1/2a+2/3b=50 when b=30?

Answer:

x=8

Step-by-step explanation:

All we need to do is to make the bases equal. We know 625=25² so we apply that to the equation:

\( {25}^{3x + 2} = {25}^{2(2x - 3) } \\ {25}^{3x + 2} = {25}^{4x - 6} \)

Now that the bases are equal, we can set the exponents equal too.

\(3x + 2 = 4x - 6 \\ 3x - 4x = - 6 - 2 \\ - x = - 8 \\ x = 8\)

Hope this helps!

The maximum period of time they could reserve the meeting space is 9 hours.

Mathematical expressions with the symbols > and are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

An algebraic inequality expression is a mathematical statement that uses the it as a sign to connect an expression to a value, a variable, or another expression. One type of variable inequalities can have solutions that can be graphed either in a coordinate plane or on a number line.

Inequality expression is 31 + 5.9*t < 84.10.

To understand it, collect all constant on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10 % 5.9 = 9 hours.

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Correct Question:

To rent a certain meeting room, a college charges a reservation fee of $31 and an additional fee of $5.90 per hour. The chemistry club wants to spend less than $84.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answer:

8?

Step-by-step explanation:

i am not sure

since we were given the key ( how it should be sort out or used )

then we get all the numbers out which are:

21, 23, 30, 32, 32, 35, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

then we go ahead to answer the questions:

a) Range = highest number minus Lowest number

55 - 21 = 34

b) 17 (by counting all individual ages ).

c) Median = the middle age

(but before that, we must arrange the ages either a cording to their sizes either from biggest to smallest (descending order) or from smallest to biggest (ascending order)

so we arrange in ascending order but the numbers are already arranged so we don't have to stress ourselves:

Median = 46 (the number in the middle ).

Hope you ace your tests, Good luck ✅.

Answer:

Step-by-step explanation:

Hope this helps and i DID NOT use a Calculator!

The equation of the line through the points (2, 8) and (-4, 5) in slope-intercept form is y = (1/2)x + 7.

To determine the equation of the line through the points (2, 8) and (-4, 5) and express it in slope-intercept form, follow these steps:

1. Calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1)
  In our case, (x1, y1) = (2, 8) and (x2, y2) = (-4, 5).
  m = (5 - 8) / (-4 - 2) = (-3) / (-6) = 1/2

2. Use the slope-intercept form equation, y = mx + b, and plug in the slope (m) and one of the points (x, y) to solve for the y-intercept (b).
  Let's use the point (2, 8).
  8 = (1/2) * 2 + b
  8 = 1 + b
  b = 7

3. Now, plug the slope (m) and y-intercept (b) back into the slope-intercept form equation.
  y = mx + b
  y = (1/2)x + 7

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You cant simplify further than that. Look at the file attached to this.

EDIT:

If that was wrong, try,

Answer:

D. The store will need exactly 38 boxes for the shipment, with  1/3 pound of clay going into the last box

Step-by-step explanation:

We need to divide the number of pounds by the numbers of pounds per box

28 ÷ 3/4

Copy dot flip

28 * 4/3

112/3

37 1/3

We will have to round up to pack all the clay

38 boxes with 1/3 in the 38th box

Answer:

4 hours to paint all 4 of walls

Step-by-step explanation:

well is it takes her 20 minutes to paint 1/3 of a wall and there is 4 walls to 1/3 on each it would take her 20 minutes for 1/12(total of 4 walls) you would do 20x12 which is 240 then divided by 60 which is 4 so the answer is 4.

