The type of galaxy matched to its description.
Elliptical galaxy: B) Forms a perfect sphere or an ellipse and is flattened to some degree
Galaxy: D) Is a collection of several billion stars and interstellar matter isolated in space
Lens galaxy: A) Has a large flattened core
Spiral galaxy: C) Has a central core from which curved arms spiral outward
Elliptical galaxy: An elliptical galaxy is a type of galaxy that typically forms a perfect sphere or an ellipse shape. It is characterized by its smooth and featureless appearance, lacking the distinct spiral arms seen in spiral galaxies. Elliptical galaxies often have a flattened shape due to their rotation and gravitational interactions with other galaxies.
Galaxy: A galaxy refers to a vast collection of stars, interstellar gas, dust, and dark matter, all held together by gravity. Galaxies come in various shapes and sizes, and they can contain billions or even trillions of stars. They are the building blocks of the universe and are distributed throughout the cosmos.
Lens galaxy: A lens galaxy is a type of galaxy that has a large flattened core. It gets its name from the gravitational lensing effect it produces. Gravitational lensing occurs when the gravitational field of the lens galaxy bends and distorts the light from objects behind it, creating a lens-like effect.
Spiral galaxy: A spiral galaxy is a type of galaxy that has a central core or bulge from which curved arms spiral outward. These arms are made up of stars, gas, and dust, and they give spiral galaxies their distinct appearance. Spiral galaxies often have a flattened disk shape with a central bulge and extended arms that can stretch out across the disk.
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17 Question Evaluate y=−4(5)x y = − 4 ( 5 ) x for x
The equation y=−4(5)x y = − 4 ( 5 ) x can be simplified to y = -20x. This equation is a linear function with a slope of -20. As x increases, y decreases at a rate of 20 units for every one unit increase in x. Therefore, the value of y will decrease rapidly as x increases.
Is Y= 4x^3+6....
A. Linear
B. Nonlinear
C. Both
D. Neither
Answer:
The given equation Y=4x^3+6 is a nonlinear equation because it contains a term with a power of 3, which means that the relationship between Y and x is not linear. In a linear equation, the power of the variable is always 1. Therefore, the answer is B. Nonlinear.
Step-by-step explanation:
Josh lit a 14-inch candle. She noticed that it was getting an inch shorter every 30 minutes. Let x be the number of hours and y be the total height of the candle
The height of the candle after x hours is given by the equation y = 2x + 14.
Let's first convert the time interval to hours. There are 60 minutes in an hour, so 30 minutes is equivalent to 0.5 hours.
After x hours, the candle will have burned down by 2x inches (since it burns 1 inch every 0.5 hours).
If y is the total height of the candle, then we can write the equation:
y - 2x = 14
We can solve for y:
y = 2x + 14
So the height of the candle after x hours is given by the equation y = 2x + 14.
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the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?
The numbers chocolate chip cookie would be assigned to the group is equals to the 40 belongs to 60-100. So, right choice is option(a).
We have a data values for a random number ranges within 1 to 100 need to be assigned for each event.
Probability for the chocolate cookies purchased for a fundraiser = 0.40
Probability for the butter cookies purchased for a fundraiser = 0.15
Probability for the peanuts butter cookies purchased for a fundraiser = 0.15
Probability for the lemon cookies purchased for a fundraiser = 0.30
The number would be assigned to the chocolate chip cookie group = 0.40× 100
= 40%
The difference between 60-100 is 40.
Hence, required number is 60-100.
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Complete question:
The above figure complete the question.
the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?
a) 60-100
b) 71-100
c) 20-100
the asq (american society for quality) regularly conducts a salary survey of its membership, primarily quality management professionals. based on the most recently published mean and standard deviation, a quality control specialist calculated the z-score associated with his own salary and found it was -2.50. this tells him that his salary is
This tells him that his salary is significantly below the average salary of quality management professionals surveyed by the ASQ, and that he is in the bottom percentile of salaries in this group.
The z-score is a statistical measure that indicates the number of standard deviations that a data point is from the mean of a distribution. A negative z-score indicates that the data point is below the mean.
In this case, the quality control specialist's z-score of -2.50 indicates that his salary is 2.50 standard deviations below the mean salary of the quality management professionals surveyed by the ASQ.
