Tell whether the ratios form a proportion.

13,721

Answer:

50

Step-by-step explanation:

There are 50 candies in the bag.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

John ate 40% of the candies in a bag.

If John ate 20 candies.

let the total number of Candies be x.

So, 40% of x = 20

40/ 100 x = 20

x = 2000/ 40

x= 50

Hence, there are total 50 Cadies.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Probability that 79 or more seeds germinate is 0.138, or about 13.8%.

To approximate the probability that 79 or more seeds germinate, we can use a normal approximation to the binomial distribution. First, we need to find the mean and standard deviation of the number of seeds that germinate.

The mean is the expected value of a binomial distribution, which is equal to the product of the number of trials (90) and the probability of success (0.84):

mean = 90 x 0.84 = 75.6

The standard deviation of a binomial distribution is equal to the square root of the product of the number of trials, the probability of success, and the probability of failure (1 minus the probability of success):

standard deviation = sqrt(90 x 0.84 x 0.16) = 3.11

Next, we can use the normal distribution to approximate the probability that 79 or more seeds germinate. We need to standardize the value of 79 using the mean and standard deviation we just calculated:

z = (79 - 75.6) / 3.11 = 1.09

Using a standard normal distribution table (or calculator), we can find the probability that a standard normal variable is greater than 1.09:

P(Z > 1.09) = 0.138

This means that the approximate probability that 79 or more seeds germinate is 0.138, or about 13.8%.

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True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.

When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.

Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

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Answer:

3.6=30%    3.6+12=15.6       $15.6

Step-by-step explanation:

I hope this helps! Have a fantastic fri-yay! May I have brainliest!

Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

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Answer:

Step-by-step explanation

Answer:14

Step-by-step explanation:

The age of the person who entered the room is 26.

From the information, the ages of the people are

23 , 19 , 12 , 21 , 13. Therefore the addition of the ages will give 88.

When another person entered, the person enters the room, the mean age of the 6 people is now 19. Therefore, the total ages will be:

= 19 × 6

= 114

Therefore, the age of the last person will be:

= 114 - 88

= 26

Therefore, the age of the person who entered the room is 26.

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There are 56,448 ways for eight men and five women to stand in a line so that no two women stand next to each other. This can be answered by the concept of Permutation and combination.

Firstly, we need to arrange the eight men in a line. There are 8! = 40,320 ways to do this. Now, we have nine gaps between the men where the women can be placed. We can place one woman in each gap, and then arrange the remaining two women among the gaps in 9P2 = 72 ways. However, this count includes arrangements where two women are standing next to each other.

To exclude these arrangements, we need to subtract the cases where two women stand next to each other. There are eight such cases, where two adjacent gaps are occupied by women. In each of these cases, there are 7! ways to arrange the men and 7P2 ways to arrange the remaining three women among the remaining seven gaps. Therefore, the total number of ways to arrange eight men and five women so that no two women stand next to each other is:

8! * 72 - 8 * 7! * 7P2 = 56,448.

Therefore, there are 56,448 ways to arrange eight men and five women so that no two women stand next to each other

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Answer:

B=30,000

Y=The Plane's altitude

M= -2,000

X= Minutes

Equation: y=-2,000x+30,000

Slope= ?

Y-intercept= the point where you start at

what is the altitude after 10 minutes?=10,000

How Long does it take to get to 0 altitudes?=15 (Minutes)

Step-by-step explanation:

What are the choices for slope

Load vs deformation behavior of wet-mix and dry-mix shotcrete with different reinforcement can be summarized as follows:

Load vs Deformation Behavior of Wet-mix Shotcrete:

- Wet-mix shotcrete exhibits a gradual increase in load with deformation.

- The initial stiffness is relatively low, allowing for greater deformation before reaching its peak load.

- Wet-mix shotcrete tends to exhibit more ductile behavior, with a gradual post-peak load decline.

- The reinforcement in wet-mix shotcrete helps in controlling crack propagation and enhancing overall structural integrity.

Load vs Deformation Behavior of Dry-mix Shotcrete:

- Dry-mix shotcrete exhibits a relatively higher initial stiffness, resulting in less deformation before reaching the peak load.

- It typically shows a brittle behavior with a rapid drop in load after reaching the peak.

- The reinforcement in dry-mix shotcrete primarily helps in preventing the formation and propagation of cracks.

When to Use Wet-mix Shotcrete:

- Wet-mix shotcrete is commonly used in underground construction, such as tunnel linings and underground mines.

- It is suitable for applications where greater flexibility and ductility are required, such as seismic zones or areas with ground movement.