In year 1, the GDP price deflator is calculated to be 0.66 (or 66%), and in year 2, it is 0.77 (or 77%). The rate of inflation between years 1 and 2, as measured by the GDP price deflator, is approximately 16.67%. In contrast, the CPI rate of inflation is calculated to be 20%. The differences in these results can be attributed to the differences in the composition and weighting of the goods included in the GDP price deflator and the Consumer Price Index (CPI).

a) The GDP price deflator measures the average price change of all goods and services produced in an economy. To calculate the GDP price deflator in year 1, we use the formula: (Nominal GDP / Real GDP) * 100. Given the quantities and prices of broccoli and cauliflower in year 1, the nominal GDP is (100 million * $0.50) + (30 million * $0.80) = $65 million, and the real GDP is (100 million * $0.50) + (30 million * $0.50) = $55 million. Thus, the GDP price deflator in year 1 is (65/55) * 100 = 118.18%. In year 2, the nominal GDP is (80 million * $0.60) + (60 million * $0.85) = $88 million, and the real GDP is (80 million * $0.50) + (60 million * $0.50) = $70 million. Therefore, the GDP price deflator in year 2 is (88/70) * 100 = 125.71%. The rate of inflation between years 1 and 2, as measured by the GDP price deflator, is ((125.71 - 118.18) / 118.18) * 100 = 6.36%.

b) The Consumer Price Index (CPI) measures the average price change of a basket of goods and services typically consumed by households. To calculate the CPI in year 1, we assign weights to the prices of broccoli and cauliflower based on their consumption quantities. The CPI in year 1 is (100 million * $0.50) + (30 million * $0.80) = $65 million. In year 2, the CPI is (80 million * $0.60) + (60 million * $0.85) = $81 million. The CPI rate of inflation between years 1 and 2 is ((81 - 65) / 65) * 100 = 24.62%.

c) The differences in the results between parts (a) and (b) can be attributed to the differences in the composition and weighting of goods included in the GDP price deflator and the CPI. The GDP price deflator considers the prices of all goods and services produced in the economy, reflecting changes in production patterns and the overall price level. On the other hand, the CPI focuses on a fixed basket of goods and services consumed by households, reflecting changes in the cost of living. The differences in the weighting and composition of goods between the two measures result in variations in the calculated inflation rates.

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Statistics indicate that 45% of all small businesses fail after three years. This is a concerning statistic for entrepreneurs who are considering starting their own business.

It is important for potential business owners to understand the reasons why small businesses fail and take steps to mitigate these risks. Some common reasons for failure include poor management, insufficient funding, lack of market demand, and competition.

One way to mitigate these risks is by having a solid business plan in place that includes a realistic assessment of the market, a clear understanding of the competition, and a plan for securing financing. Additionally, having a strong risk tolerance and the ability to adapt to changing market conditions can also increase the chances of success for small businesses.

Ultimately, the key to success for small businesses is a combination of careful planning, strong management, and a willingness to take calculated risks.

One of the contributing factors to this failure rate is the business owner's risk tolerance (3) B), which may lead them to take on more financial obligations than they can handle. Additionally, securing proper financing (4) D) is crucial for the success and growth of a small business, and a lack of adequate funding may contribute to the high failure rate.

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Answer:

The graph in the lower left corner does not belong.

Step-by-step explanation:

It does not belong because the other praghs have already intercected or are going to eventually like the upper right corner one.

Have a great day!

Please rate!

Answer:

0.00486

Step-by-step explanation:

since the exponet is -3 the decimal point moves 3 places to the left

0.00486

The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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16/27 is the value of quantity.

What is a linear equation in math?

\(\frac{3^{2} * 3^{-5} }{4^{2} } = \frac{3^{-3} }{4^{-2} }\)

\(\frac{1}{3^{3} }\)  ÷  \(\frac{1}{4^{2} }\)

\(\frac{1}{27} * 16 = \frac{16}{27}\)

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The probability of picking a 4 and then picking a 2 is 1/9

From the question, the given parameters are

Cards = 2, 3 and 4

Also, from the question, we have

The selected card is returned to the pack

So, the probability of selecting a card with number 4 is

P(4) =n(4)/Total

This gives

P(4) = 1/3

Also, the probability of selecting a card with number 2 is

P(2) =n(2)/Total

This gives

P(2) = 1/3

The required probability is

P(4 and 2) = 1/3 * 1/3

Evaluate

P(4 and 2) = 1/9

Hence, the probability is 1/9

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Answer:

x = 7 and 15

Step-by-step explanation:

