Number 9. Emulate the logarithm using the change of base formula. Round you result to three decimal places.
Log3(14)

Answer: y = -4x + 1. Brainliest?

Step-by-step explanation:

To write a function rule that has a greater rate of change than the given function, we need to find the slope of the given function. We can use the two points (-2, 7) and (2, -5) from the table to calculate the slope as:

slope = (change in y) / (change in x) = (-5 - 7) / (2 - (-2)) = -3

So the slope of the given function is -3. To create a new function rule with a greater rate of change, we can choose a larger slope. Let's choose a slope of -4. We also need to find the y-intercept (b) of the new function, which we can do by plugging in one of the points from the table and solving for b. Let's use the point (0, 1):

y = mx + b

1 = (-4)(0) + b

b = 1

So the function rule with a greater rate of change and passing through the point (0, 1) is:

y = -4x + 1

1. The difference between the longest and shortest pencil is 4 5/12

2. The total length is 22 3/4 inches

3. The statement is false

4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches

A word problem is a math problem written out as a short story or scenario. This statements are interpreted into mathematical equation or expression.

1. The difference between longest and shortest pencil = 8⅔ - 4¼

= 26/3 - 17/4

= (104-51)/12

= 53/12 = 4 5/12

2. The total length of pencils less than 5 ½ inches = 5×2 + 17/4 × 3

= 10+ 51/4 = 40+51)/4

= 91/4 = 22 3/4 inches

3. The Statement is false because the pencils less than 6 inches is 8 and not upto half of the total pencil

4. There are 9 pencils that measure more than 5½ inches and less than 7 2/4 inches.

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Okay, here are the steps to solve this problem:

* The recipe calls for 3/4 teaspoon of cinnamon for every 4 cups of granola mix.

* So for 1 cup of granula mix, you need 3/4 / 4 = 3/12 teaspoon of cinnamon.

* For 12 cups of granula mix, you would need 12 * (3/12) = 3 teaspoons of cinnamon.

Therefore, for 12 cups of granola mix you would need 3 teaspoons of cinnamon.

Answer:

It will take approximately 6.89 years for the investment to grow to $9737.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the present value of the investment

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know that P = $7000, r = 0.034, n = 4 (since the interest is compounded quarterly), and we want to find t when A = $9737.

$9737 = $7000(1 + 0.034/4)^(4t)

Divide both sides by $7000:

1.391 = (1 + 0.034/4)^(4t)

Take the natural logarithm of both sides:

ln(1.391) = ln[(1 + 0.034/4)^(4t)]

Use the power rule of logarithms:

ln(1.391) = 4t * ln(1 + 0.034/4)

Divide both sides by 4 ln(1 + 0.034/4):

t = ln(1.391) / [4 * ln(1 + 0.034/4)]

Using a calculator, we find:

t ≈ 6.89 years

Therefore, it will take approximately 6.89 years for the investment to grow to $9737.

The 7.34 cubic yards of concrete needed to pour the foundation walls, which is calculate the volume of the walls and then add the waste factor of 6%.

To find the volume of the concrete needed to pour the foundation walls, we first need to find the total area of the walls. We can do this by breaking it down into three sections

The two 26 ft x 1 ft walls

Area = 2 x (26 ft x 1 ft) = 52 sq ft

The two 42 ft x 1 ft walls

Area = 2 x (42 ft x 1 ft) = 84 sq ft

The 12 in x 15 in x 12 ft wall

First, we need to convert the dimensions to feet:

Length = 12 in ÷ 12 = 1 ft

Breadth = 15 in ÷ 12 = 1.25 ft

Height = 12 ft

Area = (1 ft + 1.25 ft) x 2 x 12 ft = 51 ft²

Total area of the walls = 52 sq ft + 84 sq ft + 51 sq ft = 187 sq ft

Now, we need to add the waste factor of 6% to this to account for any material that may be lost or wasted during the pouring process

Total area with waste factor = 187 sq ft + 6% of 187 sq ft = 198.22 sq ft

Finally, we need to calculate the volume of concrete needed, assuming a thickness of 1 ft

Volume = area x thickness = 198.22 sq ft x 1 ft = 198.22 cubic ft

Since 1 cubic yard is equal to 27 cubic feet, we can convert the volume to cubic yards

Volume in cubic yards = 198.22 cubic ft ÷ 27 = 7.34 cubic yards

Therefore, we need 7.34 cubic yards of concrete to pour the foundation walls with a 6% waste factor.

