Which logarithm bases can you use to solve for x in the exponential equation 4^3+x=25 ? (Select all that apply.) the plus x is part of the exponent.
log base 25
log base 4
log base x
log base 10

Answer:

Therefore, the value of the unknown base is n = 16.

Step-by-step explanation:

Using the definition of logarithms, we have:

log_n(1/4) = -1/2

This equation can be rewritten as:

n^(-1/2) = 1/4

To solve for n, we can raise both sides to the -2 power:

n^(-1/2)^(-2) = (1/4)^(-2)

n = 16

Therefore, the value of the unknown base is n = 16.

A petition is just a formal request outlining the grounds for requesting a court order. It is often the first stage of a lawsuit and can be filed by an individual, a group, or an institution.

A petition is a formal letter or written request asking someone or an organization to take a certain action or make a certain change.

The petition is typically signed by a number of people who agree with the subject or problem being raised.

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In this case, Sarah has paid a total of $595 for her membership and Cheyenne has paid a total of $605 for her membership. This is because Sarah's gym had a $45 sign up fee and cost $50 per month, while Cheyenne's gym cost $55 a month with no sign up fees.

Membership is a type of relationship between a person and an organization or group. It implies that the person has certain responsibilities and privileges as a member of the group. Depending on the organization or group, these responsibilities and privileges might include attending meetings, paying dues or fees, voting privileges, access to services and discounts, or having the right to hold office.

Cheyenne's gym is more expensive due to its lack of a sign up fee and the higher monthly rate of $55. However, Sarah has paid more money overall due to her sign up fee. Even though Cheyenne's gym is more expensive on a month-to-month basis, the sign up fee makes Sarah's total cost higher.

The difference in cost between Sarah and Cheyenne's memberships is not substantial, but it is worth noting that the sign up fee can make a difference in the overall cost of a membership. It is also important to factor in the cost of any additional fees when comparing gym memberships. This can help someone determine which gym membership is a better value for their money.

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Area of a triangle is 88.37cm²

The area of a triangle is given by the formula:

[tex]Area = \frac{(base * height)}{2}[/tex]

where "base" refers to the length of the base of the triangle, and "height" refers to the height of the triangle measured perpendicularly from the base to the highest point of the triangle.

As per figure we have to find out the area of triangle, first we have to find out the height of triangle,

by using sine rule:

Sin 67° = [tex]\frac{height}{12 cm}[/tex]

height = 12 Sin 67°       (Here, Sin 67° = 0.92)

height = 12 × 0.92

height = 11.046cm

[tex]Area = \frac{(base * height)}{2}[/tex]

[tex]Area = \frac{(16 X 11.046)}{2}[/tex]

[tex]Area = 88.37cm^{2}[/tex]

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

44

Answer:

Step-by-step explanation:

Let [tex]c[/tex] be the total cookies.

[tex]\frac{1}{2}c+12+10=c[/tex]

[tex]\frac{1}{2}c+22=c[/tex]

[tex]c+44=2c[/tex]     (multiplied both sides by 2)

[tex]44=c[/tex]             (subtracted c from both sides)

[tex]c=44[/tex]

She began with 44 cookies.

No matter how many miles are travelled, only the standard rental fee of equation $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

The following equation is used to calculate the overall cost of renting a car:

C(x) = 0.20x + 64

where x is the amount of miles driven and C(x) is the rental car's total cost.

No matter how many miles are travelled, only the standard rental fee of $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.

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The area after dilation with a scale factor of 2 will be 56 sq feet.

When a figure is dilated with a scale factor of 2, the area of the figure is multiplied by the square of the scale factor.

So, if the original area is 14 sq feet, then the new area after dilation will be:

New area = Original area x (scale factor)^2

= 14 x 2^2

= 14 x 4

= 56 sq feet.

Therefore, the new area of the figure after dilation with a scale factor of 2 is 56 sq feet.

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The answer of the given question based on finding the area of the triangle the answer is  the area of the given triangle is 15 square units.

A triangle is three-sided polygon, which means it is closed shape with three straight sides and three angles. Triangles are some of  most basic shapes in geometry and can be found in the many different contexts, from simple constructions to complex mathematical models.

To find the area of the triangle, we can use the formula A = (1/2)bh, where A is the area, b is the base, and h is the height.

Looking at the given triangle, we can see that the base is the line segment from (0, 0) to (6, 0), which has a length of 6 units.

The third vertex of the triangle appears to be at the point (2, 5), so we need to find the distance from this point to the base.

The equation of the base is y = 0, so the distance from the point (2, 5) to the base is:

d = |0(2) - 1(5) + 0| / sqrt(0² + 1²) = 5 / 1 = 5 units

Therefore, the height of the triangle is 5 units.