Divide both sides by -4...

| x - 11 | = 4

because

| -4 | = 4 and

| 4 | = 4

x - 11 = -4 and x - 11 = 4

solve for x in both equations.

x = 7 and x = 15

Answer:

f(0) = 1

Step-by-step explanation:

f(0) means what is the value of y when x = 0

from the diagram this is the point (0, 1 ) , then

f(0) = 1

Answer:

A

Step-by-step explanation:

Because X=1976 is given just substitute the value

Using Euler's method with a step size of 0.2, the estimate for y(1.4) is 2. When the step size is reduced to 0.1, the estimated value for y(1.4) remains approximately the same.

Euler's method is a numerical approximation technique used to estimate the solution of a first-order ordinary differential equation (ODE) given an initial condition. In this case, we are given the initial-value problem y′ = x - xy, y(1) = 0.1, and we want to estimate the value of y(1.4).

To apply Euler's method, we start with the initial condition y(1) = 0.1. We then divide the interval [1, 1.4] into smaller subintervals based on the chosen step size. With a step size of 0.2, we have two subintervals: [1, 1.2] and [1.2, 1.4]. For each subinterval, we use the formula y(i+1) = y(i) + h * f(x(i), y(i)), where h is the step size, f(x, y) represents the derivative function, and x(i) and y(i) are the values at the current subinterval.

By applying this formula twice, we obtain the estimate y(1.4) ≈ 2. This means that according to Euler's method with a step size of 0.2, the approximate value of y(1.4) is 2.

If we reduce the step size to 0.1, we would have four subintervals: [1, 1.1], [1.1, 1.2], [1.2, 1.3], and [1.3, 1.4]. However, the estimated value for y(1.4) remains approximately the same at around 2. This suggests that decreasing the step size did not significantly impact the approximation.

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Answer:

Step-by-step explanation:

Yes they are similar.

The triangles are similar by AA~ postulate.

Answer:

Step-by-step explanation:

As per given we have:

If two angles of one triangle are congruent with another, they triangles are similar

Correct choice is C

Yes, the two-sample z test is appropriate here. This test is used to compare the means of two independent groups and determine whether they are statistically different.

In this experiment, the two groups are the participants who received the drink with the artificial sweetener and the participants who received the drink without it. The test will determine if there is a significant difference in their blood glucose levels after consuming each drink. The fact that the same participants are measured on two different days is not an issue, as long as the order in which they receive the drinks is randomized to avoid any potential order effects. The z test requires certain assumptions to be met, such as normality and equal variances between the groups, so the researcher should check these assumptions before conducting the test. Overall, the two-sample z test is a suitable statistical method for analyzing the impact of the new artificial sweetener on blood glucose in this experiment.

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Since there isn't a picture of the graphs, I attached one, of my graph, to this answer.

I'm also assuming (y2 2x+1) is actually (y< 2x+1).

Possible solutions are within the purple section of the attached image.

I hope this is helpful to you.

Graph that represents both the inequality is attached below.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

First, we make the graph,

The border of the inequality y = 2x + 1 has a slope of 2 and a y-intercept of 1. Plotting the y-intercept at (0, 1) and using the slope to determine further points will allow us to draw this line.

For instance, if we move two units up (in the positive y-direction) and one unit to the right (in the positive x-direction), we get the point (1, 3).

The answer to y < 2x + 1 may be represented by connecting these points with a dashed line and darkening the area below the line.

A boundary line for the inequality y -2x - 3 has a slope of -2 and a y-intercept of -3. Plotting the y-intercept at (0, -3) and using the slope to determine further points will allow us to draw this line.

For instance, if we move two units down (in the negative y-direction) and one unit to the right (in the positive x-direction), we get the point (1, -5).

The answer to y < -2x - 3 may be represented by connecting these points with a dashed line and coloring the area below the line.

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Using the Factor Theorem, the polynomial is factored as follows:

f(x) = (x - 2)(x + 1)(x² + 2).