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a. Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex]  B. Weight of the empty tank  [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]

a. The weight of 25 gallons of water can be calculated by multiplying the weight of one gallon of water by 25.

Given:

Weight of 1 gallon of water = 8 1/3 lbs

Calculation:

Weight of 25 gallons of water = (Weight of 1 gallon of water) × 25

[tex]= 8 1/3 lbs \times 25[/tex]

To perform the multiplication, let's convert the mixed number 8 1/3 to an improper fraction:

[tex]8 1/3 = (8 \times 3 + 1)/3 = 25/3[/tex]

Substituting back into the equation:

Weight of 25 gallons of water [tex]= 25/3 \times 25[/tex]

Now, we can multiply the fractions:

Weight of 25 gallons of water [tex]= (25 \times 25)/(3)= 625/3 lbs[/tex]

b. The weight of the empty 25-gallon tank can be calculated as 1/10 of the weight of water it can hold.

Given:

Weight of 25 gallons of water = 625/3 lbs

Calculation:

Weight of the empty tank = (Weight of 25 gallons of water) × (1/10)

[tex]= (625/3 lbs) \times (1/10)[/tex]

We can simplify the fractions:

Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10)[/tex]

[tex]= 625/30 lbs[/tex]

c. The weight of a 25-gallon tank filled with water would be the sum of the weight of the empty tank (calculated in part b) and the weight of 25 gallons of water (calculated in part a).

Given:

Weight of 25 gallons of water = 625/3 lbs

Weight of empty tank = 625/30 lbs

Calculation:

Weight of tank filled with water = Weight of 25 gallons of water + Weight of empty tank

[tex]= 625/3 lbs + 625/30 lbs[/tex]

We can find a common denominator for the fractions and add them:

Weight of tank filled with water [tex]r = (625 \times 10)/(3 \tiimes 10) + (625)/(30)[/tex]

[tex]= (6250/30) + (625/30)= 6875/30 lbs[/tex]

We can simplify the fraction:

Weight of tank filled with water [tex]= 229 5/6 lbs[/tex]

Therefore,a.Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex]  B. Weight of the empty tank  [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]

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a. Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex]  B. Weight of the empty tank  [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]

a. The weight of 25 gallons of water can be calculated by multiplying the weight of one gallon of water by 25.

Given:

Weight of 1 gallon of water = 8 1/3 lbs

Calculation:

Weight of 25 gallons of water = (Weight of 1 gallon of water) × 25

[tex]= 8 1/3 lbs \times 25[/tex]

To perform the multiplication, let's convert the mixed number 8 1/3 to an improper fraction:

[tex]8 1/3 = (8 \times 3 + 1)/3 = 25/3[/tex]

Substituting back into the equation:

Weight of 25 gallons of water [tex]= 25/3 \times 25[/tex]

Now, we can multiply the fractions:

Weight of 25 gallons of water [tex]= (25 \times 25)/(3)= 625/3 lbs[/tex]

b. The weight of the empty 25-gallon tank can be calculated as 1/10 of the weight of water it can hold.

Given:

Weight of 25 gallons of water = 625/3 lbs

Calculation:

Weight of the empty tank = (Weight of 25 gallons of water) × (1/10)

[tex]= (625/3 lbs) \times (1/10)[/tex]

We can simplify the fractions:

Weight of the empty tank [tex]= (625 \times 1)/(3 \times 10)[/tex]

[tex]= 625/30 lbs[/tex]

c. The weight of a 25-gallon tank filled with water would be the sum of the weight of the empty tank (calculated in part b) and the weight of 25 gallons of water (calculated in part a).

