F=kx, F is the force, k is the spring constant, and x is the displacement.  Plug in and solve:

F=0.3(1.5)

F=0.45N

Hope this helps!!

1 - 8

2 - 16

3 - 32

x - +200

Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.

4 - (32 x 2 = ) 64

8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.

5 - (64 x 2 = ) 128

120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.

ANSWER

A.

It satisfies the top equation but not the bottom equation.

EXPLANATION

The given equations are;

2x-3y=18

5x+3y=3

When we substitute x=6 and y=-2 into the top equation we get,

2(6)-3(-2)=18

12+6=18

18=18

This is true. Hence the point satisfy the top equation.

But when we substitute x=6 and y=-2 into the bottom equation we get,

5(6)+3(-2)=3

30-6=3

24=3

Hence the bottom equation is not satisfied.

The first choice is correct.

Final answer:

The probability that Judy guesses at least 3 questions correctly in a multiple-choice test is calculated using the binomial probability formula. For the survey question, the hypergeometric distribution is used to find the probability of 4 or fewer out of 9 people entering a profession related to their major. Exact probabilities require mathematical computation.

Explanation:

Probability of Answering Multiple-Choice and Survey Questions Correctly

For question 1, we must calculate the probability that Judy guesses at least 3 questions correctly on a 7-question multiple-choice test, where each question has 4 possible answers. Since only one answer is correct per question, her probability of guessing a question correctly is 1/4. To find the total probability of answering 3 or more questions correctly, we use the binomial probability formula which considers the probability of success (1/4) and the number of trials (7 questions). We sum the probabilities of getting exactly 3, 4, 5, 6, or all 7 questions correct.

For question 2, regarding the survey of 300 college graduates, we use the hypergeometric distribution since the samples are taken without replacement. We need to determine the probability that 4 or fewer of the randomly selected 9 survey subjects entered a profession closely related to their college major. We know that 63% of the entire group, which is 189 individuals, entered a relevant profession. We sum the probabilities of 0, 1, 2, 3, and 4 people from our sample of 9 falling into the group who are working in their field.

The correct probabilities from the provided choices are not directly calculable without doing the necessary computations using the respective formulas for each scenario, which are beyond the scope of this response as we do not have the calculations or the respective formulas provided within the context of this interaction.

x = 180° - 67° - 52°

x = 61°

So, the value of x is 61°

Check the picture below.

Answer:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation is [tex]\frac{x-2}{4}=2[/tex]

- The value of x is 10

- We want to a statement reason to each step to complete the proof

* Lets write each step with statement reason

1. [tex]\frac{x-2}{4}=2[/tex]  ⇒ Given

2. [tex]4(\frac{x-2}{4})=4*2[/tex]  ⇒ simplifying multiplication property of equality

3. x - 2 = 8  ⇒ Simplifying

4. x - 2 + 2 = 8 + 2                      

5. x = 10  ⇒  addition property of equality

- In step 2 we multiply both sides by 4 to cancel the denominator of

 the left hand side (simplifying multiplication property of equality)

- Then we simplify the two sides to get (x - 2 = 8)

- Then we add two to both sides to cancel -2 in the left hand side

- Then after adding we find (x = 10) , (addition property of equality)

* The answer is:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

Answer:

$35

Step-by-step explanation:

since it is 60% off, $14 is 40% of original price.

1% of original price (original price is 100%)

= $14 ÷ 40

= $0.35

original price

= $0.35 × 100

= $35

Answer:

The area of ABCD is 50 units²

The area IJKL is 80 units²

The area of QRST is 100 units²

The area of UVWX is 300 units²

Step-by-step explanation:

* Lets revise the area of the rectangle

- The area of any rectangle = its length × its width

- To solve the problem find the lengths of two adjacent sides and

  consider that one of them is the length and the other is the width

- Use the rule of the distance between two points (x1 , y1) and (x2 , y2)

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

# In rectangle ABCD

∵ A = (-9 , 8) , B = (-5 , 5) , C = (1 , 13)

∴ AB = √[(-5 - -9)² + (5 - 8)²] = √[(4)² + (-3)²] = √[16 + 9] = √25 = 5 units

∴ BC = √[(1 - -5)² + (13 - 5)²] = √[(6)² + (8)²] = √[36 + 64] = √100 = 10 units

∴ The area of ABCD = 5 × 10 = 50 units²

# In rectangle EFGH

∵ E = (30 , 20) , F = (39 , 29) , G (49 , 19)