Without knowing the specific mean and standard deviation provided by the survey, it is difficult to determine the exact value of the specialist's salary. However, we can use the z-score to estimate the percentile rank of his salary compared to the rest of the survey respondents.
Using a standard normal distribution table, we can see that a z-score of -2.50 corresponds to a percentile rank of approximately 0.0062 or 0.62%. This means that only about 0.62% of quality management professionals surveyed by the ASQ earn a salary lower than that of the quality control specialist.
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what is 7 + 9d = 7d +3?
Answer:
-2
Step-by-step explanation:
7+9d=7d+3
7+2d=3
2d=-4
d=-2
I NEED HELP WITH THIS ONE AND ANOTHER PLEASE
The missing lengths of BE and IJ using the concept of similar quadrilaterals are:
BE = 32
IJ = 18
How to find the lengths of similar quadrilaterals?Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.
Thus:
GJ/BE = IJ/DE = HI/CD
Thus:
12/BE = 6/16
BE = (16 * 12)/6
BE = 32
Similarly:
IJ/48 = 6/16
IJ = (48 * 6)/16
IJ = 18
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How go i get the probability
The probability that we want to get is 0.167
How to find the probability?To get this probability, we need to take the quotient between the number of students that preffers athletics and literature and the total number of students in the table.
We have:
Total number = 5 + 3 + 2 +8 = 18
number that preffers athletics and literature = 3
Then the probability is:
P = 3/18 = 0.167
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Marcia drew a plan for a rectangular piece of material that she will use for a blanket. Three of the vertices are (-1.3, -3.5), (-1.3, 1.4), and (3.9,1.4) . What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex is (3.9, 6.3,0).To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
We can find the length and slope of one side of the rectangle and then use that information to find the coordinates of the fourth vertex.
Let's start by finding the length and slope of the side connecting (-1.3, -3.5) and (-1.3, 1.4). The length of this side is the difference between the y-coordinates, which is:
1.4 - (-3.5) = 4.9
Since this side is vertical, its slope is undefined.
Next, let's find the length and slope of the side connecting (-1.3, 1.4) and (3.9, 1.4). The length of this side is the difference between the x-coordinates, which is:
3.9 - (-1.3) = 5.2
Since this side is horizontal, its slope is 0.
Since opposite sides of a rectangle are equal in length, the length of the side connecting (-1.3, 1.4) and (3.9, 1.4) must also be 4.9. We can use this length to find the y-coordinate of the fourth vertex, which is:
1.4 + 4.9 = 6.3
Now we know that the fourth vertex has coordinates (x, 6.3). To find the x-coordinate, we can use the length of the vertical side connecting (-1.3, -3.5) and (-1.3, 1.4), which is also 5.2. The x-coordinate of the fourth vertex is:
-1.3 + 5.2 = 3.9
Therefore, the coordinates of the fourth vertex are (3.9, 6.3,0).
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naproxen 375 mg PO daily. If each scored tablet contains 250 mg,
how many tablets will you administer?
To administer a daily dose of 375 mg of naproxen using 250 mg scored tablets, the patient would need to take 1.5 tablets, rounded up to 2 tablets of 250 mg each.
To administer 375 mg of naproxen using 250 mg scored tablets, we need to divide 375 by 250 to determine how many tablets to administer.
375 mg / 250 mg per tablet = 1.5 tablets
Therefore, the dosage of 375 mg of naproxen would require 1.5 tablets.
Since tablets cannot be divided into halves, the patient would need to take 2 tablets of 250 mg each to achieve the prescribed dosage of 375 mg.
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Circle Q has a diameter AB. If the distinct point C is also on the circle then triangle ABC must be
If point C is on the circle with diameter AB, then triangle ABC must be a right triangle. This is because the diameter of a circle is the longest chord and it passes through the center of the circle.
If we draw a line from point C to the center of the circle (which is the midpoint of AB), we get a perpendicular bisector of AB, meaning that it cuts AB into two equal parts and forms right angles with it. This also means that AC and BC are equal in length (since they both form radii of the circle), and the angle at point C must be a right angle (since it forms a straight line with the center of the circle). Thus, triangle ABC satisfies the criteria for a right triangle.
In summary, if point C lies on the circle with diameter AB, then triangle ABC must be a right triangle with AC and BC as its legs and AB as its hypotenuse. This is a fundamental property of circles and right triangles, and it is important to understand in order to solve various geometry problems involving circles and triangles.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer:
Inga can use the following steps to solve the quadratic equation 2x^2 + 12x - 3 = 0:
Divide both sides by 2 to simplify the equation: x^2 + 6x - 3/2 = 0.Add 3/2 to both sides to eliminate the constant term on the left-hand side: x^2 + 6x = 3/2.Complete the square by adding (6/2)^2 = 9 to both sides: x^2 + 6x + 9 = 3/2 + 9.Factor the left-hand side as a perfect square: (x + 3)^2 = 27/2.Take the square root of both sides, remembering to include both the positive and negative square roots: x + 3 = ±√(27/2).Simplify the square root: √(27/2) = (√27/√2) = (3√3/√2).Subtract 3 from both sides: x = -3 ± (3√3/√2).Rationalize the denominator by multiplying the numerator and denominator of the second term by √2: x = -3 ± (3√6/2).Therefore, the steps that Inga could use to solve the quadratic equation are:
2(x^2 + 6x + 9) = -3 + 2(9) (Option 1)
2(x^2 + 6x) = 3 (Option 2)
x + 3 = ±√(27/2) (Option 3)
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Solve for x Trigonometry
The size of the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
For the given triangle;
sin X = 3/5 {opposite/hypotenuse}
X = sin⁻¹(3/5) {cross multiplication}
X = 36.8699°
Therefore, the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
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Keshia is working on a math worksheet with 50 problems she has completed 20 problems in 25 mins if she continue at this pace what will be her total time for her compete worksheet
It will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.
To find the amount of total time it will take Keshia to complete the entire worksheet at the same pace, we can use a proportion:
20 problems / 25 minutes = 50 problems / x minutes
To solve for x, we can cross-multiply and simplify:
20 problems * x minutes = 25 minutes * 50 problems
20x = 1250
x = 1250 / 20
x = 62.5
Therefore, it will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.
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Here is a list of statistical questions. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use.
What is a typical height of female athletes on a team in the most recent international sporting event?
Are most adults in the school football fans?
How long do drivers generally need to wait at a red light in Washington, DC
You can collect data on the heights of all female athletes on a team using recent international sporting event and This data can be gotten by using official event records or by carrying out a survey of the athletes. Heights are said to be measured in centimeters (cm) or feet and inches (ft, in).
Are most adults in the school football fans?To address this question, you can gather information regarding the quantity of school staff members who are passionate about football and compare it against the full count of school staff members. Gathering this information is possible through either conducting a survey or analyzing the number of tickets sold for school football games. The information can be shown using ratio or a percentage.
How long do drivers generally need to wait at a red light in Washington, DC
One can get information on the durations motorists must wait at various traffic signals in Washington, DC. One can ask this information by either installing sensors or cameras at different intersections or by gathering input from drivers through a survey. The duration of waiting periods is commonly quantified in units of seconds (s) or minutes (min).
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Part C
What does the absolute value of the correlation coefficient say about the predictions in part B? How do you know? Write
an explanation of about one to two sentences.
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The shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.
How to calculate the speed?The average speed of Luther's pitches when he throws 80 pitches will be:
y = -0.511x + 91.636
= -0.511(80) + 91.636
= 50.756
= 51
Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:
y = -0.511x + 91.638
64 = -0.511x + 91.638
0.511x = 91.638 - 64
0.511x = 27.636
x = 54
Therefore, the number of pitches will be 54.
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Answer:
Because the absolute value of the correlation coefficient, 0.9672, is very close to 1, Luther can be very confident in the predictions.
Step-by-step explanation: Edmentum Answer
A small country emits 103,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5% per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 103,000 kilotons and the emissions will decrease 5% in each successive year. How many kilotons of carbon dioxide would the country emit over the course of the 14 year period, ?
The total amount of carbon dioxide emitted over the 14-year period is 879,594.08 kilotons.
The small country emits 103,000 kilotons of carbon dioxide per year and agreed to cut its emissions by 5% per year for the next 14 years, starting with 103,000 kilotons in the first year.
