Which of the following illustrates the product rule for logarithmic equations?
log (4x) = log24 = log2x
log2(4x) = log24-log2x
o log2 (4x) = log24-log2x
log2(4x) = log24+log2x

Answer:

Step-by-step explanation:

B

Answer:

the answer is B

Step-by-step explanation:

Out of 58 cities, 26 have either a lake or a river, which simplifies to a fraction of 13/29 of the cities having one of these features.

To find the fraction of 58 cities that have either a lake or a river running through them, we need to determine how many cities have at least one of these features. It is important to check if any city has both a lake and a river, but since the question does not provide this information, we will assume that there are no cities that have both. The question tells us that 3 cities have a lake and 23 have a river. We simply add these counts together to find the total number of cities with at least one water feature.

The calculation would be:

3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river)

To find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with a water feature by the total number of cities:

26 (cities with a lake or a river) / 58 (total cities) = 13/29 (simplified fraction).

Final answer:

Of the 58 cities, 26 have either a lake or a river, which means the fraction of cities with a lake or a river is 26/58.

Explanation:

To determine what fraction of the 58 cities have a lake or a river running through them, we must consider that the question does not specify whether some cities might have both a lake and a river. Assuming that the cities with lakes and the cities with rivers do not overlap, we simply add the number of cities with each feature.

There are 3 cities with a lake and 23 with a river. To find the total number of cities with either a lake or a river, we add these two numbers together:

3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river).

Now, to find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with water features by the total number of cities:

26 / 58 = fraction of cities with a lake or a river running through them.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that [tex]0 \le x \le 8 \:and\: $0 \le y \le 4$.[/tex]

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: [tex]x + y \le 4[/tex]) are:

[tex](0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)[/tex]

n(A)=15

Therefore:

[tex]P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}[/tex]

Final answer:

To find the probability that a randomly selected point with integer coordinates satisfies "x + y ≤ 4", we counted the number of qualifying points and divided by the total number of possible points. With 15 points meeting the condition out of 45 possible points, the probability is 1/3.

Explanation:

The probability question asks for the likelihood that a point (x, y) with integer coordinates will satisfy the condition "x + y ≤ 4" when 0 ≤ x ≤ 8 and 0 ≤ y ≤ 4. To solve this, we first count the total number of possible points with integer coordinates within the given ranges for x and y. Since x can take 9 values (0 through 8) and y can take 5 values (0 through 4), there are 45 possible points (9 times 5).

Next, we identify the points that satisfy the condition "x + y ≤ 4". These points are (0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), and (4,0), which results in a total of 15 points satisfying the condition.

The probability is therefore the number of satisfying points divided by the total number of possible points, which is 15/45 or simplified to 1/3. Thus, the probability that a randomly selected point with integer coordinates will have "x + y ≤ 4" is 1/3.

Answer:

1920.5

Step-by-step explanation:

Final answer:

To find the volume of a cone with specific dimensions, use the formula V = 1/3 π r² h. Substitute the given values for radius and height, then calculate the volume rounded to the nearest tenth.

Explanation:

The volume of a right circular cone can be found using the formula V = 1/3 × π × r² × h, where r is the radius and h is the height of the cone.

Plugging in the values (r = 9.6 cm, h = 19.9 cm) gives V = 1/3 × 3.142 × 9.62 × 19.9 = 200.5 cm³

Answer:

That time is  35.4 minutes.

Step-by-step explanation:

The mean time of delivery follows a Normal Distribution pattern.

So we need to apply Z-scores to find out.

99% confidence  in delivery time means  P(z > value) = 0.01  = 1%

So    z > 2.325

so.      Pr [ (x - 21.2) /  6.1   >  2.325 ] = 1%

so  x  >  2.325*6.1 + 21.2

x  >  35.3825 minutes  would be out of the 99th percentile

Final answer:

To calculate the 99th percentile of pizza delivery times, use the z-score corresponding to a 0.99 probability and apply the formula X = μ + (z * σ), where X represents the delivery time, μ is the mean, and σ is the standard deviation.

Explanation:

The student is asking for the 99th percentile of the pizza delivery time, given that the times are normally distributed with a mean of 21.2 minutes and a standard deviation of 6.1 minutes. To find the 99th percentile, one would typically use a z-score table or a statistical software to find the z-value that corresponds to the 0.99 probability. Once the z-score is found, the formula X = μ + (z * σ) is used to calculate the specific time that corresponds to the 99th percentile, where X is the delivery time, μ is the mean delivery time, σ is the standard deviation, and z is the z-score. Since the student is asking for a guaranteed delivery time that covers 99% of the deliveries, this time will be longer than the average to account for the variability represented by the standard deviation.

Answer:

Hence there were total of 19 pizza and were ate among the 76 children in party.

Step-by-step explanation:

Given:

8 slices for each pizza

No of pizza ate are =12+3+4=19

To Find:

How many children were are party

Solution:

Given that each children ate 2 slices per head so

Total pizza=19

and each pizza is sliced in 8 parts so

19 pizza will give =19 *8=152 slices

Hence there are 152 total number of slices

So 2 slices/child and 152 slices

152 slices/ 2 slices/child

=(152/2)children

=76 children.

When wearing the magic ring, health points increase by 30% more.

Some expressions that could represent how many health points the spell restores are:

1.3(H)

H + 0.3(H)

Hope this helps!! :)

The healing spell with the magic ring restores 130% of the health points, represented as 1.30 imes H.

If Eiko's healing spell restores H health points without the magic ring, then with the ring, the spell's power increases by 30%. Thus, the total healing power with the ring can be expressed as H + 0.30 x H, which can also be simplified to 1.30 x H. This means, with the ring, Eiko would restore 130% of the health points that the spell would normally heal without the ring.

Answer:

36 Yellow pieces

Step-by-step explanation:

-Given the total number of pieces is 80 and the probability of choosing a yellow piece at random is 0.45.

-To find the number of yellows pieces in the container, we multiply its probability by the total number of pieces;

[tex]n_y=P(yellow)\times n\\\\=0.45\times 80\\\\=36[/tex]

Hence, the total number of yellow pieces is 36

Final answer:

To find the total number of yellow game pieces in the container, we can use the given probabilities to calculate the number of yellow pieces. By setting up equations based on the information provided, we determine that there are 8 yellow game pieces in the container.

Explanation:

Let's first calculate the total number of game pieces in the container.

Let x be the total number of yellow game pieces. The total number of game pieces is 80.

Given that the probability of choosing a green piece is 0.2 and the probability of choosing a yellow piece is 0.45:

Let the number of green pieces be (80 - x), so 0.2(80 - x) = 4 - 0.2x

Now, we know the number of yellow pieces is x, so 0.45x = 0.45x

Solving the equations, we get x = 8, thus there are 8 yellow game pieces in the container.

Answer:

A

Step-by-step explanation:

The rest are incorrect

A solution is a homogeneous mixture composed of a solute dissolved in a solvent. It can be separated by passing it through a filter.

A solution is a homogeneous mixture composed of a solute dissolved in a solvent. From the given options, property (c) is most characteristic of a solution. A solution can be separated by passing it through a filter, which removes the solute particles, resulting in a purified solvent. Gravity does not separate the parts of a solution, and the average diameter of solute particles can vary depending on the nature of the solute. Additionally, the composition of a solution is uniform throughout, so there is no distinction between the top and bottom layers.

https://brainly.com/question/31373221

#SPJ6

Answer: edgen

B 2=(1+0.065/12)^12t

Step-by-step explanation:

To the nearest year, it will take about 10.7 years to double the original investment.

In this case, the principal P is $1,000, the interest rate r is 6.5% or 0.065 (in decimal form), the number of times compounded per year n is 12 (compounded monthly), and we want to find the time t when the investment doubles, so A is $2,000.

[tex]2000 = 1000(1 + 0.065/12)^{12t}[/tex]

[tex]2 = (1 + 0.065/12)^{12t}[/tex]

ln(2) = 12t * ln(1 + 0.065/12)

t = ln(2) / (12 * ln(1 + 0.065/12))

t ≈ 10.7

Read more on compounded monthly here https://brainly.com/question/31242519

#SPJ2

Answer:

0.07,

0.7,

7.0

That is the answer

Answer:0.07,0.7,7.0

Step-by-step explanation:

Answer:

49.43£

Step-by-step explanation:

Given that £3 is equal to €4

There fore one euro is equal to

£3  = €4

1 € = 3/4 £ = 0.75 £(pound)

to find value of €65.90 in terms of pound we multiply both side of above equation with 65.90

=> 65.90 € = 0.75 * 65.90 £

=>  65.90 € = 49.425£ (Answer)

65.90 € is equal to 49.43 rounded to two decimal points.

Answer:

$25.20

Step-by-step explanation:

$35 x 0.28

= $9.80

35-9.80

= $25.20

Answer:

20%

Step-by-step explanation:

35 x .2 = 7

35 - 7 = 28

Hope this helps & best of luck!

Feel free to message me if you need more help! :)

The graph is stretched vertically, shifted left 5 units, shifted up 7 units.

We have to determine the effect of the transformations on the graph of ƒ(x) = x^2 when changed to ƒ(x) =1/2(x − 5)^2 + 7

The vertex form of the quadratic equation is f(x) = a(x-h)^2 + k.

ƒ(x) =1/2(x − 5)^2 + 7 compare with vertex form therefore we have

a=1/2,h=5 k=7.

a=1/2 means the closer to zero the a value, the wider, so this will stretch vertically.

h=5 and this means that the graph is shifted left 5 units.

k=7 this means that the graph is shifted up 7 units.

The answer is stretched vertically, shifted left 5 units, shifted up 7 units.

To learn more about the vertex form visit:

https://brainly.com/question/525947

Final answer:

The graph of f(x) = x^2 undergoes a vertical compression, horizontal shift to the right by 5 units, and a vertical shift up by 7 units to become f(x) = 1/2(x - 5)^2 + 7, corresponding to option B.

Explanation:

When comparing the original function f(x) = x^2 with the transformed function f(x) = 1/2(x − 5)^2 + 7, we can analyze the effects of transformation as follows:

Vertical Compression: The coefficient 1/2 in front of (x − 5)^2 causes a vertical compression by a factor of 1/2 compared to the original function.

Horizontal Shift: The term (x − 5) inside the function indicates a horizontal shift to the right by 5 units.

Vertical Shift: The constant +7 added outside the square indicates the graph is shifted up by 7 units.

Therefore, the correct description of the transformations applied to f(x) = x^2 to obtain f(x) = 1/2(x − 5)^2 + 7 is option B: compressed vertically, shifted right 5 units, and shifted up 7 units.

Answer:

An apple costs $2.25. A mango costs $1.25.

Step-by-step explanation:

Let a = price of 1 apple.

Let m = price of 1 mango.

Cameron:

4 apples + 7 mangoes ----> total $17.75

4a + 7m = 17.75

Gavin:

2 apples + 5 mangoes ----> total $10.75

2a + 5m = 10.75

We have a system of 2 equations in 2 unknowns.

4a + 7m = 17.75

2a + 5m = 10.75

We can use the elimination method to eliminate the variable a. Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Then add the equations.

           4a + 7m = 17.75

(+)       -4a - 10m = -21.5

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

                    -3m = -3.75

Divide both sides by -3.

m = 1.25

A mango costs $1.25.

Now we use the first equation and substitute 1.25 for m and solve for a.

4a + 7m = 17.75

4a + 7(1.25) = 17.75

4a + 8.75 = 17.75

4a = 9

a = 2.25

An apple costs $2.25.

Answer: An apple costs $2.25. A mango costs $1.25.

Answer:

2.25 ; 1.25

Step-by-step explanation:

4A + 7M = 17.75

2A + 5M = 10.75

2A = 10.75 - 5M

4A = 21.5 - 10M

21.5 - 10M + 7M = 17.75

3.75 = 3M

M = 1.25

4A = 21.5 - 10(1.25)

4A = 9

A = 2.25

Answer:

The answers is in the problem 30 cubes

The total number of cubes are there in the box will be 75. And the table is completed below.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Then the value of x is given as,

x + x + 0.4 = 1

2x = 0.6

x = 0.3

The table is given below.

Color                       Blue              Red            Yellow

Probability               0.4                0.3                0.3

If the number of blue cubes is 30. Then the total number of cubes is given as,

Total cubes = 30 / 0.4 = 75

The total number of cubes are there in the box will be 75.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

Answer:   0.159

other answer is wrong i did the quiz

Answer:

x = 27°

Step-by-step explanation:

You know that both sections together add up to 180°, so you want to set up an equation:

2x + 99 + x = 180

3x + 99 = 180

3x = 81

x = 27°

Answer:

-2n-15 1/3

Step-by-step explanation:

-2n+5/3-6(4)+7

-2n+5/3-24+7

-2n+1 2/3-17

-2n-15 1/3

Answer:

I believe A. is 82.352941176471%

Step-by-step explanation:

Answer:

y is 14x

Step-by-step explanation:

every time she travels 14 miles, she is on her bike for one hour

Answer:

y=14x and 21 miles

Answer:

1.631

1.861

-2.322

Step-by-step explanation:

The value of logarithm log₅20 is 1.861.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithms are log₃6, log₅20 and log₂(1/5).