∴ EF = √[(39 - 30)² + (29 - 20)²] = √[9² + 9²] = √[81 + 81] = √162 unit

∴ FG = √[(49 - 39)² + (19 - 29)²] = √10² + (-10)²] = √[100 + 100] = √200 units

∴ The area of EFGH = √162 × √200 = 180 units²

# In rectangle IJKL

∵ I = (-6 , 2) , J = (2 , 2) , K = (2 , -8)

∴ IJ = √[(2 - -6)² + (2 - 2)²] = √[8² + 0²] = √8² = 8 units

∴ JK = √[(2 - 2)² + (-8 - 2)²] = √[0² + (-10)²] = √10² = 10 units

∴ The area IJKL = 8 × 10 = 80 units²

# In rectangle MNOP

∵ M = (5 , 5) , N = (11 , 5) , O = (11 , -5)

∴ MN = √[(11 - 5)² + (5 - 5)²] = √[6² + 0²] = √6² = 6 units

∴ NO = √[(11 - 11)² + (-5 - 5)²] = √[0² + (-10)²] = √10² = 10 units

∴ The area of MNOP = 6 × 10 = 60 units²

# In rectangle QRST

∵ Q = (10 , 0) , R = (15 , 5) , S = (25 , -5)

∴ QR = √[(15 - 10)² + (5 - 0)²] = √[5² + 5²] = √[25 + 25] = √50 units

∴ RS = √[(25 - 15)² + (-5 - 5)²] = √[10² + (-10)²] = √[100 + 100] = √200 units

∴ The area of QRST = √50 × √200 = 100 units²

# In rectangle UVWX

∵ U = (0 , 5) , V = (15 , 20) , W = (25 , 10)

∴ UV = √[(15 - 0)² + (20 - 5)²] = √[15² + 15²] = √[225 + 225] = √450 units

∴ VW = √[(25 - 15)² + (10 - 20)²] = √[10² + (-10)²] = √100 + 100 = √200 units

∴ The area of UVWX = √450 × √200 = 300 units²

Answer:

h=20

Step-by-step explanation:

h=3 (V/lw)

h= 3 (960/12*12)

- The equation of this line is x=3.

- And I think it's also, This graph is a function of whose range is set at {3}.

Answer:

D. The equation of this line is x=3

E. This graph is not a function because the value x=3 is assigned to mre than one y-value.

Step-by-step explanation:

The range is all real numbers.

The domain of this graph is x=3, but it is not a function

The graph is a vertical line whose equation is x=3 because the graph passes through (3,y).

This graph cannot represent a function because it will not pass the vertical line test.

In other words, the x-value of 3 is assigned to more than one y-value.

Therefore the correct answers are:

Option D and E

The answer should be 3840

The degree of a polynomial is the highest exponent.

The highest exponent in this equation is 17x^4

The degree is 4.

Answer:

  216

Step-by-step explanation:

Each of the three digit positions can have any of 6 values, so there are ...

  6^3 = 216

possible numbers that can be formed.

Answer:

110.9 sq ft

Step-by-step explanation:

split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh

A=(1/2)(8)(13.86)= 110.9

Answer:

A =  64√2 ft² = approx. 90.5 ft²

Step-by-step explanation:

Because this is an equilateral triangle, the interior angles are also equal and are 60° each.  We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle.  We see from the diagram that the base is 16 ft.  

Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get

sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that

 h        1

----- = -----

16      √2                              16

and so √2*h = 16, and h = -------

                                              √2

                                                                                        1      16     16

Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------

                                                                                         2      1       √2

           128           128√2

or A = -------     = ------------ = 64√2 ft² = approx. 90.5 ft²

            √2               2

Snake wnemwmammwmenkk ju jxi I I i I jus uo I j i I i I i I i I i i izj

A scatter plot has a good fit when data points cluster near the line of best fit and show a clear positive or negative correlation, suggesting a strong relationship between variables. A bad fit is characterized by scattered data points with no apparent pattern and large residuals between the points and the line, indicating a weak or no correlation.

When a scatter plot has a good fit, it means that the line of best fit accurately represents the trend in the data. This line minimizes the distances, or residuals, between itself and all the points on the graph. You can tell if a scatter plot has a good fit if the data points form a pattern that closely follows the line of best fit, indicating that the variables have a strong correlation. Conversely, a bad fit is evident when the data points are widely scattered and do not follow a distinct pattern, suggesting a weak or no correlation between the variables.