To find the total amount of carbon dioxide emitted over the 14-year period, follow these steps:
1. Determine the initial amount of emissions: 103,000 kilotons in the first year.
2. Calculate the reduction rate per year: 5% or 0.05.
3. Calculate the total emissions for each year using the formula:
Emissions = Initial Emissions * (1 - Reduction Rate)^Year
4. Sum up the emissions for all 14 years.
Hence,
Year 1: 103,000 * (1 - 0.05)^0 = 103,000 kilotons
Year 2: 103,000 * (1 - 0.05)^1 = 97,850 kilotons
Year 3: 103,000 * (1 - 0.05)^2 = 93,057.50 kilotons
...
Year 14: 103,000 * (1 - 0.05)^13 = 56,516.87 kilotons
Now, add up the emissions for all 14 years:
Total Emissions = 103,000 + 97,850 + 93,057.50 + ... + 56,516.87 = 879,594.08 kilotons.
Therefore, the total amount of carbon dioxide emitted over the 14-year period is approximately 879,594.08 kilotons.
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Jorge bought a pedometer to measure how many miles he walks each day. he walks 1.4 miles on monday. this was 1/6 of his totalfor the week. what is his total distance ?
The total distance of Jorge for the week is 8.4 miles.
Let's assume that Jorge walks x miles in a week. According to the problem, he walks 1.4 miles on Monday, which is 1/6 of his total for the week. We can use this information to set up the following equation:
1/6 x = 1.4
To solve for x, we can multiply both sides by 6:
x = 1.4 x 6
x = 8.4
Therefore, Jorge walks a total distance of 8.4 miles in a week.
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A researcher is 95% confident that the interval from 3. 6 hours to 8. 1 hours captures y = the true mean amount of daily
screen time for US adults.
Is there evidence that the true mean number of hours of screen time for US adults is greater than 3. 5?
For the given case, there is evidence that the true mean number of hours of screen time for US adults is greater than 3.5.
Here, the researcher is 95% confidence interval from 3.6 hours to 8.1 hours captures y = the true mean amount of daily screen time for US adults.
If 3.5 hours falls below this interval, it is likely that the true mean number of hours of screen time for US adults is greater than 3.5 hours.
A confidence interval is a measure of values that is used to evaluate a statistical parameter which tends to involve the true form of the parameter a predetermined proportion of the time if the procedure of searching the group of values is repeated numerous times.
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simple interest earned for principal of $2000 at and 8% rate for 5 years
Simple Interest is equal to ($800) (2000 x 8 x 5) / 100. The simple interest earned is therefore $800.
What is interest?The measure of cash returned or earned over a set period of time on a principal sum of money is referred to as interest. It is frequently stated as a share of the principal sum and it may be either simple or complicated. Compounding interest is computed on the principal amount as well as any accrued but unpaid interest, whereas simple interest is assessed just on the principal amount. Loans, investments, and bank deposits frequently include interest.
given
We can use the following calculation to determine the simple interest received for a $2000 principal at an 8% rate over a 5-year period:
S.I = (Principal x Rate x Time)/100
In this instance, Principal is $2000, Rate is 8% annually, and Term is 5 years.
With these values entered into the formula, we obtain:
Simple Interest is equal to ($800) (2000 x 8 x 5) / 100. The simple interest earned is therefore $800.
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Yesterday, of the coffee shop's customers ordered flavored coffee. of the
orders were for chocolate flavored coffee. What part of the coffee shop's
customers ordered chocolate flavored coffee?
67
56
14
Tres cargas puntuales, q1=5uc,q3=5uc y q2=-2. 0uc, se encuentran en los vértices de un triángulo rectángulo la longitud de los catetos del triángulo es de 10 cm cuál es la fuerza resultante sobre q3
La fuerza resultante sobre q3 debe calcularse considerando la interacción de las cargas q1, q2 y q3.
How to calculate the resultant force on q3?Para determinar la fuerza resultante sobre q3, debemos calcular la magnitud y la dirección de las fuerzas ejercidas por q1 y q2 sobre q3.
Usando la Ley de Coulomb, podemos calcular la fuerza entre dos cargas puntuales utilizando la fórmula: F = k * (|q1| * |q2|) / r^2, donde k es la constante de Coulomb, |q1| y |q2| son los valores absolutos de las cargas, y r es la distancia entre las cargas.