Given:

Weight of 25 gallons of water = 625/3 lbs

Weight of empty tank = 625/30 lbs

Calculation:

Weight of tank filled with water = Weight of 25 gallons of water + Weight of empty tank

[tex]= 625/3 lbs + 625/30 lbs[/tex]

We can find a common denominator for the fractions and add them:

Weight of tank filled with water [tex]r = (625 \times 10)/(3 \tiimes 10) + (625)/(30)[/tex]

[tex]= (6250/30) + (625/30)= 6875/30 lbs[/tex]

We can simplify the fraction:

Weight of tank filled with water [tex]= 229 5/6 lbs[/tex]

Therefore,a.Weight of 25 gallons of water [tex]= (25 \times 25)/(3) = 625/3 lbs[/tex]  B. Weight of the empty tank  [tex]= (625 \times 1)/(3 \times 10) = 625/30 lbs[/tex] C. Weight of tank filled with water[tex]= 229 5/6 lbs[/tex]

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If a 9v battery produces a current of 18 amps then the resistance of the circuit element is 0.5 ohms.

We can use Ohm's law to determine the resistance (R) of a circuit element

Given the voltage (V) and current (I) through it:

R = V / I

In this case, the voltage (V) is 9 volts and the current (I) is 18 amps. Substituting these values into the formula, we get:

R = 9 V / 18 A

Simplifying the expression on the right-hand side, we get:

R = 0.5 Ω

Therefore, the resistance of the circuit element is 0.5 ohms.

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The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, the length of side WX is 13 mm.

If the scale factor of figure STUV to figure WXYZ is 3:1, it means that every length in figure STUV is three times longer than the corresponding length in figure WXYZ.

To find the length of side WX, we need to first identify the corresponding sides of the two figures. We know that ST is three times longer than W, and SV is three times longer than Y. So, we can set up the following proportion:

ST/WX = SV/YZ

Substituting the given values, we get:

39/WX = 51/YZ

We need to find the value of WX, so we can solve for it by cross-multiplying the proportion:

39 * YZ = 51 * WX

Since we don't know the value of YZ, we need to find it in terms of WX. We can use the scale factor of 3:1 to relate the lengths in the two figures:

ST = 3 * W

SV = 3 * Y

Substituting the first equation, we get:

W = ST/3 = 39/3 = 13 mm

Substituting the second equation, we get:

Y = SV/3 = 51/3 = 17 mm

Now we can substitute these values into the proportion:

39/WX = 51/17

Solving for WX, we get:

WX = (39 * 17) / 51 = 13 mm

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Complete question is:

The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?

The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a positive actual number that is not exactly one.

A logarithm is the power to which a number must be raised in order to receive extra values. The simplest approach to express really large numbers is in this way. A number of important features of a logarithm demonstrate the fact that multiplication and division of logarithms can also be used to represent addition and subtraction logarithms.

The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a real number that is positive but not equal to one.

i.e., [tex]b^y=a[/tex] ⇔ [tex]log_b[/tex] a = y

In this case, "A" and "B" are two positive real numbers.

Y is an actual number.

Argument occurs inside the log as "a" by the name argument.

It is said that the base, or "b," is at the bottom of the log.

To put it another way, the logarithm provides a solution to the problem of "How many times is a number divided to get the other number?"

How numerous times must three be multiplied, for instance, to yield the number 27?

27 is the outcome of multiplying 3 times by 3.

Consequently, the logarithm is 3.

The logarithm form is written as follows:

[tex]log_3[/tex] (27) = 3 - equation 1

The base 3 logarithm of 27 is therefore 3.

It is also possible to write the above logarithm form as:

3x3x3 = 27

3³ = 27 - equation 2

Equations (1) and (2) are hence equivalent.

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The height of the pole is 18.18 feet

Given data ,

Elka uses similar triangles to find the height of the pole. The situation forms two similar right triangles: one with the pole and the mirror, and another with Elka's eyes and the mirror.

Let's denote the height of the pole as "h" feet.

Distance from the base of the pole to the mirror = 20 feet

Distance Elka moves back away from the mirror = 5.5 feet

Height of Elka's eyes above the ground = 5 feet

Using the concept of similar triangles, we can set up the following proportion:

h / 20 = 5 / 5.5

Multiply by 20 on both sides , we get

h = 100 / 5.5

h = 18.18 feet

Hence , the height of the flagpole is approximately 18.18 feet

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Answer:

x = - 12

Step-by-step explanation:

the central angle subtended by the arc with measure 45° are congruent, that is central angle is 45°

the 3 angles on the diameter then sum to 180° , that is

45 + 65 + x + 82 = 180

x + 192 = 180 ( subtract 192 from both sides )

x = - 12

The volume of the given right cone is approximately 597.9 cubic units.

In this problem, we are going to find the volume of a right cone. A cone is a three-dimensional object that has a circular base and tapers to a point. The term "right" means that the axis of the cone is perpendicular to its base. The formula for the volume of a right cone is V = (1/3)πr²h, where V is the volume, r is the radius of the circular base, and h is the height of the cone.

Now, let's apply this formula to the given cone. We are given that the radius of the circular base is 16 and the height of the cone is 7. So, we can substitute these values into the formula to get:

V = (1/3)π(16)²(7) V = (1/3)π(256)(7) V = (1/3)(1,792π) V ≈ 597.9

We round our answer to the nearest tenth as requested. So, the final answer is V ≈ 597.9.

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Answer:

149

Step-by-step explanation:

The equivalent speed in still water to achieve the actual speed is 27.172 km/h

Given data ,

The boat's velocity vector in still water will have two components: one along the north direction (opposite to the current) with magnitude "v" km/h, and one along the northwest direction (due to the current) with magnitude 4 km/h.

Since the boat is moving in a direction that is 45 degrees between north and northwest, we can use trigonometry to find the component of velocity in the northwest direction. By using the cosine of 45 degrees, we get:

Component of velocity in northwest direction = 4 km/h x cos(45 degrees) = 4 km/h x 0.707 = 2.828 km/h

Now , adding the components of velocity in the north and northwest directions should result in a speed of 30 km/h, which is the real speed needed to go through still water.

v + 2.828 = 30

v = 27.172 km/h

Hence , the equivalent speed of the boat in still water to achieve an actual speed of 30 km/h is approximately 27.172 km/h

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Answer:

choice 1

Step-by-step explanation:

62 and x are a linear pair and sum to 180 , that is

62 + x = 180 ( subtract 62 from both sides )

x = 118

Answer:

1. 118

Step-by-step explanation:

Given the image provided:

Solve for x:

Since, the image is of a supplementary angle that adds up to 180° and one angle is 62°, then we take 180 minus 62.

Answer:

Therefore, x = 118 and the answer is 1.

Answer:

The Correct answer is B

Step-by-step explanation:

The graph that shows a proportional relationship between x and y is given as follows:

Graph D.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the equation y = kx we have that it is a linear function with intercept of zero, meaning that the graph D represents the proportional relationship for this problem.

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Considering the given graph,  we infer that while rolling a dice is random, the median values do exhibit some patterns that can be analyzed and used to make predictions about the expected values.

Looking at the median data from the graph, we can infer that option A is not true, as the median appears to be equally likely to fall between any two numbers from 1 to 6. However, we can also infer that option B is not entirely accurate.

While it is true that rolling a dice is random and each roll is independent, we can observe patterns in the median data.

For example, the median values are more likely to be closer to 3.5, which is the theoretical median value of a fair six-sided dice. This suggests that the more times the dice is rolled, the more likely the median value will approach the expected value.

We can also observe that the spread of the median values tends to decrease as the number of rolls increases, indicating that more rolls lead to more consistent results.

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Te advertiser's cost per viewer for a 30-second ad is $0.01025.

Cost per view means an ads model that charges the advertiser whenever a user watches an ad for a set duration.

To calculate the cost per viewer for the advert, we need to divide the advertising fee by the number of viewers which gives us:

Cost per viewer = Advertising fee / Number of viewers

Substituting the values, we get:

= $165,000 / 16.1 million viewers

= $165,000 / 16,100,000 viewers

= 0.0102484472 per viewer

= $0.01025 per viewer.

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Therefore, 1t5e twelve represents the number 3239 in base ten.

what is system of equations?

A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is a set of values for the variables that satisfy all the equations in the system simultaneously.

For example, consider the following system of two equations:

x + y = 5

2x - y = 3

This is a system of two equations with two variables, x and y. The solution to this system is the values of x and y that make both equations true at the same time. In this case, the solution is x = 2 and y = 3, because when we substitute these values into the equations.

In base twelve, the place values increase by a factor of twelve at each position, starting from the rightmost position. The rightmost position has a place value of 1, the next position to the left has a place value of 12, the next position to the left has a place value of 12^2 = 144, and so on.