Now we can use the formula A = (1/2)bh to find the area:

A = (1/2)(6)(5) = 15 square units

Therefore, the area of the given triangle is 15 square units.

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Answer: The linear equation in slope-intercept form that models this situation is:

y = 37x + 85

In this equation, the variable x represents the time spent repairing the vehicle in hours.

The variable y represents the total cost of the repair in dollars.

Step-by-step explanation:

The value of the given expression is -60. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," are said to be able to describe all real numbers. The four mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given two functions as f(x) = [tex]\frac{2x}{3}[/tex] + 7 and g(x) = 2x + 15

So,

⇒f (0) = [tex]\frac{0}{3}[/tex] + 7

⇒f (0) = 7

Similarly,

⇒g (-8) = 2 (-8) + 15

⇒g (-8) = -16 + 15

⇒g (-8) = -1

Now, on substituting these in the expression, we get

⇒-8 * f (0) + 4 * g (-8)

⇒-8 * 7 + 4 * (-1)

Now using the arithmetic operations, we get

⇒-56 -4

⇒-60

Hence, the value of the given expression is -60.

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Question:

If the following equations represent the functions f(x) and g(x).

f(x) = 2/3x + 7 and g(x) = 2x + 15

Calculate the value of -8 * f(0) + 4 * g(-8)

Option (a) is correct i.e., the margin of error is equal to ± 0.8 and the confidence interval is equal to 10.5

In a random survey sample,  a “margin of error” is a measurement (calculation) that takes into consideration the difference between actual and sample data findings.

Let μ be the unknown population mean. To determine the ‘population mean’ we use the sample mean as a point estimate (approximate) μ.

The “margin of error” determines how far the actual population value will likely be from the survey's value. It evaluates the accuracy (precisely) of a survey's results. The survey's results are more likely to be accurate (precise) values if the “margin of error” is less.

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Complete question:

After a set of surveys was compiled and analysed , the mean value was reported as 10.5 ± 0.8 . Select the true statement for this data

a) The margin of error is equal to ± 0.8 and the confidence interval is equal to 10.5.

b) The estimate is equal to 10.5 and the margin of the error is equal to

± 0.8.

c) The estimate is equal to 10.5 and the confidence interval is equal to

± 0.8.

d) The margin of error is  equal to 10.5 and the estimate is equal to ± 0.8.

Answer:

The estimate is equal to 10.5 and the margin of error is equal to ± 0.8.

Answer:

A) True

Step-by-step explanation:

The statement is true. Conditional probability is a fundamental concept in probability theory that allows us to calculate the probability of an event given that another event has already occurred. The notation for conditional probability is P(B|A), which represents the probability of event B occurring given that event A has already occurred. In other words, we restrict our attention to the sample space where event A has occurred and calculate the probability of event B in that space.

Therefore , the solution of the given problem of triangle comes out to be a length measures about 5.64 units in length.

If a polygon has more than one extra sections, it is a hexagon. It has a straightforward square form. Something like this configuration can only be distinguished from a conventional triangle by the sides A and B. The borders continue to be precisely collinear, but Euclidean geometry only yields a section rather than the entire cube. A triangular has three sides and three angles.

Here,

Let's determine the length of side b using the sine function:

opposite/hypotenuse of sin(A)

=> b/9 sin(50) = 9*sin(50) b = 7.021

Side B is therefore roughly 7.021 units long.

We can use the knowledge that the sum of the angles in a triangle is 180 degrees to determine the size of angle B:

=> angle B = 180 - angle A - 90

=>  angle B = 180 - 50 - 90

=>  angle B = 40 degrees

B's angle therefore has a 40 degree value.

The Pythagorean formula can also be used to determine the length of side a:

The equation is:

=> a² + b² = c²

=> a² + 7.021² = 9²

=> a² + 49.24 = 81

=> a² = 31.76

=> a ≈ 5.64

Side a therefore measures about 5.64 units in length.

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Answer: To calculate the real value of your savings after inflation, you need to adjust your savings for the increase in the price level. Here's how to do it:

Calculate the amount of inflation:

Inflation rate = (New price level index - Old price level index) / Old price level index

In this case, the old price level index is 100, and the new price level index is 109 (100 + 9%). So:

Inflation rate = (109 - 100) / 100 = 0.09

Adjust your savings for inflation:

Real value of savings = Nominal value of savings / (1 + inflation rate)

In this case:

Real value of savings = 8,295 / (1 + 0.09) = 7,614.22

Therefore, the real value of your savings after inflation is $7,614.22.

