Write the given expression as the sum and/or difference of
logarithms. Express all exponents as coefficients.
log3 (x^10z^5) =

Answer:

D and F

Step-by-step explanation:

Answer:D and F

Step-by-step explanation:

Answer:

A: triangle 4

Step-by-step explanation:

all other triangles have a right angle and triangle number 4 doe not

Answer:

$1269.23

Step-by-step explanation:

Since Sarah is paid biweekly (every 2 weeks), and there are 52 weeks in a year...

\(52\) ÷ \(2=26\)

Sarah is being paid 26 weeks out of the year.

Divide 33,000 by 26 (I only list 4 places after the decimal):

\(33000\) ÷ \(26=1269.2307\)

Round 1269.2307 to the nearest cent (hundredth):

\(1269.23\)

When you are adding or subtracting a negative fraction, you usually want to consider the numerator as negative. The method is just the same, except now you may need to add negative or positive numerators. Example 1: ... To add the fractions with unlike denominators, rename the fractions with a common denominator.

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

The ordered pair (5, 35) in this context indicates that 5 boxed lunches were ordered and the total cost of those lunches was $35.

In the given graph, the x-coordinate represents the number of boxed lunches ordered (in this case, 5), and the y-coordinate represents the total cost of the lunches (in this case, $35). The point (5, 35) indicates the specific combination of the number of boxed lunches and the corresponding total cost on the graph.

Answer:

4 17/24

Step-by-step explanation:

3/8=9/24

1/3=8/24

8+9=17

sorry first know it had to be a fraction so I'm pretty sure this is what you are looking for 113/24.

Step-by-step explanation:

this is the right answer please mark me as Brainliest

hope this helps

Answer:

hol up

x=-1/8  negative one over eight

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Hey there! I'm happy to help!

Let's write this equation out.

2/3+1/3x=2x

We want to get all of the variables on the left side and all the numbers on the right side so we can see what number x is equal to. First, Let's subtract 2/x from both sides.

2/3+1/3x-2x=0

We subtract 2/3 from both sides.

1/3x-2x=-2/3

We combine our x values.

-5/3x=-2/3

We divide both sides by -5/3.

x=-5

Have a wonderful day and keep on learning! :D

Answer:

23

Step-by-step explanation:

The solution of the equation is c= 2/5 and d= 3/2.

We have Equation.

5c + 4d = 8

-5c + 2d = 1

Solving above equation we get

5c + 4d = 8

-5c + 2d = 1

___________

         6d = 9

          d = 3/2

and, 5c + 4(3/2)= 8

5c = 8 - 6

5c = 2

c= 2/5

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Answer:

Should be store B :) The unit rate for store A (rounded) is 0.11 and the rounded unit rate for store B is 0.10

Step-by-step explanation:

Answer:

Store B has the better deal

Unit rate:

Store A = $0.11

Store B = $0.10

Step-by-step explanation:

Store A :

8pencils = $0.89

1 pencil = $0.89/8 = $0.111

Store B:

12pencils = $1.25

1 pencil = $1.25/12 = $0.104

Store B sells 1 pencil at $0.104 and store A at $0.111

Therefore Store B sells the better deal.

a) There are 36 sample points that are possible.

b) The probability of obtaining a value of 7 is 1/12.

c) The probability of obtaining a value of 8 or greater is 1/6.

(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.

(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.

(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.

Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.

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Answer:

x+2y+3z=38

Step-by-step explanation:

here you go!

The perimeter of the rectangle is_52cm___ centimeters.

To find the perimeter of the rectangle, we need to know the lengths of its sides.

However, we only have information about the area and one side length. Without additional information, we cannot determine the lengths of the other sides or calculate the perimeter.

If we assume that the rectangle is a square, with one side length of 13 centimeters, then we can calculate the perimeter.

In this case, all sides of the square would be equal.

\(Perimeter $ of a square = 4 \times side length\)

So, the perimeter of the square (rectangle) would be:

\(Perimeter = 4 \times 13 cm = 52 cm\).

If we assume that the rectangle is a square, then the perimeter would be 52 centimeters.

However, if the rectangle is not a square and has different side lengths, we would need additional information to calculate the perimeter.

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Answer:

Average speed

= 5 5/6 mph , or

= 5.83 mph (to 2 decimals)

Step-by-step explanation:

Average speed is total distance divided by the total time it takes to cover the given distance.

Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.

Let

x = distance uphill, and also distance downhill.

Total distance = 2x miles

Total time = x/5 + x/7 hours  = 12x/35 hours

Average speed

= total distance/total time

= 2x / (12x/35) mph

= 70x / 12x

= 5 5/6 mph

= 5.83 mph (to 2 decimals)

Answer:

x^3(-x+3)(x+3)

Step-by-step explanation:

-x^5 + 9x^3

factor out x^3

x^3(-x^2+9)

9 and -x^2 are perfect squares so we can factor out a 3 and an x to get (-x+3)(x+3)

the fully factored form would be x^3(-x+3)(x+3)

Answer:

-x^3(x - 3)(x + 3).

Step-by-step explanation:

-x^5+9x^3

the greatest common factor = x^3 so we can write it as

x^3(-x^2 + 9)

= -x^3(x^2 - 9)

The expression in the parentheses is the difference of 2 squares so we have:

-x^3(x - 3)(x + 3)   Answer.

Answer:

55

Step-by-step explanation:10 percent of 50 is 5 +50 equals 55

Answer:

$55

Step-by-step explanation:

Find how much is 10% of 50 which is 5 and add it to the cost to store.

