The equation 1- 4/3 x = 1/2 (-x+7) has what type of solution set

Answer:

yes

Step-by-step explanation:

2 bases 3 rectangles, folds properly.

Answer:

When solving the literal equation rx = sx + t for x, are there any restrictions? There are no restrictions.

Step-by-step explanation:

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The quantity of energy moved or transformed per unit of time is referred to as power. The amount of energy that is consumed by the hairdryer in 15 minutes will be 0.3 kWh.

The quantity of energy moved or transformed per unit of time is referred to as power.

Formula: Power = Energy / Time

Units: kW = kWh / hour

The power of electric equipment is given by the formula,

P = E/t

where E is the energy consumed in kWh and t is the time in hours.

Given the power of the hairdryer is 1.200 kW while the time for which it is kept on is 15 minutes, therefore, 0.25 hours. Now, the energy consumed by the dryer in 15 minutes will be,

1.200 kW = E / 0.25

0.3 kWh = E

Hence, the amount of energy that is consumed by the hairdryer in 15 minutes will be 0.3 kWh.

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A system of equations to have no real solution, the lines of the equations must be parallel to each other. There were 10 multiple choice question, while 15 descriptive type questions.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

Let the number of multiple choice questions be represented by x, while the number of descriptive questions be represented by y. Therefore, the total questions can be written as,

x + y = 25

Solving for x,

y = 25 - x

The total score of Ronald can be written as,

3x + 8y = 150

3x + 200 - 8x = 150

-5x = -50

x = 10

Substitute the value of x in any one of the equation,

x + y = 25

10 + y = 25

y = 15

Hence, there were 10 multiple choice question, while 15 descriptive type questions.

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To construct a stem and leaf plot, you first need to separate each data point into a stem and a leaf. The stem represents the leading digit(s) of the data point, while the leaf represents the trailing digit(s).

Once you have organized the data in this way, you can create the plot. The stems are listed vertically, and the leaves are placed horizontally next to their corresponding stems. Make sure to arrange the leaves in ascending order.

Regarding how the stem and leaf plot suggests the sample mean and median will compare, we can look at the distribution of the data. If the leaves are evenly distributed across the stems, it suggests a symmetrical distribution. In this case, the sample mean and median will be similar.

However, if the leaves are concentrated in certain stems, it suggests an asymmetrical distribution. In this scenario, the sample mean and median may differ. The median tends to be less affected by extreme values, while the mean can be influenced by outliers.

Therefore, by examining the stem and leaf plot, you can get a sense of whether the sample mean and median will be similar or different based on the distribution of the data.

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Answer:yes

Step-by-step explanation:Bc I am right and right

Answer:

∠Q = 35.5°

Step-by-step explanation:

We are given;

q = 6.5 inches

o = 8.6 inches

∠P = 55°

Let's first use cosine rule to find p.

p² = q² + o² - 2qo cos P

Plugging in the relevant values;

p² = 6.5² + 8.6² - (2 × 6.5 × 8.6 × cos 55)

p² = 42.25 + 73.96 - 32.0629

p² = 84.1471

p = √84.1471

p = 9.17 inches

Using sine rule, we can find ∠Q;

p/sin P = q/sin Q

sin Q = (q•sinP)/p

sin Q = (6.5 × sin 55)/9.17

sin Q = 0.5806

Q = sin^(-1) 0.5806

Q ≈ 35.5°

Answer:

47.5  

Step-by-step explanation:

From delta math

Answer:

width = 14 feet

Step-by-step explanation:

the 7 part of the ratio relates to the length of the garden , then

24.5 feet ÷ 7 = 3.5 feet ← value of one part of the ratio , so

width = 4 × 3.5 feet = 14 feet

Step-by-step explanation:

Apply rule: 3x+3x =-1

Add similar elements: 6x=-1

Divide both sides by six

Simplify: x= -1/6

To determine the type and number of triangles based on the given measures, we can use the triangle inequality theorem and the properties of angles in triangles.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, we have the measures of angles C, b, and c as 59, 67, and 58 respectively.

To determine the type of triangle, we need to check the relationship between these angles:

Now, let's analyze the given measures:

Based on the measures of the angles, we can conclude that the triangle is acute.

Therefore, the correct answer is B - 1 acute triangle.

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The rate of change here represents the time in seconds it takes her to perform a certain number of skills task

The rate of change is defined as the rate at which one quantity is changing with respect to another quantity. Mathematically:

rate of change = change in y /  change in x

Given that: The x-coordinate is the skills task number and the y-coordinate is the time in seconds

Thus, rate of change = time in seconds / skills task number  

Therefore, the rate of change in this context represents the time in seconds it takes  to perform a certain number of skills task

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The null hypothesis is that the mean speed of the cable Internet connection is equal to or less than three Megabits per second (H0: μ ≤ 3). The alternative hypothesis is that the mean speed is greater than three Megabits per second (Ha: μ > 3).