Step-by-step explanation:

Therefore, the missing side length is 162 when triangle ABC and XYZ are similar.

A triangle is a closed two-dimensional plane figure with three straight sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points with line segments. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angle measures, and they have important properties and applications in various fields, including mathematics, science, engineering, and art.

Here,

Since triangles ABC and XYZ are similar, their corresponding sides are in proportion. We can set up the following proportion using the given side lengths:

AC/XY = BC/YZ

Substituting the given values, we get:

2/54 = 6/x

Cross-multiplying, we get:

2x = 54 × 6

2x = 324

Dividing both sides by 2, we get:

x = 162 units

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Answer:

The given differential equation is:

2dv/dt = -kv

where k is a constant.

a) To find the general solution to this differential equation, we can use separation of variables.

2dv/v = -k dt

Integrating both sides, we get:

2ln|v| = -kt + C1

where C1 is the constant of integration.

Taking exponential of both sides, we get:

|v|^2 = e^(C1) e^(-kt)

Since v can be either positive or negative, we can simplify the above equation as:

v = ±√(Ae^(-kt))

where A = e^(C1).

Therefore, the general solution to the given differential equation is:

v(t) = ±√(Ae^(-kt))

b) We are given that the initial velocity is 40 m/s and after 2 seconds, the velocity has decreased to 30 m/s. Let's use this information to find the value of A.

When t = 0, v = 40. Therefore,

40 = ±√(Ae^0)

40^2 = A

A = 1600

Now we can use the value of A to find the velocity after 10 seconds.

v(10) = ±√(1600e^(-10k))

We can use the information that the velocity has decreased to 30 m/s after 2 seconds to find the value of k.

30 = ±√(1600e^(-2k))

900 = 1600e^(-2k)

e^(-2k) = 0.5625

-2k = ln(0.5625)

k = -0.5 ln(0.5625)

Now we can substitute this value of k into the expression for v(10) to get:

v(10) = ±√(1600e^(5ln(0.5625)))

v(10) = ±√(1600(0.5625)^5)

v(10) = ±20.11 m/s

Therefore, the velocity of the object after ten seconds will be approximately 20.11 m/s.

Therefore , the solution of the given problem of unitary method comes out to be 25 vehicles had precisely two of the available options.

By multiplying the data obtained with such a nanosection variable whilst also two that used the unilateral strategy, the job can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set or the colour space of both production runs is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.

Here,

We can apply the inclusion-exclusion concept to resolve this issue. To begin, let's draw a Venn diagram to symbolise the supplied data:

where A is the proportion of vehicles with air conditioning, B is the proportion of vehicles with automatic gearbox, and C is the proportion of vehicles with power steering.

The information provided lets us know:

=> A = 87 + 8 + 24 = 119

=> B = 99 + 8 + 9 = 116

=> C = 73 + 8 + 9 = 90

=> A ∩ B ∩ C = 8

=> A ∩ B ∩ C' = 24 - 8 = 16

=> A ∩ B' ∩ C = 9

=> A ∩ B' ∩ C' = 64 - 9 - 8 - 16 = 31

=> A' ∩ B ∩ C = 0

=> A' ∩ B ∩ C' = 35 - 9 - 8 - 16 = 2

=> A' ∩ B' ∩ C = 0

=>  A' ∩ B' ∩ C' = 24 - 8 - 16 - 2 = -2

Since there cannot be fewer than 0 cars without any extras, this number must be negative.

=> (A ∩ B' ∩ C) + (A ∩ B ∩ C') + (A' ∩ B ∩ C) = 9 + 16 + 0 = 25

As a result, 25 vehicles had precisely two of the available options. There may have been a mistake in the problem or the answer alternatives since the correct response is not one of the available choices.

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Answer:

Since ΔQPT ≅ ΔARZ, we know that their corresponding angles are congruent.

Step-by-step explanation:

The congruent angle pair is:

C) ∠T ≅ ∠Z.

Note that ∠Q and ∠R are not necessarily congruent to each other, ∠P and ∠A are not necessarily congruent to each other, and ∠P and ∠Z are not necessarily congruent to each other.

An equation of the line in slope-intercept form drawn on the graph is y = 3x/2 + 8.

In Mathematics and Geometry, the point-slope form of any straight line can be determined by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the slope;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (20 - 8)/(8 - 0)

Slope (m) = 12/8

Slope (m) = 3/2

At data point (0, 8) and a slope of 3/2, a linear equation for this line can be determined by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 8 = 3/2(x - 0)  

y = 3x/2 + 8

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The expected value of the proposition is $18.23.

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain to occur.

Given by the question.

Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

The probability of drawing a card with a value of five or less is:

4 cards with a value of 2 + 4 cards with a value of 3 + 4 cards with a value of 4 + 4 cards with a value of 5 + 4 aces = 20/52 = 5/13

The probability of not drawing a card with a value of five or less is:

1 - 5/13 = 8/13

The expected value of the proposition can be calculated as follows:

Expected value = (probability of winning * amount won) + (probability of losing * amount lost)

Expected value = (5/13 * $49) + (8/13 * (-$25))

Expected value = $18.23 (rounded to two decimal places)

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The equation for the shifted graph is y = x + 6.This equation represents the same line as the original equation, y = x + 1, but shifted up by 5 units.

Shifting a graph involves moving it horizontally or vertically while maintaining the same shape and orientation.

To shift the graph of y = x + 1 up by 5 units, you need to add 5 to the y-coordinate of every point on the graph.

The original graph of y = x + 1 is a straight line with slope 1 and y-intercept 1.

To create the shifted graph, you can start by plotting a few points on the original graph and then adding 5 to their y-coordinates to get the corresponding points on the shifted graph.

Alternatively, you can use the general equation for a straight line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation for the shifted graph.

The slope of the original graph is 1, so the slope of the shifted graph is also 1.

To find the y-intercept of the shifted graph, you can plug in x = 0 and y = 6 (since you want the graph to pass through the point (0, 6)) and solve for b:

6 = 1(0) + b

b = 6

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Answer:

Toyin weighs 50 kg, which is 20 kg more than Amara.

Step-by-step explanation:

If Amara weighs 30 kg and the ratio of the weight of Amara to the weight of Toyin is 3:5, then we can set up a proportion:

3/5 = 30/x

where x is the weight of Toyin in kg.

To solve for x, we can cross-multiply:

3x = 150

x = 50

Therefore, Toyin weighs 50 kg, which is 20 kg more than Amara.

Answer:

Since wave heights at Folly Beach are normally distributed with a mean of 4 feet and a standard deviation of 1.5 feet, we can use the normal distribution formula to find the probability of a wave having a height of exactly 3 feet.

The formula for the normal distribution is:

P(x) = (1 / (σ * sqrt(2π))) * e^(-(x - μ)^2 / (2 * σ^2))

where:

P(x) is the probability density function

σ is the standard deviation

μ is the mean

e is the base of the natural logarithm

x is the value of the variable

Substituting the values given in the problem, we get:

P(3) = (1 / (1.5 * sqrt(2π))) * e^(-(3 - 4)^2 / (2 * 1.5^2))

P(3) = 0.176

Therefore, the probability that a wave has a height of exactly 3 feet is 0.176 or approximately 17.6%.

Answer: (4,-2)

Explanation: (I was forced to put one)

The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

Answer:

Counting the number of sign changes in the function f(x)

The number of positive roots is equal to the number of sign changes in the function f(x) or less than that by an even integer.

Here, f(x)=3x^4-5x^3-x^2 has two sign changes (from + to -, and from - to +), so the number of positive roots is either 2 or 0.

Counting the number of sign changes in the function f(-x)

The number of negative roots is equal to the number of sign changes in the function f(-x) or less than that by an even integer.

Here, f(-x)=3x^4+5x^3-x^2 has one sign change (from - to +), so the number of negative roots is either 1 or 0.

Counting the number of non-real roots (complex roots)

The number of non-real roots (complex roots) is equal to the difference between the total number of roots (4 in this case) and the number of real roots (which we found above).

Therefore, the possible number of positive roots is 2 or 0, the possible number of negative roots is 1 or 0, and the possible number of complex roots is 2 or 4.

Step-by-step explanation:

The square pyramid-shaped clock has a surface area of 144 square inches, including the base.

Surface area is the total area of the exposed surfaces of a 3-dimensional object, or an object with length, width and height. It is the sum of all of the areas of the faces of the object, including curved surfaces. It is measured in square units, such as square centimeters or square meters. Surface area is important in fields such as engineering and materials science, where it is used to calculate the amount of material needed for a given object.

To calculated to the total area, multiply by the length of the base, b, by the height, h. A = b × h is the equation- for to the area, A, of a square or rectangle area.

Surface area and arc length of curves differ in a number of ways, one of which is that surface area cannot simply be defined as the maximum area of polyhedral shapes that approximate a given smooth surface.

Since each of the triangle has one side as 9,

if we split it down to the middle and should rearrange it,

we get a 3×9 rectangle

that is = 27 inches

there are 4 of for those = 4x27 = 108.

the square in the middle is = 36 inches

36+108= 144

144 square inches

The surface area of the clock is 144 square inches.

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Answer:

Step-by-step explanation: 0.3375 by simple algebra.