To convert the number 1t5e in base twelve to base ten, we need to multiply each digit by its corresponding place value, and then add up the results:

1t5e (base twelve) = 1 * 12^3 + 10 * 12^2 + 5 * 12^1 + 11 * 12^0

= 1 * 1728 + 10 * 144 + 5 * 12 + 11 * 1

= 1728 + 1440 + 60 + 11

= 3239

Therefore, 1t5e twelve represents the number 3239 in base ten.

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The correct statement and value should be matched as follows;

The percent of time that customers at the old store bought milkshakes: 20%.

The percent of time that customers at the new store bought milkshakes: 26%.

The percent of total sales that were Ice Cream sales in both shops: 78%.

The percent of new store sales out of the total sales for both shops: 35%.

First of all, we would have to determine the total number of sales for both the Old store with respect to the number of servings of ice cream and milk shakes that were sold;

Total sales = 52,100 + 13,400

Total sales = 65,500

Next, we would determine the percent of time that customers at the old store bought milk shakes;

Percent = 13,400/65,500 × 100

Percent = 20.46 ≈ 20%.

Similarly, we would determine the percent of time that customers at the new store bought milk shakes;

Total sales = 25,800 + 9,200

Total sales = 35,000

Percent = 9,200/35,000 × 100

Percent = 26.29 ≈ 26%.

Total sales in both stores = 52,100 + 13,400 + 25,800 + 9,200

Total sales in both stores = 100,500

Percent of ice cream in both stores = (52,100 + 25,800)/100,500 × 100

Percent of ice cream in both stores = 77.51 ≈ 78%.

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There are 18 possible combinations of ice cream, topping, and sprinkles.

Probability P(Chocolate, Fudge, Rainbow) = 1/18

There are 18 different possible sundaes that can be made when choosing one flavor of ice cream, one topping, and one color of sprinkles.

To visualize all the possible outcomes, we can use a tree diagram:

                              Ice Cream

                                       |

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

                      |                |                |

           Chocolate        Vanilla         Strawberry

                       |                |                |

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

                       |              | |              | |              |

 Fudge     Marshmallow   Fudge     Marshmallow   Fudge     Marshmallow

                       |              |                |               |

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

                     |              | |              | |              |

     Rainbow  Chocolate  Rainbow  Vanilla   Rainbow  Strawberry

So there are 18 possible combinations of ice cream, topping, and sprinkles.

To answer part b) which asks for the probability of choosing Chocolate ice cream with Fudge topping and Rainbow sprinkles, we need to know the total number of possible outcomes (which we just calculated as 18) and the number of outcomes that match the specific combination of Chocolate ice cream, Fudge topping, and Rainbow sprinkles. There is only one outcome that matches this combination, so the probability is:

P(Chocolate, Fudge, Rainbow) = 1/18

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The polynomial function that best fits the graph is f(x) = 130(x+3)(x-2)²(x-5).

The given graph exhibits three x-intercepts at x = -3, 2, and 5, and the y-intercept is positioned at (0, 2). The graph passes through the x-axis linearly at x = -3 and x = 5, indicating that the corresponding factors of the polynomial will be linear. However, at x = 2, the graph bounces off the x-axis at the intercept, implying that the corresponding factor of the polynomial will be quadratic. Therefore, the polynomial function can be expressed as follows:

f(x) = a(x+3)(x-2)²(x-5)

To find the stretch factor 'a,' we can use another point on the graph, such as the y-intercept (0, 2). By plugging in the values, we obtain:

f(0) = a(0+3)(0-2)²(0-5)

-2 = a(0+3)(0-2)²(0-5)

-2 = -60a

a = 130

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Answer:

Step-by-step explanation:

[tex]\textit{since we know that }\triangle FGH \cong \triangle CDE \\\\[-0.35em] ~\dotfill\\\\ HF=EC\implies -3s+44=-3t+50 \\\\\\ HG=ED\implies 6s=t+43\implies \boxed{6s-43=t} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{-3s+44=-3(6s-43)+50}\implies -3s+44=-18s+129+50 \\\\\\ 15s+44=129+50\implies 15s+44=179\implies 15s=135 \\\\\\ s=\cfrac{135}{15}\implies \boxed{s=9}\hspace{9em}\stackrel{ 6(9)-43 }{\boxed{t=11}}[/tex]