Based on the terms provided and the context of the question, we can establish the null and alternative hypotheses as follows:

1. Null Hypothesis (H0): The mean speed (µ) of your cable Internet connection is equal to 3 Megabits per second. Mathematically, this is expressed as H0: µ = 3.

2. Alternative Hypothesis (H1): The mean speed (µ) of your cable Internet connection is greater than 3 Megabits per second. Mathematically, this is expressed as H1: µ > 3.

The alternative hypothesis is that the mean speed is greater than three Megabits per second (Ha: μ > 3).

To summarize, your null hypothesis (H0) states that the mean speed of your Internet connection is 3 Megabits per second, while your alternative hypothesis (H1) states that the mean speed is greater than 3 Megabits per second.

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Dan used a total of 5 17/24 gallons of gas on Saturday and Sunday combined.

To find the total number of gallons Dan used on Saturday and Sunday, we shall add the amount of gas he used each day.

On Saturday, Dan used 1 3/8 gallons.

On Sunday, Dan used 4 1/3 gallons.

To add these two amounts, we shall find a common denominator by determining the least common multiple (LCM) of 8 and 3 is 24.

Converting 1 3/8 to an improper fraction:

1 3/8 = (8 * 1 + 3) / 8 = 11/8

Converting 4 1/3 to an improper fraction:

4 1/3 = (3 * 4 + 1) / 3 = 13/3

Now we can add the fractions using a common denominator, which is 24 in this case:

Let's convert both fractions:

11/8 = (11 * 3) / (8 * 3) = 33/24

13/3 = (13 * 8) / (3 * 8) = 104/24

Now we can add the fractions:

33/24 + 104/24 = (33 + 104) / 24 = 137/24

So, simplifying the fraction, we have:

137/24 = 5 (remainder 17)

5 17/24 gallons.

Hence, Dan used a total of 5 17/24 gallons of gas on Saturday and Sunday combined.

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Answer:

B

Step-by-step explanation:

The distance between the cars changes by 60.42mph.

Distance is a measurement of how far apart two objects or locations are. Distance in physics or common language can refer to a physical length or an assumption based on other factors. |AB| is a symbol that can be used to represent the distance between two points. "Distance from A to B" and "Distance from B to A" are frequently used interchangeably. A distance function or metric is a technique to describe what it means for elements of some space to be "close to" or "far away" from each other in mathematics. It is a generalization of the idea of physical distance. Through dimensions like time, space, and isolation, an object may be psychologically distanced from itself.

Calculations:

\(d=\sqrt{80^{2}+50^{2} } \\\)

d=94.34

1st car -- 40mph/hr

2nd car-- 50 mph/hr

The positions of cars at 4pm

Distance travelled by 1st car = 80m

Distance travelled by 2nd car = 50m

\(d^{2}=a^{2} +b^{2}\)

2d.dd/dt=2a(da/dt) +2b(db/dt) =d(dd/dt) =a(da/dt)+b(db/dt)=94.34(dd/dt)=50*50+80*40

dd/dt=(2500+3200)(94.34)  =60.419

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Answer:

The volume of a box is:

V = 560 cubic inches or  \(20\frac{20}{27}\)  cubic inches.

Step-by-step explanation:

Given

The width of a box = w = 2 2/3 inches

i.e. \(\:w=2\frac{2}{3}=\frac{8}{3}\)

The length of a box = l = 3 1/3 inches

i.e. \(l=\:3\frac{1}{3}=\frac{10}{3}\)

The height of a box = h = 2 1/3 inches

i.e. \(\:h=2\frac{1}{3}=\frac{7}{3}\)

Using the formula to determine the volume of a box

\(V=w\times l\times h\)

substitute  \(\:w=2\frac{2}{3}=\frac{8}{3}\),   \(l=\:3\frac{1}{3}=\frac{10}{3}\)  and  \(\:h=2\frac{1}{3}=\frac{7}{3}\),  

\(V=\frac{8}{3}\times \frac{10}{3}\times \frac{7}{3}\)

Apply the fraction rule:  \(\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

   \(=\frac{8\times \:10\times \:7}{3\times \:3\times \:3}\)

   \(=\frac{560}{27}\)   or   \(20\frac{20}{27}\)  cubic inches

Therefore, the volume of a box is:

V = 560 cubic inches or  \(20\frac{20}{27}\)  cubic inches.