When to Use Dry-mix Shotcrete:

- Dry-mix shotcrete is often used in above-ground applications, such as architectural finishes, structural repairs, and protective coatings.

- It is preferred in situations where rapid strength development is required, as it typically achieves higher early strength than wet-mix shotcrete.

- Dry-mix shotcrete can be used in areas where a more rigid and less deformable material is desired, such as in structural elements subjected to high loads.

Therefore, wet-mix and dry-mix shotcrete exhibit different load vs deformation behavior due to their distinct mixing and application methods. Wet-mix shotcrete offers greater ductility and deformation capacity, making it suitable for applications with dynamic loading or ground movement.

On the other hand, dry-mix shotcrete provides higher early strength and is preferred for applications requiring rapid strength development or where rigidity is essential. The choice between wet-mix and dry-mix shotcrete depends on the specific project requirements, structural considerations, and the anticipated loading conditions.

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(a) The null hypothesis is H0: p1 = p2 and the alternative hypothesis is H1: p1 ≠ p2.

(b) The test statistic is 2.025.

(c) The critical value is 2.706.

Test the null hypothesis: Since the test statistic of 2.025 is less than the critical value of 2.706, the null hypothesis is not rejected. There is not sufficient evidence to conclude that p1 ≠ p2 at the 0.10 level of significance. Therefore, the correct conclusion is "Do not reject the null hypothesis. There is not sufficient evidence to conclude that p1 ≠ p2."The contingency table is as follows:

Treatment B Total Success Failure Treatment A Success 41 16 57 Failure 22 24 46 Total 63 40 103Where p1 represents the proportion of success for Treatment A and p2 represents the proportion of success for Treatment B. The population proportions differ at the 0.10 level of significance using the given contingency table as follows:

(a) The null hypothesis is H0: p1 = p2 and the alternative hypothesis is H1: p1 ≠ p2.

(b) The test statistic is 2.025.

(c) The critical value is 2.706. Therefore, the correct conclusion is "Do not reject the null hypothesis.

There is not sufficient evidence to conclude that p1 ≠ p2."

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Answer:

A, B & D

Step-by-step explanation:

They have no solution because the variable x in each of the equation cancels out.

Answer:

4(x+3)+2x=6(x+2)

Step-by-step explanation:

4x+12+2x=6x+12

(Group like terms)

4x+2x-6x=12-12

6x-6x=0

0=0

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer:

D) two solutions

Step-by-step explanation:

because the first one is: x = 5y + 4

and the second one is: -2x+10y=8

and the equals in the first one is just how to get the value of x and it doesn't count as a third solution

ABCD ∽ EFGH, meaning both quadrilaterals are similar, therefore the proportionos of their corresponding sides are equal, thus

\(\cfrac{AB}{EF}~~ = ~~\cfrac{CD}{HG}\implies \cfrac{\stackrel{AB}{3}}{\underset{EF}{2}}~~ = ~~\cfrac{\stackrel{CD}{4.5}}{\underset{HG}{y}}\implies 3y=9\implies y=\cfrac{9}{3}\implies y=3\)

The required solutions of the situation of the function are  x = 3/4  or x = -1/4.

A unique connection where each input only produces one output. A common notation for it is "f(x)," where x denotes the input value. as in f(x) = x/2 ("f of x equals x divided by 2") Since there is only one output ("x/2") for each input ("x"), it is a function: • f(2) = 1.

We have,

f(x)=2x-1

g(x)=3/8x

To find the value of x for f(x) = g(x).

f(x) = g(x)

2x-1 = 3/8x

16x² - 8x = 3

16x² - 8x - 3 = 0

16x² - 12x + 4x - 3 = 0

4x(4x - 3) + (4x - 3) = 0

(4x - 3)(4x + 1) = 0

x = 3/4  or x = -1/4

Thus, required solution are  x = 3/4  or x = -1/4.

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If the eluent were above the 1.5 cm line on the chromatographic paper, it would be considered an unexpected observation.

Normally, during chromatography, the eluent is applied below the baseline or reference line on the paper.

If the eluent exceeds the expected limit and goes above the 1.5 cm line, it can have several implications:

Smearing or spreading: The excess eluent can cause the compounds being separated to spread out more than intended. This can lead to a loss of resolution and poor separation of the individual components.

Incomplete separation: The higher eluent level can disrupt the chromatographic process, resulting in incomplete separation of the compounds. This means that the different components may not be adequately resolved into distinct bands or spots.