Dado que las cargas q1 y q3 son iguales, y q2 tiene una carga negativa, las fuerzas ejercidas por q1 y q2 en q3 tendrán direcciones opuestas. Debido a la simetría del triángulo rectángulo, las fuerzas tendrán componentes horizontales y verticales iguales en magnitud.
La magnitud de la fuerza resultante sobre q3 se calcula sumando las magnitudes de las fuerzas ejercidas por q1 y q2. La dirección de la fuerza resultante será la misma que la de las fuerzas individuales ejercidas por q1 y q2.
Por lo tanto, para calcular la fuerza resultante sobre q3, debemos encontrar la magnitud de la fuerza ejercida por q1 y la magnitud de la fuerza ejercida por q2, y luego sumarlas. La dirección será la misma que las fuerzas individuales.
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what percent of stainless steel in the tank is used to make the two ends
Answer:
The percentage of stainless steel used to make the two ends of the tank cannot be determined without additional information. Please provide more details about the tank and its construction.
Step-by-step explanation:
To calculate the percentage of stainless steel used to make the two ends of the tank, we need to know the total amount of stainless steel used to make the entire tank, as well as the amount used to make the ends. Without this information, it is impossible to determine the percentage of stainless steel used for the ends.
For example, if the tank is made entirely of stainless steel, then the percentage of stainless steel used to make the ends would be 100%. However, if the tank is made of multiple materials, then the percentage of stainless steel used for the ends would depend on the amount of stainless steel used for the entire tank and the amount used for the ends.
Therefore, to calculate the percentage of stainless steel used for the ends of the tank, we need additional information about the tank's construction and materials.
Part A: An angle is two collinear rays with a common endpoint Find an example that contradicts this definition How would you change the delito
accurate? (5 points)
Part B: Give an example of an undefined term and how it pertains to angles (5 points)
PLEASE HELP ME !!
Part A: The given definition states that an angle is two collinear rays with a common endpoint. Part B : A point is an example of an undefined term.In relation to angles, a point is crucial as it serves as the common endpoint of the two rays that form the angle.
Part A : The given definition states that an angle is two collinear rays with a common endpoint. However, this definition is incorrect as it contradicts the correct definition of an angle. In the correct definition, an angle is formed by two non-collinear rays with a common endpoint.
An example that contradicts the given definition is when you have two rays, AB and BC, with B being the common endpoint. If they were collinear, they would lie along the same straight line, and thus, no angle would be formed between them. To make the definition accurate, you would need to change it to: "An angle is formed by two non-collinear rays with a common endpoint."
Part B: An undefined term in geometry is a term that cannot be defined using other known geometric terms, but its meaning is generally understood. One example of an undefined term is a point. A point is a basic element in geometry, and it has no size, shape, or dimensions. It is merely a location in space. For instance, when discussing angle ABC, point B is the common endpoint of rays AB and BC.
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The total municipal debt for the state of Illinois can be represented as the exponential function M (t) = 41. 24(1. 052)^t
where M represents the total municipal debt for the state in billions of dollars and t is the number of years since 2000
Determine the statement that interprets the function M (t).
A) The total municipal debt in Illinois was $41. 24 million in 2000 and increases about 1. 052% each year.
B) The total municipal debt in Illinois was $43. 38 billion in 2000 and increases about 5. 2% each year.
C) The total municipal debt in Illinois was $39. 20 billion in 2000 and increases about 105. 2% each year.
D)The total municipal debt in inois was $41. 24 billion in 2000 and increases about 5. 2% each year
The correct statement that interprets the function M(t) is:
B) The total municipal debt in llinois was $43.38 billion in 2000 and increases about 5.2% each year.
According to the question the function M(t) =41.24(1.052)^t represents the total municipal debt for the state of llinois in billions of dollars, where t is the number of years since 2000.
The incorrect options are:
Option A is incorrect as the function does not represent an increase of 1.052% each year, but rather an increase of 5.2% each year (since 1.052=1+0.052)
Option C is also incorrect because it suggests an increase of 105.2% each year, which is not possible.
Option D is also incorrect because it states that the total municipal debt was $41.24 billion in 2000, and increases about 5.2% each year.
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Information into an equation and solve the
equation
The sum of a number n and 11 is equal to 25. Find the number n
The resultant equation is n + 11 = 25 and the number n is 14.
Algebraic equation:
An algebraic equation is a mathematical statement that equates two expressions using one or more variables. Solving a single variable equation can be done by adding or subtracting the same integer on both sides. Similarly multiplying or dividing by the same integer.
The information we have
The sum of a number n and 11 is equal to 25.
The statement can represent an equation and solve for n as follows
Here sum of two numbers indicates adding
Hence, n + 11 = 25
To solve for n, isolate n on one side of the equation.
This can be done by subtracting 11 from both sides of the equation:
=> n + 11 - 11 = 25 - 11
=> n = 14
Therefore,
The resultant equation is n + 11 = 25 and the number n is 14.
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The Worthington Family is applying for a loan to purchase a new home. In order to qualify they
must have a net worth greater than $100,000.
• Mr. Worthington is a dentist, so he has $85,400 in student loans to pay off.
•Mrs. Worthington earns $42,500 per year at her job.
•The Worthington family has a savings account with a balance of $18,800.
•They own two vehicles that are worth a combined total of $64,600.
• Mrs. Worthington owns an antique necklace valued at $6,200.
"Run.
• The Worthingtons have been saving for their children's college fund.
currently has a balance of $24,700
The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.
To calculate the net worth of the Worthington family, we need to add up all their assets and subtract their liabilities (debts). Let's start by listing them:
Assets:
- Savings account: $18,800
- Vehicles: $64,600
- Antique necklace: $6,200
- College fund: $24,700
Total assets: $114,300
Liabilities:
- Mr. Worthington's student loans: $85,400
Total liabilities: $85,400
To calculate the net worth, we subtract the liabilities from the assets:
Net worth = Total assets - Total liabilities
Net worth = $114,300 - $85,400
Net worth = $28,900
The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.
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Help please! solve problem in the photo
Check the picture below.
[tex]6^2=[4+(2x+5)](4)\implies 36=(9+2x)(4)\implies \cfrac{36}{4}=9+2x \\\\\\ 9=9+2x\implies 0=2x\implies \cfrac{0}{2}=x\implies 0=x~\hfill \stackrel{ 2(0)+5 }{{\Large \begin{array}{llll} GH=5 \end{array}}}[/tex]
A quantitative data set has mean 25 and standard deviation 2. At least what percentage of the observations lie between 19 and 31 ?
At least 95% of the observations lie between 19 and 31.
To see why, we can use Chebyshev's theorem, which states that for any data set, regardless of the shape of the distribution, at least 1 - (1/k²) of the observations lie within k standard deviations of the mean. In this case,
we want to know the percentage of observations that lie within two standard deviations of the mean, since 19 and 31 are both two standard deviations away from the mean of 25.
So, we can use k = 2 in Chebyshev's theorem, which gives us:
1 - (1/2²) = 1 - (1/4) = 0.75
Therefore, at least 75% of the observations lie within two standard deviations of the mean. However, since we know the data set is normally distributed (since we know the mean and standard deviation), we can use the empirical rule,
which states that for normally distributed data, approximately 68% of the observations lie within one standard deviation of the mean, and approximately 95% of the observations lie within two standard deviations of the mean.
Therefore, we can conclude that at least 95% of the observations lie between 19 and 31.
To know more about Chebyshev's theorem, refer here:
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Write a derivative formula for the function.
f(x) = 2x√7x+8 + 96
The derivative formula of the given function f(x) is:
f'(x) = 2√(7x+8) + 7x/(√(7x+8))
This formula gives the value of the derivative of the function f(x) for any value of x.
How we find derivative?The derivative of f(x) using the product rule and chain rule:
f'(x) = 2√(7x+8) + 2x(1/2)(7x+8)^(-1/2)(7)
f'(x) = 2√(7x+8) + 7x/(√(7x+8))
Simplify the derivative
The derivative of the function f(x) is given by f'(x) = 2√(7x+8) + 7x/(√(7x+8))
In this formula, the first term represents the derivative of the function 2x√(7x+8) using the chain rule, and the second term represents the derivative of the function 96, which is a constant and has a derivative of zero.
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