Signs of a Good Fit in Scatter Plots

Signs of a Bad Fit in Scatter Plots

Whether the X and Y variables in a scatter plot are good candidates for linear regression depends on the aforementioned signs. If there is a clear positive or negative correlation and data points approximate a linear trend, they are good candidates for linear regression.

Answer:

27.90

Step-by-step explanation:

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The amount of money that is left with Lisa after buying tickets is $27.90.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The total number of members in the family is 5 (Parents+2sisters+Lisa). Also, the cost of a single ticket in Atlanta is $14.42, therefore, the cost of five tickets will be,

The cost of 5 tickets = $14.42 × 5 = $72.10

The amount Lisa has to spend is $100, therefore, the money left with Lisa after buying the tickets is,

Amount left = $100 - $72.10 = $27.90

Hence, the amount of money that is left with Lisa after buying tickets is $27.90.

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Answer:

x = 11

Step-by-step explanation:

If a radius bisects a chord ( as in the lower chord )then it is perpendicular to the chord.

Thus both chords are equidistant from the centre ( both 12 ) and are therefore congruent.

Hence x = 11

Answer:

The answer is 62208

Step-by-step explanation:

The reason is because 18*2=36 12*2=24 and 36*2=72

36*24*72=62208

Can I get brainliest

Answer:

(0, 1)

Step-by-step explanation:

all of the points are the same number away: 2√5

Answer:

  (0, 1)

Step-by-step explanation:

A, B, and C are points on a circle. You are being asked to find the center of the circle. You can do that any of several ways.

I find it useful to plot the points on a graph. Doing so reveals that AB is perpendicular to BC, so ABC is a right triangle, and the center you want is the midpoint of the hypotenuse (AC).

  (A+C)/2 = ((2, -3) +(-2, 5))/2 = (2-2, -3+5)/2 = (0, 1) . . . . . coordinates of center

___

From a construction point of view, the center of the circle is the point of intersection of the perpendicular bisectors of the chords. In the attached, we have used a geometry program to draw the perpendicular bisectors of AB and BC. They meet at (0, 1).

___

From an algebra point of view, the points on the circle with center (h, k) and radius r satisfy the equation ...

  (x -h)^2 +(y -k)^2 = r^2

Filling in the point values, you get three equations in the three unknowns (h, k, r):

Finding the difference between any two pairs of these will result in two linear equations in h and k, so are easily solved.

  First - second: (4 -4h +h^2) +(9 +6k +k^2) -(16 -8h +h^2) -(9 -6k +k^2) = r^2 -r^2

  -12 +4h +12k = 0 . . . simplify

  h +3k = 3 . . . . . . . . . put in standard form

  Second -third: (16 -8h +h^2) +(9 -6k +k^2) -(4 +4h +h^2) -(25 -10k +k^2) = r^2 -r^2

  -4 -12h +4k = 0 . . . . simplify

  3h -k = -1 . . . . . . . . . put in standard form

Now, we can add 3 times the second of these equations to the first to find h:

  (h +3k) +3(3h -k) = (3) +3(-1)

  10h = 0

  h = 0

Then either of the equations can be used to find k = 1.

The center is (h, k) = (0, 1).

(x+4)(x-3)=30

x^2 +x -12 =30

x^2 +x =42

x^2 +x -42 =0

(i solved it by factorising: _x^2 × -42)

x^2 -6x +7x -42 =0

x(x-6) +7(x-6) 0

(x-6)(x+7)=0

x=6; x=-7

since it's a length, x can't be a negative number, so it must be 6

Answer:

  x = 30°

Step-by-step explanation:

x° is the other acute angle of the right triangle with 60° as the acute angle at the center of the circle. (The tangent line makes a right angle with the radius at the point of tangency.)

[tex]\textrm{97 percent accurate for individual with the virus}[/tex]

[tex]\text{3 percent inaccurate}[/tex]

[tex]\textrm{99 percent accurate for an individual}[/tex]

[tex]\textrm{1 percent inaccurate probability}[/tex]

[tex]\textrm{Probability of infected:}[/tex]

[tex].0055[/tex]

[tex]\textrm{Probability of not being infected}[/tex]

[tex]1 - .0055 = .9945[/tex]

[tex]\textrm{Combine it all together}[/tex]

[tex]0.0055 * 0.03 + 0.9945 * 0.01 = 0.01011[/tex]

[tex]\textrm{The probability that a randomly chosen person gets an incorrect result is 0.01011}[/tex]

[tex]\textbf{Answer}[/tex]

[tex]\textrm{0.01011}[/tex]

The probability of an incorrect result for the test to detect respiratory syncytial virus is calculated by considering the test's sensitivity and specificity, along with the prevalence of the virus in the population.

In order to calculate the probability that a randomly chosen person gets an incorrect result, we first need to understand how test accuracy works. Sensitivity refers to how often the test correctly identifies the presence of a disease when it is indeed there, while specificity refers to how often it correctly identifies the absence of a disease when it isn't there. In this case, the sensitivity is 97%, meaning it correctly identifies the virus in 97% of individuals who have the virus; the specificity is 99%, meaning it correctly identifies no virus in 99% of individuals who do not have the virus.

For the given population, 0.55% are infected. Hence, the probability of an incorrect result for a person with a virus is 3% (100% - 97%), and for a person without the virus is 1% (100% - 99%). Therefore, the total probability of getting an incorrect result is (0.55%/100 * 3%) + [(1 - 0.55%/100) * 1%].

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Answer:

4.22 meters per second.

Step-by-step explanation:

First multiply the revs per second by pi:

= 11pi = 34.558.

Now multiply this by the diameter which is 2*6.1 = 12.2 cm = 0.122 m.

Linear velocity =  0.122 * 34.558

= 4.22 m/s.

Linear velocity of the gear in meters per second is  4.22 m/s.

Linear velocity is the measure of “the rate of change of displacement with respect to time when the object moves along a straight path.” It is a vector quantity.

Given

Gear of radius = 6.1 cm

Gear of diameter = [tex]2 \times 6.1 = 12.2 cm[/tex] = 0.122 m

Revolutions per second = [tex]11\pi[/tex] = 34.558

Linear velocity of the gear  =  diameter × Revolutions per second

Linear velocity = 0.122 × 34.558

= 4.22 m/s

Linear velocity of the gear in meters per second is  4.22 m/s.

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Answer:

x = 17

Step-by-step explanation:

For the parallelogram to be a rhombus then then the diagonal must bisect the given angle, thus

3x - 11 = x + 23 ( subtract x from both sides )

2x - 11 = 23 ( add 1 to both sides )

2x = 34 ( divide both sides by 2 )

x = 17

Answer:

The missing number is 8

Step-by-step explanation:

Hope this helps (3

it will be 297,088 as the answer

For this problem, you need to know how to use sin, cos, and tan or 'SOH-CAH-TOA' sin- opposite/hypotenuse cos-adjacent/hypotenuse toa- opposite/adjacent

in this case, you can use tan or toa

the equation should be set up like this:

4/x=1/0.848

solve, and you will get 3.39...

(you need to use the sin,cos,tan degree chart to find 0.848)

Answer:

1

Step-by-step explanation:

-2(1) = -2

then -2 - 4 = -6

-6 = -6

Answer:

1

Step-by-step explanation:

Move all terms that don't contain x to the right side & solve.

Answer:

The inverse of f(x) is  [tex]f ^ {- 1}(x) = x + 2[/tex]

Step-by-step explanation:

To find the inverse of the function [tex]f (x) = x-2[/tex], perform the following steps:

1) do [tex]y = f (x)[/tex]

[tex]y = x-2[/tex]

2) Solve the equation for the variable x.

[tex]y + 2 = x -2 +2[/tex]

[tex]y + 2 = x[/tex]

3) exchange the variable x with the variable y

[tex]y + 2 = x[/tex] ----> [tex]x + 2 = y[/tex]

4) Change the variable y by [tex]f ^{- 1}(x)[/tex]

Finally the inverse function is:

 [tex]f ^ {- 1} (x) = x + 2[/tex]

Answer:

f-1(x)=x+2

Step-by-step explanation:

Multiply the price before the tip by .20

[tex]45 * .20 = 9[/tex]

Add 9 to the total:

[tex]45 + 9 = $54[/tex]

So, the total cost for Thom's meal is $54

The total cost for Thom's meal is $54.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.

Given

Thom's restaurant bill is $45

20 percent tip = 20 % of 45 = 20/100*45 = 9

Total cost =  Thom's restaurant bill + 20 percent tip

                = 45+ 9 = 54

Therefore, The total cost for Thom's meal is $54.

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