The Factor Theorem states that a polynomial function with roots(also called zeros) \(x_1, x_2, \codts, x_n\) is given by the following rule.

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

In this problem, the polynomial is given by:

f(x) = x^4 - x³ - 2x - 4.

This polynomial is factored applying the inverse factor theorem, finding the roots of the polynomial, which are given as follows:

For the complex roots, we have that 1.41² = 2, hence the term corresponding to the two complex roots is:

x² + 2.

Then the complete factored polynomial is:

f(x) = (x - 2)(x + 1)(x² + 2).

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Answer:75.708L

Step-by-step explanation:

Answer:

504 combos

Step-by-step explanation:

Cannot use digits twice and last is '7'

 9 digits for first place choice  

     8 digits for second place

         7 digits for third place

               only  '7' for fourth place       9 x 8 x7 = 504 combos

You can use the rule of product from combinatorics to find out how many ways can the remaining digits be chosen.

The remaining digits for the given condition can be chosen in 504.

Option B: 504

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in   ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

Since 7 is already fixed and there is constraint that no two digits can be used, thus, we initially have only 10-1 = 9 digits.

For first place, we can chose 1 digit out of 9 digits in ways,

⁹C₁ = 9 ways

For second place, as one of the digit is used, thus, 1 digit out of 8 digits can be chosen in ways,

⁸C₁ = 8 ways

For third place, as two of the digits is used, only 7 digits are remaining to chose from. Thus, 1 digit out of 7 remaining digits can be chosen in ways.

⁷C₁ = 7 ways

Using product rule, we get:

Total possible number of choices for choosing digits for first, second and third position of lock with given constraints is given as

= 9 x 8 x 7

= 504 ways

Thus, The remaining digits for the given condition can be chosen in,

Option B: 504

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Answer:

Step-by-step explanation:

okay so basically 6+4=10 so the probability of doritos is 3/5 and 5+3=8 so the probabliliy is 5/8. I think the answer is A. but i 100% could be wrong, im sorry if i am

The probability you will end up with Doritos and Coke is; P(Doritos and Coke) = 0.375

We are told the components of the box are;

6 bags of Doritos

4 bags of Cheetos

Second box contains;

5 cans of Coke.

3 cans of Pepsi.

Probability of picking doritos in first box = 6/10

Probability of picking coke in second box = 5/8

Thus;

P(Doritos and Coke) = 6/10 * 5/8

P(Doritos and Coke) = 0.375

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In 1990, the average person in the United States consumed approximately 0.000532 lb (or 0.24 grams) of artificial sweeteners per year, based on USDA data.

In 1990, according to the USDA, each person in the United States consumed an average of 133 lb of artificial sweeteners per year.
To calculate the average consumption of artificial sweeteners per person, you can divide the total consumption by the population of the United States in 1990.
Let's assume that the population of the United States in 1990 was 250 million people.
To find the average consumption per person, you would divide the total consumption of 133 lb by the population of 250 million people:
133 lb / 250,000,000 people = 0.000532 lb/person
Therefore, in 1990, the average person in the United States consumed approximately 0.000532 lb (or 0.24 grams) of artificial sweeteners per year.

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The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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Saturn has the densest crown based on Gizmo densities, with a density of 687 kg/m³.

The density of an item is calculated theoretically as its mass divided by its volume.

The weight of an object is defined as its mass. The volume of a thing is the amount of space that the object or substance takes up.

As a result, density refers to the ratio or numerical connection between an object's mass and the quantity of space it occupies.

Saturn is the densest planet in terms of both mass and volume. Saturn is denser than a rock, quarter, cruise ship, or beach ball, according to what we can see from the Gizmos.

See the table below for their densities.

Objects     Relative Density

Rock                2.6g/cc³

Cruise Ship     9.0g/cm³

Quarter           8.9 g/ml³

Saturn            687 kg/m³

Beach ball       10 g/cc³

Thus, we selected Saturn as the Gizmo with the densest crown.

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