Answer:

7 telephone poles

Step-by-step explanation:

Given that:

Length of track = 5(3/5) feet long

No pole is needed at the atart of the track

Poles are however placed every 4/5 foot apart

Number of telephone poles needed :

Length of track / distance between each placed poles

= length of track = 5(3/5) = 28/5 feet

Distance between poles = 4/5 foot

Hence,

(28 /5) ÷ (4 /5)

= 28 /5 × 5 / 4

= (28 * 5) / 20

= 140 / 20

= 7

Number of poles required = 7

Step-by-step explanation:

5 5/6 / 5/12

Keep Change Flip

35/6 * 12/5

cross simplify

7/1 * 2/1= 14/1= 14

Answer:

8 hours

Step-by-step explanation:

3 1/5 cups, he drinks 2/5 cups every hour

to find the number of hours he has water for, divide the 2 numbers

3 1/5 = 16/5

16/5 divided by 2/5 is equal to 16/5 times 5/2

80/10 equals 8, so he will have water for 8 hours

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

english please

Step-by-step explanation:

The volume of empty space left inside the cylindrical container is 2153.64 \(cm^{3}\).

The cubic capacity refers to the volume of a cylinder between the upper point inside the cylinder head to the bottom dead center of the piston.

We must first determine the volume of the cylinder containing the three spheres and then deduct the sum of the volumes of the three balls to determine the volume of the remaining space inside the container.

The cylinder has a height equivalent to one ball's diameter, or 14 cm, and a radius of 7 cm. As a result, the cylinder's capacity is:

\(= \pi r^{2} h\\= 3.148 * 7^{2} *14\)

= 2156.64 \(cm^{3}\)

Since the radius of each ball is 7 centimeters, the volume is:

The volume of a ball is Vball is = \(\frac{4}{3} \pi r^{3}\)

= \(\frac{4}{3} \ * 3.148 * (7)^{3}\)

= 1436.76 cm³

The three spheres' combined volume is equal to Vtotal = 3Vball

= 3 * 1436.76 cm³

= 4310.28 cm³

The container's remaining interior area has the following volume:

Vcylinder = Vtotal - Vempty

                = 2156.64 \(cm3\) - 4310.28\(cm3\\\)  

                = -2153.64 \(cm3\)

We round the result to the closest hundredth and calculate the absolute value because we cannot have a negative volume:

|Vempty| = 2153.64 \(cm3\)

As a result, there is roughly 2153.64 \(cm3\) of empty space inside the container.

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To determine the height of the platform above the ground, we can break down the projectile motion into horizontal and vertical components.

We can calculate the height of the platform (h) by subtracting the vertical displacement (Δy) from the initial height of the projectile:

h = Δy - Δy = ((2 * V₀y²) / g) - ((2 * V₀y²) / g)

First, let's analyze the horizontal motion of the projectile. The horizontal range (R) is given as 37 m. The horizontal component of the initial velocity (V₀x) can be found using:

V₀x = V₀ × cos(θ)

where V₀ is the initial speed (10.1 m/s) and θ is the launch angle (22.8 degrees).

V₀x = 10.1 m/s × cos(22.8°)

Next, let's consider the vertical motion of the projectile.

The vertical component of the initial velocity (V₀y) can be found using:

V₀y = V₀ × sin(θ)

V₀y = 10.1 m/s × sin(22.8°)

Since the projectile is launched from the edge of the platform, the initial vertical displacement (Δy) is equal to the height of the platform (h). We need to find h.

We can use the equation for vertical displacement to relate Δy, V₀y, and time (t):

Δy = V₀y × t + (1/2) × g × t²

where g is the acceleration due to gravity (approximately 9.8 m/s²).

The time of flight (t) can be found using the formula:

t = 2 × V₀y / g

Substituting the expression for t in terms of V₀y into the equation for vertical displacement, we have:

Δy = V₀y × (2 × V₀y / g) + (1/2) × g × (2 × V₀y / g)²

Simplifying the equation gives:

Δy = (V₀y² / g) + (2 × V₀y²) / (2 × g)

Δy = (V₀y² / g) + (V₀y² / g)

Δy = (2 × V₀y²) / g

Finally, substituting the expressions for V₀y and V₀x into the equation for the horizontal range, we can solve for h:

R = V₀x × t

37 m = V₀x × (2 × V₀y / g)

37 m = (10.1 m/s × cos(22.8°)) × (2 × (10.1 m/s × sin(22.8°)) / 9.8 m/s²)

Now we can calculate the height of the platform (h) by subtracting the vertical displacement (Δy) from the initial height of the projectile:

h = Δy - Δy = ((2 × V₀y²) / g) - ((2 × V₀y²) / g)

Simplifying the equation gives us the height of the platform.

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The situation involving the food establishment has a probability of "2.08 % " points higher than the situation involving the financial establishment

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The question is incomplete, as the required table which is not given.

we have the following parameters:

The probability that the establishment earns up to $25k = 10.59%

The probability that the establishment earns between $25k - $50k or $50k - $75k = 8.56%

Using the above values, the difference in the probabilities are;

d = 10.59% - 8.56

d = 2.03%

Hence, the true statement about the probability is option (d)

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Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Answer: a

Step-by-step explanation:

Tell me if it is correct

Answer:

Calculus in baseball. In baseball, calculus can be used to optimize the pitcher’s throw to achieve maximum efficiency. Also, calculus can be used to calculate the projectile motion of baseball’s trajectory and to predict if runners can make it to the next base on time given their running speed and the speed of a hit ball.

Step-by-step explanation:

Answer:

936

Step-by-step explanation:

You multiply 31.2 by 10, so you move the decimal one place to the right, so it's 312, And then, you multiply those numbers by 6 like 3, 1, and 2. For the ones digit 2 x 3 = 6,  for the tens digit, 1 x 3 = 3, and for the hundreds digit, 3 x 3 = 9. Therefore, the answer is 936!