The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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Store C offers the best deal

Based on the lowest cost per minute, Store C has the best deal. It charges $45 for a 1.5 hour lesson, which works out to $0.30 per minute. The other stores charge more per minute: Store A charges $0.56 per minute, Store B charges $0.50 per minute, and Store D charges $0.40 per minute for each of the three 1 hour lessons.

Store A has the highest cost that is $0.56 per minute

Next Store B comes in the 2nd place which costs around $0.50 per minute.

After that Store D charges at the rate of $0.40 per minute.

Store C offers the best deal which is $0.30 per minute.

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Answer:

yep

Step-by-step explanation:

what should we do?

11x+6=12x-4

6-4=12x-11x

therefore x=2

simple

Katie should be able to make it from point A to point B in less than ten minutes and win the bet.

A minute is a unit of time equal to 60 seconds or one sixtieth of an hour. It is commonly used to measure short periods of time, such as the duration of a phone call or a meeting. The symbol for minute is "min".

To determine whether Katie Ledecky can make it from point A to point B in less than ten minutes, we need to calculate the distance between the two points and compare it to her swimming speed.

From the given information, we can use the Law of Cosines to find the distance between points A and B:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

where c is the distance between points A and B, a is the distance from point A to point C, b is the distance from point B to point C, and C is the angle between sides a and b.

Plugging in the given values, we get:

\(c^2 = 620^2 + 455^2 - 2(620)(455) cos(150°)\\\\c^2 = 383,825\)

c ≈ 619.5 yards

So the distance between points A and B is approximately 619.5 yards.

Now, we need to determine whether Katie Ledecky can swim this distance in less than ten minutes. We are given that she swam 1,000 yards in 8 minutes and 59.65 seconds, which is approximately 8.99 minutes. So her average speed for the 1,000 yard freestyle was:

speed = distance / time

speed = 1,000 yards / 8.99 minutes

speed ≈ 111.23 yards/minute

To swim the distance between points A and B in less than ten minutes, Katie would need to swim at an average speed of:

speed = distance / time

speed = 619.5 yards / 10 minutes

speed = 61.95 yards/minute

Katie's Olympic level swimming speed of 111.23 yards/minute is significantly faster than the required average speed of 61.95 yards/minute to swim from point A to point B in under ten minutes. Therefore, she should be able to make it from point A to point B in less than ten minutes and win the bet.

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If a does not divide bc, then a does not divide b because a is not a factor of the product bc.

When we say that a does not divide bc, it means that the product of b and c cannot be expressed as a multiple of a. In other words, there is no integer k such that bc = ak. Suppose a divides b, which means there exists an integer m such that b = am.

If we substitute this value of b in the expression bc = ak, we get (am)c = ak. By rearranging this equation, we have a(mc) = ak. Since mc and k are integers, their product mc is also an integer. Therefore, we can conclude that a divides bc, which contradicts the given statement. Hence, if a does not divide bc, it logically follows that a does not divide b.

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(a) The partial derivative of the utility function with respect to x_2 is:
∂U/∂x_2 = -(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

(b) The expression is MRS = αρx_1^(-ρ) / (1-α)ρx_2^(-ρ)

(c) the preferences represented by this function are homothetic.

(a) To find the marginal utility of both goods, we need to take the partial derivatives of the utility function with respect to each good.

The partial derivative of the utility function with respect to x_1 is:
∂U/∂x_1 = -αρx_1^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

Similarly, the partial derivative of the utility function with respect to x_2 is:
∂U/∂x_2 = -(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

(b) The Marginal Rate of Substitution (MRS) represents the rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility.

In this case, the MRS is the negative ratio of the partial derivatives of the utility function:
MRS = -∂U/∂x_1 / ∂U/∂x_2

= (-αρx_1^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)) / (-(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1))

Simplifying the expression, we get:
MRS = αρx_1^(-ρ) / (1-α)ρx_2^(-ρ)

(c) Homothetic preferences mean that the consumer's preferences do not change with changes in their income.

To determine whether the preferences represented by this function are homothetic, we need to check whether the MRS depends on the ratio of x_1 to x_2 or on the levels of x_1 and x_2 individually.

By looking at the expression for MRS, we can see that it depends on the ratio of x_1 to x_2 (x_1/x_2), not on their individual levels.

Therefore, the preferences represented by this function are homothetic.

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Answer:

5

Step-by-step explanation:

In the case when we multiplied 0.014 by 100,000 so it comes

= 0.014 × 100,000

= 1,400

Since The value 0.014 were times by 5 zeros.

Therefore the decimal point would move 5 places to the right

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

\( \frac{909}{10000} \)

Step-by-step explanation: