Q35
Express the equation in exponential form (a) log, 4 = 2. That is, write your answer in the form 24 = B. Then A= and B= - (b) log, 125 = 3. That is, write your answer in the form 5° = D. Then C= and D

Answer:

Equation;

(3/4)x = 2/3

Solving;

x = 8/9

she would need 8/9 of her sugar to make a full batch.

Step-by-step explanation:

Let x represent the amount of sugar that would be needed to make the whole batch.

Given that;

Pia used 2/3 of her sugar to make 3/4 of a batch of cookies.

Since 2/3 of her sugar is needed to make 3/4 of a batch of cookies, then;

(3/4)x = 2/3

Solving the equation, dividing both sides by 3/4;

(3/4)x ÷ 3/4 = 2/3 ÷ 3/4

x = 2/3 × 4/3

x = 8/9

Therefore she would need 8/9 of her sugar to make a full batch.

\( {2}^{8} \times( \frac{3}{2} ) ^{4} \\ = \frac{ {2}^{8} \times {3}^{4} }{ {2}^{4} } \\ = {2}^{8 - 4} \times {3}^{4} \\ = {2}^{4} \times {3}^{4} \\ = (2 \times 3) ^{4} \\ = {6}^{4} \)

Answer:

\( {6}^{4} \)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

the answer is 6^4

Step-by-step explanation:

hopef that helped

Answer:

I think it is b and d .

Step-by-step explanation:

Answer:

Hello again! Both D and B are rectangles.

Step-by-step explanation:

You know that a rectangle has 4 sides like a quadrilateral but it is different. Both of the oppiosite sides are the same length. C would not be one because it is not connected therefore it is not a full shape. Because of  A´s even sides, A is not a rectangle. I hope this helps! :]

Sorry I messed up! :]

The volume of a cube whose edge is 6 cm long is 216

Answer:

scal factor = 1.5

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, that is

scale factor = \(\frac{C'D'}{CD}\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1.5

Answer:

All solutions or infinite.

Step-by-step explanation:

Turn 2y = -4x + 6 into standard form - divide by 2

Y = -2x + 3

2x + y = 3

Substitute the y equation in for y.

2x - 2x + 3 = 3

The x variables cancel out.

3 = 3

Which is true so it means all solutions.

Hope this helps.

(a) The derivative of y with respect to x, y', is given by -sin(x) + v(dy/dx) + y(dv/dx) = 0. (b) Solving the equation for y and differentiating gives y' = [(cos(x))(dv/dx)]/v^2. (c) Substituting the expression for y into the solution from part (a) confirms the consistency of the solutions.


To find the derivative of y with respect to x, we can use implicit differentiation. Let's go through the steps:

(a) To find y', we differentiate both sides of the equation cos(x) + vy = 6 with respect to x.
Differentiating cos(x) with respect to x gives us -sin(x).
For the term vy, we need to use the product rule. Let u = v and v = y.
Differentiating u = v with respect to x gives us du/dx = dv/dx.
So, differentiating vy with respect to x gives us v(dy/dx) + y(dv/dx).
Since we are differentiating with respect to x, the term dv/dx is the derivative of v with respect to x.
Now, we can put these results together to find y':
-sin(x) + v(dy/dx) + y(dv/dx) = 0

(b) To solve the equation explicitly for y, we rearrange the equation cos(x) + vy = 6 to isolate y.
Subtracting cos(x) from both sides gives vy = 6 - cos(x).
Dividing both sides by v gives y = (6 - cos(x))/v.
To find y' in terms of x, we need to differentiate y = (6 - cos(x))/v with respect to x.
Using the quotient rule, we have:
y' = [(v(0) - (6 - cos(x))(dv/dx))/(v^2)]
Simplifying, we get:
y' = [(cos(x))(dv/dx)]/v^2

(c) To check the consistency of our solutions, we substitute the expression for y from part (b) into the equation from part (a).
cos(x) + v[(6 - cos(x))/v] = 6
Canceling out v on the right side gives:
cos(x) + (6 - cos(x)) = 6
Simplifying, we have:
cos(x) - cos(x) + 6 = 6
0 + 6 = 6
This is a true statement, confirming the consistency of our solutions.
So, the final expression for y' is [(cos(x))(dv/dx)]/v^2.

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Answer:

610 feet

Step-by-step explanation:

From the question :

1 scarf = 2.5 yards of yarn

84 scarves = x yards

Cross Multiply

1 scarf × x yards = 84 × 2.5 yards

x yards = 210 yards

Hence, 84 scarves require 210 yards

Converting yards to feet

1 yard = 3 feet

210 yards = x feet

x feet × 1 yard = 210 yards × 3 feet

x feet = 210 yards × 3 feet/1 yards

x feet = 610 feet

Hence, if Janet wants to make 84 scarves, she need to buy 610 feet of yarn

The formula has been given already, just substitute the values.

m is the slope = 3

y1 = -2

x1 = 6

y - (-2) = m (x - (6))

y + 2 = 3(x - 6)

Answer:

Slope:  

3 /5

y-intercept:  

− 6

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C because the symbol means Greater then or Equal too

So anything 90 or above would be true

Let's translate the argument into symbolic form using the following symbols:

B: Brazil has a huge foreign debt.

A: Argentina has a huge foreign debt.

The argument can be represented as follows:

B → (B ∨ A)

To determine the validity of the argument, we can construct a truth table for the expression (B → (B ∨ A)). The truth table will include all possible combinations of truth values for B and A, and we will evaluate the truth value of the entire expression for each combination.

The truth table for the argument is as follows:

B A B ∨ A B → (B ∨ A)

T T T T

T F T T

F T T T

F F F T

As we can see from the truth table, regardless of the truth values of B and A, the expression B → (B ∨ A) always evaluates to true. Therefore, the argument is valid because the conclusion is always true when the premise is true.

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Answer:

I think its D bc the scale factor is 1:5 so 12:60 therefore the answer I think is D

I hopeit helps but if its wrong im very sorry :(

Step-by-step explanation:

The expected number of boxes to be produced is given as 3,000 boxes. So, the correct answer is 0.3, indicating that the takt time in minutes is 0.3 minutes.

The production line operates for two eight-hour shifts each day, which means there are 16 hours of production time available. Since there are 60 minutes in an hour, the total available time in minutes would be 16 hours multiplied by 60 minutes, which equals 960 minutes.

The expected number of boxes to be produced is given as 3,000 boxes.

To calculate the takt time in minutes, we divide the total available time (960 minutes) by the expected number of boxes (3,000 boxes):

\(Takt time = Total available time / Expected number of boxes\)

\(Takt time = 960 / 3,000\)

By performing the calculation, we find that the takt time is approximately 0.32 minutes, which is equivalent to 0.3 minutes rounded to one decimal place.

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The statement "the midpoint method is commonly used to compute elasticity because it gives the same answer regardless of the direction of change" is the correct option from the given options.

Generally, the midpoint method is used to calculate elasticity since it is not affected by the direction of change. As a result, the coefficient will be constant regardless of the direction of change.To calculate the slope of a straight line, the standard formula is used:

slope=change in y/change in x.

The slope of the line is the same whether we move from left to right or right to left because the numerator and denominator will have opposite signs, but the slope will always be the same.The same holds true for the concept of elasticity. Elasticity measures the responsiveness of one variable to changes in another variable. We use the same formula for the midpoint method:

elasticity=(change in Q/average Q)/(change in P/average P).

To compute elasticity, we must first determine the average values. The midpoint method calculates the elasticity by comparing two points, which is accomplished by taking the average of the two points. The denominator is the average price and quantity, which is the midpoint between the initial and final price and quantity. As a result, the numerator and denominator will have opposite signs, and the same elasticity will be calculated regardless of the direction of change.In contrast, using the standard method to calculate elasticity may yield differing results based on the direction of change. Because of the difference between the starting and ending points, the elasticity will be computed differently when moving from left to right versus right to left.

Thus, we can conclude that the midpoint method is commonly used to compute elasticity because it gives the same answer regardless of the direction of change.

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Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.

What is photosynthesis?

Photosynthesis is the process in which green plants prepare their own food in the presence of sunlight and light energy is converted into chemical energy by the process of cellular respiration.

The process of photosynthesis takes place in green plants only due to presence of chlorophyll and materials such as sunlight, water, carbon dioxide is required for the process of photosynthesis.

The equation of photosynthesis is represented below:

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.

The process of food manufacturing in plant is done through photosynthesis and the plants are known as autotrophs as they are the producers.

In the process of photosynthesis the reactant have 6 carbon dioxide molecules and six water molecules, and light energy converted into chemical energy due to presence of chlorophyll.

Therefore, Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.

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The probability that the three pieces can be assembled into a triangle is 25%

Let the length of the stick be 1, so each break can occur at a position in the interval [0,1]. Let x and y be the two breaks in the stick. Then the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is the probability of the triangle.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for  y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for  y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square,

Thus, the probability that the three pieces can be assembled into a triangle is 25%

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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The angle measurements of angle B as represented in the diagram shown is 150°

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠A = ∠B (alternate interior angles)

Hence:

8x - 10 = 3x + 90

x = 20

∠B = 3(20) + 90 = 150°

The angle measurements of angle B as represented in the diagram shown is 150°

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Answer:

35 miles

Step-by-step explanation:

You add up all of the miles on the chart to get 35 miles. Have a great day! I hope this helped.

The percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

\($$\begin{aligned}& \mu=\$ 35,000 \\& \sigma=\$ 8,000\end{aligned}$$\)

we need to calculate probability for

\(& P(24000 < x < 46,000)\\ \\& =P\left(\frac{24000-35,000}{8,000} < \frac{x-\mu}{\sigma} < \frac{46,000-35,000}{8000}\right)\\ \\& =P(-1.37 < z < 1.315) \\\\& =P(z < 1.37)-P(z < -1.37)\)

\(& =0.9147-0.0853\)          \(=0.9162-0.0838 \\\)

\(& =0.8294\)    \(=0.8324 \\\)

\(& =82.94 \% \\\)    \(& =83.09\)

Therefore, the percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

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Answer:

1 is the result of equation.

Step-by-step explanation:

Given that,

→ x = 1

The equation will be,

→ [{((x × 2) + 4) ÷ 2} - 2]

Then the result of the eq. will be,

→ [{((1 × 2) + 4) ÷ 2} - 2]

→ [{(2 + 4) ÷ 2} - 2]

→ [{6 ÷ 2} - 2]

→ [3 - 2] = 1

Hence, 1 is the value of equation.

The 95% confidence interval would be given by (60.554;81.446)  

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population means that sits between an upper and lower interval is frequently stated as a percentage.

Here, we have

Given Data: 92 34 40  105 83 55  56 49 40  76 48 96  93 74 73  78 93 100  53 82

We can calculate the mean and the deviation from these data with the following formulas:

X = ∑ᵃ 1ⁿxₐn

s = √∑ᵃ = 1ⁿ(xₐ - X)²n -1

X = 71  represents the sample mean for the sample  

s=22.35 represent the sample standard deviation

n=20 represents the sample size  

The confidence interval for the mean is given by the following formula:

X ± tα/2 - √n...(1)

In order to calculate the critical value tα/2  we need to find first the degrees of freedom, given by:

df = n - 1 = 20 -1 = 19

Since the Confidence is 0.95 or 95%, the value of α = 0.05 and α/2 = 0.025

and we can use excel, a calculator, or a table to find the critical value. The excel command would be:

tα/2 = 2.09

Now we have everything in order to replace into formula (1):

71 - 2.09- 2.35√20 = 60.554

71 + 2.09- 2.35√20 = 81.446

Hence, the 95% confidence interval would be given by (60.554;81.446).

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Answer:

$0.83

Step-by-step explanation:

19.97 ÷ 24 = 0.8320833333

Round to nearest cent 0.83

The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]

Solving the given question:

We know that the formula for Margin of error is:

Margin of error = z-score * (standard deviation) / root (sample size)

E = z * σ / √(n), where

E = Margin of error

z = z-score

n = Sample size

σ = standard deviation

Therefore, sample size = ( z – score * standard deviation / margin of error)²

n = ( z * σ / E )²

First, calculate the z-score for the 99% confidence level.

From the normal distribution curve, the area under 99% confidence level is given as:

Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995

From the z-score table, we find the value of z with the corresponding area of 0.995

We find the value of the z-score corresponding to 0.995 is 2.58

Also given sample mean is one unit of the population. So the margin of error is 1

E = 1

And given Standard deviation = 13.8

σ = 13.8

Putting the values in the given formula of sample size n =

n = (2.58 * 13.8 / 1 )²

n = 1267.64

n = 1268

Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )

Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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