Longer analysis time: With the eluent above the expected level, it may take longer for the eluent front to reach the desired distance, as it needs to travel a greater distance on the chromatographic paper. This can increase the overall analysis time and potentially affect the accuracy of the results.

Unreliable measurements: If the eluent exceeds the 1.5 cm line, it can make it challenging to accurately measure the migration distances of the separated compounds. This can introduce uncertainty or errors in the calculations or interpretations of the chromatogram.

In summary, if the eluent is observed above the 1.5 cm line on the chromatographic paper, it is an unexpected observation that can lead to compromised separation, longer analysis times, and potential difficulties in accurate measurements and interpretations of the chromatogram.

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Answer:



Step-by-step explanation:

Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).

To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:

Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.

Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.

Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.

y = (x² - 8x + 16 - 16) + 15 // add and subtract 16

y = (x - 4)² - 1 + 15 // factor and simplify

Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.

y = (x - 4)² + 14

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Answer:

He made a loss of $1,200.

Step-by-step explanation:

1. 5000 + 3200 - 7000 = $1,200

1. To model the relationship between the parking hours and the cost, we can use the following equation:

\(\displaystyle\sf C(h) = \begin{cases} 5.00, & \text{if } h \leq 2 \\ 5.00 + 0.25(h - 2), & \text{if } h > 2 \end{cases}\)

Here, \(\displaystyle\sf C(h)\) represents the cost \(\displaystyle\sf C\) as a function of the parking hours \(\displaystyle\sf h\).

2. To calculate how much you have to pay for parking for 10 hours, we can substitute \(\displaystyle\sf h = 10\) into the equation:

\(\displaystyle\sf C(10) = 5.00 + 0.25(10 - 2) = 5.00 + 0.25(8) = 5.00 + 2.00 = 7.00\)

Therefore, you would have to pay $7.00 to park for 10 hours.

3. To find out how many hours $10 can buy, we need to solve the equation:

\(\displaystyle\sf 10 = 5.00 + 0.25(h - 2)\)

Simplifying the equation:

\(\displaystyle\sf 10 - 5.00 = 0.25(h - 2)\)

\(\displaystyle\sf 5.00 = 0.25(h - 2)\)

Dividing both sides of the equation by 0.25:

\(\displaystyle\sf \frac{5.00}{0.25} = h - 2\)

\(\displaystyle\sf 20 = h - 2\)

Adding 2 to both sides of the equation:

\(\displaystyle\sf h = 20 + 2 = 22\)

Therefore, $10 would buy you 22 hours of parking.

To clarify, the answer is 22 hours, not 20 hours.

a) To find the gradient of the tangent T, we need to find the derivative of the curve y = x² at the point A(1,1). Using the power rule of differentiation, we have:

dy/dx = 2x

At x = 1, the derivative is:

dy/dx = 2(1) = 2

So the gradient of the tangent T is 2.

b) To find the gradient of the chord AP, we need to find the slope of the line joining A(1,1) and P. Let the coordinates of P be (x, x²). Then the gradient of AP is:

m = (x² - 1) / (x - 1)

i) When P has coordinates (2,4), we have:

m = (4 - 1) / (2 - 1) = 3

ii) When P has coordinates (1.5, 2.25), we have:

m = (2.25 - 1) / (1.5 - 1) = 1.25

iii) When P has coordinates (1.1, 1.21), we have:

m = (1.21 - 1) / (1.1 - 1) = 0.21 / 0.1 = 2.1

iv) When P has coordinates (1.01, 1.0201), we have:

m = (1.0201 - 1) / (1.01 - 1) = 0.0201 / 0.01 = 2.01

v) When P has coordinates ((1+h), (1+h)²), we have:

m = ((1+h)² - 1) / ((1+h) - 1) = (h² + 2h) / h = h + 2

c) The gradient of the tangent T is a constant value of 2, while the gradient of the chord AP changes with the position of point P on the curve. As point P approaches point A, the gradient of the chord AP approaches the gradient of the tangent T.

This is because as P gets closer to A, the chord becomes closer to the tangent at A, and the gradient of the chord approaches the gradient of the tangent.

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According to the given expressions, there was used the multiplication property for inequalities because there's being multiplied the number 61 on both sides.

Answer:

\(\frac{5k -6}{10}\)

Answer:

1/5k + 3/5

Step-by-step explanation:

2/5 * 2/2 = 4/10

4/10k + 1/10k = 5/10k = 1/2k

1/2k + 3/5

Answer:

27

Step-by-step explanation:

x-15=12

add fifteen to both sides

x-15+15=12+15

x=27

Answer:

27

Step-by-step explanation:

27-15=12