can you help me with math

Logarithmic functions and exponential functions are inverse functions of each other

The value of x in the equation  log₃ (x + 5 ) = 4  is 76

The format of the logarithmic function log₃ (x + 5 ) = 4  is

solving  the equation

3⁴ = x + 5

81 = x + 5

x = 76

the solution to the equation log3 (x + 5) = 4 is x = 76.

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The area of the flower bed in square yards is 28 Square yards.

The area of the rectangular flower bed in square yards, we need to convert the measurements from feet to yards. There are 3 feet in 1 yard, so:

Length in yards = 21 feet / 3 = 7 yards

Width in yards = 12 feet / 3 = 4 yards

Now we can calculate the area in square yards:

Area = Length × Width

Area = 7 yards × 4 yards

Area = 28 square yards

Therefore, the area of the flower bed in square yards is 28 square yards.

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The solution to the inequality is x > 7

Given data ,

To represent the inequality -3x + 5 < -16 on a number line, follow these steps:

Step 1:

Solve the inequality for x

-3x + 5 < -16

Step 2:

Subtract 5 from both sides of the inequality

-3x < -16 - 5

-3x < -21

Step 3:

Divide both sides of the inequality by -3. Note that when dividing by a negative number, the direction of the inequality sign should be reversed:

x > (-21)/(-3)

x > 7

Step 4:

Plot a closed circle on 7 (since the inequality is strictly greater than) and shade the region to the right of 7 on the number line

Hence , the inequality is x > 7

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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

   Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

  Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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Answer:

463.52 meters

Step-by-step explanation:

To find the length of the training track running around the field, we need to calculate the perimeter of the entire field.

The field is made up of a rectangle with dimensions 85m by 57m, and two semicircles with a radius of 57/2 = 28.5m.

The perimeter of the rectangle is 2(85m) + 2(57m) = 284m.

The perimeter of each semicircle is half the circumference of a full circle with radius 28.5m, which is π(28.5m) = 89.76m. So the total perimeter of both semicircles is 2(89.76m) = 179.52m.

Therefore, the total perimeter of the field is 284m + 179.52m = 463.52m.

Rounding to the nearest hundredth, the length of the training track running around the field is 463.52 meters.

These equations can be used to determine the number of bottles of soda (R) and the number of bottles of juice (J) purchased by Nayeli. The resulting system of equations is:

25R + 15J = 205

R = J + 5.

To solve this problem, we can set the following variables:

R = Number of bottles of soda purchased.

J = Number of bottles of juice purchased.

We can establish the following equations based on the information provided:

"Each bottle of soda has 25 grams of sugar": So the total amount of sugar in the bottles of soda is 25R.

"Each bottle of juice has 15 grams of sugar": Therefore, the total amount of sugar in the bottles of juice is 15J.

"Nayeli bought 5 more bottles of soda than bottles of juice": Therefore, the number of soda bottles is equal to the number of juice bottles plus 5, which can be expressed as R = J + 5.

"All together contain 205 grams of sugar": So the sum total of sugar is 25R + 15J, which equals 205.

The resulting system of equations is:

25R + 15J = 205

R = J + 5.

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The equations (x,y) | x + y > 1 and y (1/2)x + 2 have these solutions as their solutions.

To solve the system of inequalities without using graphs, we can use algebraic methods. First, we can rearrange the second inequality to slope-intercept form y < (1/2)x + 2.

This inequality represents a line with slope 1/2 and y-intercept 2. Next, we can identify the region of the coordinate plane that satisfies the first inequality, x + y > 1. This region is above the line x + y = 1. To check which side of the line satisfies the inequality, we can test a point, such as (0,1),

0 + 1 > 1

This is true, so the region above the line x + y = 1 satisfies the inequality.

Finally, we can combine the regions from the two inequalities to find the solution set. The solution set is the region above the line x + y = 1 and below the line y = (1/2)x + 2.

Therefore, the solution set can be expressed as,

{(x,y) | x + y > 1 and y < (1/2)x + 2}.

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Complete question - solve the given system of inequalities in two variables.

x + y > 1

y < 1/2x + 2

Answer:

48cm³

Step-by-step explanation:

volume = (7 X 6 X 1) + (3 X 2 X 1)

= (42 + 6)

= 48cm³

To find out how much pasta the restaurant needs, we can use the ratio of pasta to cheese given in the recipe: 8 cups of pasta for every 6 cups of cheese.

First, we need to determine the ratio of cheese to pasta. We can do this by taking the reciprocal of the original ratio, which gives us 6 cups of cheese for every 8 cups of pasta.

Next, we can set up a proportion with the known amount of cheese (15 cups) and the unknown amount of pasta (let's call it x cups):

6 cups of cheese / 8 cups of pasta = 15 cups of cheese / x cups of pasta

We can cross-multiply to solve for x:

6 cups of cheese * x cups of pasta = 8 cups of pasta * 15 cups of cheese

Simplifying this equation gives:

x = (8 cups of pasta * 15 cups of cheese) / 6 cups of cheese

x = 20 cups of pasta

Therefore, the restaurant would need 20 cups of pasta to make the large batch of mac and cheese using 15 cups of cheese, according to the recipe.

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Answer:

11.7b

Step-by-step explanation:

If you do 339.30 divided by 29 it equals 11.7 but the full equation would be c=11.7b

The proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Let's assume that each boxed lunch costs the same amount, denoted by the variable 'x'.

We are given that the company ordered 29 boxed lunches for a total cost of $339.30. Therefore, we can write the equation:

29x = 339.30

To find the cost 'c' for any number 'b' of boxed lunches, we can set up a proportion:

29x / 29 = 339.30 / b

Simplifying this equation, we get:

x = 339.30 / 29

Now, we can substitute this value of 'x' back into the equation:

c = bx = b * (339.30 / 29)

Therefore, the proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

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The length of segment BD, which represents the altitude of the triangle, is given as follows:

BD = 6.

The geometric mean theorem states that the length of the altitude of a triangle is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

BD.

The bases for this problem are given as follows:

3 and 12.

Hence the length of segment BD is obtained as follows:

(BD)² = 3 x 12 -> geometric mean formula

(BD)² = 36

(BD)² = 6².

BD = 6.

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Answer:6

Step-by-step explanation:

dependent is the varible

The formula for the test statistic depends on the type of hypothesis test being conducted. However, in general, the test statistic is calculated by taking the difference between the sample statistic (such as the sample mean or proportion) and the hypothesized population parameter, and dividing by the standard error of the statistic.

The distribution of the test statistic also depends on the type of test being conducted. For example, if conducting a t-test with a sample size less than 30, the test statistic follows a t-distribution with degrees of freedom equal to the sample size minus 1. If conducting a z-test or a large sample t-test with a sample size greater than or equal to 30, the test statistic follows a standard normal distribution (i.e., a z-distribution).

It is important to consult the appropriate distribution table and degrees of freedom when interpreting the test statistic to determine the p-value and make a decision about the hypothesis.

The formula for the test statistic and its distribution depend on the specific hypothesis test being conducted. I'll provide the information for two common tests: the t-test and the chi-square test.

1. T-test:
The formula for the test statistic in a t-test is:

t = (sample mean - population mean) / (sample standard deviation / √n)

where n is the sample size. The distribution for the test statistic is the t-distribution with (n-1) degrees of freedom.

2. Chi-square test:
The formula for the test statistic in a chi-square test is:

χ² = Σ [(observed frequency - expected frequency)² / expected frequency]

The distribution for the test statistic is the chi-square distribution with (k - 1) degrees of freedom, where k is the number of categories in the contingency table.

Remember to use the appropriate test and formula based on your specific research question and data.

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Answer:

Step-by-step explanation:

20 seconds = 8 copies

so every 2.5 seconds, 1 page is made( 20sec/8 page = 2.5 page per second)

2.5 sec = 1 page

48 sec = x page

now you cross multiply, and that goes to: 2.5x = 48

isolate for x

x= 48/2.5

x= 19.2 but it says whole pages so you round down

x = 19 pages in 49 seconds

The length of segment RT is given as follows:

[tex]RT = 36\sqrt{2}[/tex]

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The right angle in this problem is given as follows:

S, as R = T = 45º.

As the other two angles have the same measure, we have that the two sides are RS = ST = 36, hence the hypotenuse RT is given as follows:

h² = 36² + 26²

[tex]h = \sqrt{2 \times 36^2}[/tex]

[tex]RT = 36\sqrt{2}[/tex]

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Answer:

$68000

Step-by-step explanation:

Answer:

$6800

Step-by-step explanation:

30x1600+10x2000

=48000+2000

=68000

Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is approximately 0.0443 or 4.43%.

The distribution of the sample means of size n = 100 from a population with mean μ = $2500 and standard deviation σ = $300 can be approximated by a normal distribution with mean = μ = $2500 and standard deviation = σ/√n = $300/√100 = $30.

Thus, we need to find the probability that the sample mean falls between $2450 and $2460.

Z-score for $2450:

z = (2450 - 2500) / 30 = -1.67

Z-score for $2460:

z = (2460 - 2500) / 30 = -1.33

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:

P(z < -1.67) = 0.0475

P(z < -1.33) = 0.0918

Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is:

P(-1.67 < z < -1.33) = P(z < -1.33) - P(z < -1.67)

= 0.0918 - 0.0475

= 0.0443

So, the probability is approximately 0.0443 or 4.43%.

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The greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.

First, we need to determine the dimensions of the box in terms of the length of a side of a cube. We can do this by finding the smallest dimension of the box and dividing it by the length of the side of a cube.

The smallest dimension of the box is the height, which is 6 cm. Therefore, the length of the side of a cube must be a factor of 6.

The length and width of the box are both 8 cm, so the length of the side of a cube must be less than or equal to 8 cm.

We can check the factors of 6 to find the largest possible size of the cube that can fit in the box:

A cube with side length 6 cm would fit in the box, but the lid would not be able to close.

A cube with side length 4 cm would fit in the box, and the lid would be able to close, so this is the largest size cube that can fit in the box.

To determine how many 4 cm cubes can fit in the box, we need to find the volume of the box and divide by the volume of a single cube. The volume of the box is:

V_box = length x width x height

V_box = 8 cm x 8 cm x 6 cm

V_box = 384 cm³

The volume of a single 4 cm cube is:

V_cube = side length³

V_cube = 4 cm x 4 cm x 4 cm

V_cube = 64 cm³

Dividing the volume of the box by the volume of a single cube gives us the maximum number of cubes that can fit in the box:

384  / 64  = 6

Therefore, the greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.

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Para calcular la velocidad del joven, Podemos utilizar la fórmula de la velocidad promedio Por lo tanto, la posición del joven a las 9 h es 1100 km.

a) Para calcular la velocidad del joven, podemos utilizar la fórmula de la velocidad promedio:

velocidad = distancia / tiempo

La distancia recorrida por el joven es xf - xo = 500 km - 200 km = 300 km, y el tiempo transcurrido es 11 h - 8 h = 3 h. Entonces, la velocidad del joven es:

velocidad = 300 km / 3 h = 100 km/h

Por lo tanto, el joven se movió a una velocidad constante de 100 km/h.

b) La ecuación que determina la posición del joven en función del tiempo puede ser expresada como:

x = xo + velocidad × tiempo

donde x es la posición del joven en un momento dado, xo es la posición inicial (xo = 200 km), velocidad es la velocidad constante a la que se mueve el joven, y tiempo es el tiempo transcurrido desde la posición inicial.

Sustituyendo los valores conocidos, obtenemos:

x = 200 km + 100 km/h × t

donde t es el tiempo en horas.

c) Para calcular la posición del joven a las 9 h, podemos utilizar la ecuación que determina la posición del joven en función del tiempo:

x = 200 km + 100 km/h × t

Sustituyendo t = 9 h, obtenemos:

x = 200 km + 100 km/h × 9 h = 1100 km

Por lo tanto, la posición del joven a las 9 h es 1100 km.

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The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.

In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:

3.3 = log(I/0.001)

To isolate I, we need to convert the equation into exponential form:

10^(3.3) = I/0.001

Simplifying the equation, we have:

I = 10^(3.3) * 0.001

Using a calculator, we find that 10^(3.3) is approximately 1995.26.

So, the seismograph reading of the earthquake is:

I = 1995.26 * 0.001

≈ 1.99526.

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Answer:

L = J + 5

Step-by-step explanation:

Let's use "L" to represent Leanne's age and "J" to represent Jose's age.

From the given information, we know that Leanne is 5 years older than Jose, so we can write:

L = J + 5

This equation states that Leanne's age "L" is equal to Jose's age "J" plus 5 years.

The mean of a sampling distribution of mean is equal to the population mean.

The mean of a sampling distribution of the mean is equal to the population mean. This is a fundamental property of sampling distributions. When repeatedly taking random samples from a population and calculating the mean of each sample, the distribution of those sample means will have a mean that is equal to the population mean. This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution centered around the population mean. Therefore, the mean of the sampling distribution of the mean will be the same as the population mean.

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The stem and leaf for the data values is

60 | 0.8 3.5

70 | 2.8 3.8 5.5 7.8 8.3 9.7

80 | 0.6, 2.1, 4.5

From the question, we have the following parameters that can be used in our computation:

Data values:

82.1 72.8 78.3 77.8 60.8 79.7 73.8 75.5 80.6 84.5 63.5

Sort in order of tens

So, we have

60.8 63.5

72.8 73.8 75.5 77.8 78.3 79.7

80.6, 82.1, 84.5

Next, we draw the stem and leaf as follows:

a | b

Where

a = stem

b = leaf

Using the above as a guide, we have the following:

60 | 0.8 3.5

70 | 2.8 3.8 5.5 7.8 8.3 9.7

80 | 0.6, 2.1, 4.5

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Answer:

The correct answer is 12.6n2 + 7.14n.

Step-by-step explanation:

To find the product of 2.1n(6n + 3.4), we can use the distributive property of multiplication:

2.1n(6n + 3.4) = 2.1n(6n) + 2.1n(3.4)

Simplifying this expression gives:

12.6n^2 + 7.14n

Therefore, the product of 2.1n(6n + 3.4) is 12.6n^2 + 7.14n.

Answer:

12.6n2 + 7.14n.

Step-by-step explanation:

2.1×n×(6n+3.4)

Rewrite the expression

2.1×n(6n+3.4)

Calculate the product

2.1n(6n+3.4)

Apply the distributive property

2.1n×6n+2.1n×3.4

Multiply the terms

12.6n

2

+2.1n×3.4

Solution

12.6n

2

+7.14n

To calculate the average rate of ascent we need to use the following formula:

rate = (final depth - initial depth) / time

Plugging in the given values:

rate = (180 ft - (-1,320 ft)) / 60 min = 1,500 ft / 60 min = 25 ft/min

However, since the submarine is currently below the desired depth, the rate needs to be negative (i.e. descending). So, we need to subtract the ascent rate from the descent rate:

ascent rate = (-1,320 ft - (-180 ft)) / 60 min = -1,140 ft / 60 min = -19 ft/min

total rate = 25 ft/min - 19 ft/min = 6 ft/min

Therefore, the average rate of ascent needed would be 17 feet per minute (rounding to the nearest whole number).

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Use  Theoretical probability  there are 220 students in the grade.

We can use the formula for theoretical probability to find the number of students in the grade:

P(event) = number of favorable outcomes / number of total outcomes

In this case, the probability of a student trying out for the school play is 1/10, so we have:

1/10 = number of students who try out / total number of students in the grade

We can simplify this equation by multiplying both sides by the total number of students in the grade:

total number of students in the grade * 1/10 = number of students who try out

Multiplying both sides by 10, we get:

total number of students in the grade = 10 * number of students who try out

Substituting the given value of 22 for the number of students who try out, we get:

total number of students in the grade = 10 * 22

total number of students in the grade = 220

Therefore, there are 220 students in the grade.

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After 4 seconds, both containers will have the same amount of water.

Let's assume that after "t" seconds, both containers will have the same amount of water.

In "t" seconds, the first container will have 56 + t gallons of water.

In "t" seconds, the second container will have 64 - t gallons of water.

To find out when both containers will have the same amount of water, we need to solve the equation:

56 + t = 64 - t

By solving for "t", we get:

2t = 8

t = 4

Therefore, after 4 seconds, both containers will have the same amount of water.

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Answer:

21x+6

Here is the answer

Its a pleasire

Answer:

21x+6

Step-by-step explanation:

first distrbute the 3 on the brackets

and note that in mathematics when there is no sign just like after the 3 it means it's multiplication

3(2x+5)+3(5x-3)

=6x+15+15x-9

now add or subtract

=21x+6

that is the simplest we can get and we can't find the value of x cuz this is not an equation

(there is no equal sign and numbers on both sides )

The following versions of the underlined text would best accomplish this goal is an inconvenient and time-consuming process

This version of the underlined text best accomplishes the writer's goal of providing evidence to clarify the previous sentence's point about what advocates fail to consider. By mentioning that compliance with local building codes is an inconvenient and time-consuming process, it highlights a significant factor that advocates may overlook when promoting the idea of purchasing or renting land for a tiny home. This evidence emphasizes the challenges and potential barriers involved in the process, which helps to clarify the previous point and provide a more comprehensive understanding of the situation.

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