We have change of base formula: logₐx= logₙx/logₙa

Here, log₃6 = log₁₀6/log₁₀3

= 0.7781/0.4771

= 1.6308

≈ 1.631

log₅20 = log₁₀20/log₁₀5

= 1.3010/0.6989

= 1.8614

≈ 1.861

log₂(1/5) = log₁₀(1/5)/log₁₀2

= -0.6989/0.3010

= -2.3219

≈ -2.322

Therefore, the value of logarithm log₅20 is 1.861.

To learn more about the logarithmic equation visit:

https://brainly.com/question/14406101.

#SPJ7

Answer:

5.83 or E

Step-by-step explanation:

Use Pythagorean theorem. 5^2+3^2=c^2 because the diameter is perpendicular it cuts the chord in half.

25+9=c^2  

34=c^2

5.83

Answer:

x = 5.83.

Step-by-step explanation:

The diameter bisects the vertical chord so the right triangle has legs 3 and 5.

So x^2 = 3^2 + 5^2

x^2 = 34

x = 5.83.

That is odd - if we work it out another way we get a different answer. I guess that must be because the numbers given in the diagram are not possible.

If we use the intersecting chords theorem,  we get (3+6)*3 = 27

= 5 * y where y is the other leg of the right triangle giving y = 5.4

and then this will give x = 6.18.

Answer:

Maximum width of image that can be viewed clearly on the cylindrical screen is 10 ft

Step-by-step explanation:

Here we have

Circumference of screen = 2πr = 120 ft

Angle that can be viewed horizontally either side of focus = 15°

Total angle view = 30°

Size of image that can be viewed = Object within 30° of focus

Maximum width of image that can be viewed clearly = Perimeter of 30° arc section of cylinder

Maximum width of image that can be viewed clearly = 30/360×120 ft = 10 ft.

Maximum width of image that can be viewed clearly on the cylindrical screen = 10 ft.

Answer:

a) P(X = 75) = 0.30

(b) P(X ≤ 75)

= 0.2 + 0.4 + 0.3 = 0.90

(c) P(X > 50).

= 0.3 + 0.1 = 0.40

(d) P(X < 100)

= 0.2 + 0.4 + 0.3 = 0.90

(e) parts b, c & d are CDF

Answer:

the answer is C,D,B enjoy your day

Step-by-step explanation:

Answer:

adult ticket would cost 4.5 after the 45% discount and the childs ticket would cost 2.4 after the 40% discount

(i converted 2/5 into a percentage which left me with 40%)

each time the family goes to the movies the family saves 9.1

(assuming its one adult and one child)

so 40/9.1= 4.39 and round it to 4

question A

adult ticket after discount=4.5

child ticket after discount=2.4

Question B

the family would have to go at least 4 times before they start saving money.

Step-by-step explanation:

Answer:

A = 7,241.2454026112  square mm.

or exact : A = 2,304.96‬*π  sq mm

Step-by-step explanation:

Cylinder formula:   A = π* r^2 +  2 *π * r* h  +  π*r^2

is the surface area.

d = 2r = 39.2 mm

h = 39.2 mm

r = 19.6 mm

A = π* r^2 +  2 *π * r* h  +  π*r^2

A = 2* π* (19.6)^2  + 2π (19.6)*(39.2)  

A = 2,413.748467537 +  4,827.496935

A = 7,241.2454026112  square mm.

or

A =  2*pi* (768.32‬ + 384.16)

A = 2*1,152.48‬* pi

A = 2,304.96‬*π  sq mm

[tex] \qquad \qquad\large\rm{Together \: We \: Go \: Far!} \\ \qquad \qquad \sf \small{\red{♡}\:Swifties\:\red{♡}}[/tex]

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{19.6 \: mm}}\put(9,17.5){\sf{39.2 \: mm}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the diameter of the cylinder is 39.2 mm. Thus, the radius of the cylinder is 19.6 mm. The height of the cylinder is 39.2 mm. We have been asked to find or calculate the surface area of the cylinder.

To calculate the surface area of the cylinder, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh[/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(19.6 \: mm)^2 + (2)(3.14)(19.6 \: mm)(39.2\:mm) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(384.16 \: mm^2) + (2)(3.14)(768.32\:mm^2) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(1206.2624 \: mm^2) + (2)(2412.5248 \: mm^2) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 2412.5248 \: mm^2 + 4825.0496 \: mm^2 [/tex]

[tex]\sf:\implies \bf{Surface \: Area_{(Cylinder)} = 7238 \: mm^2 \: (nearest\:tenth)}[/tex]

Therefore :-

[tex]\\[/tex]

Learn more about the surface area of the cylinder at https://brainly.com/question/30914875

Have a great day! <33