According to the question approximately 83.89% of professors make more than $75,000 calculated by forming the equation.
Explain equation?When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.
This issue can be resolved using the conventional normal distribution. First, we need to standardize the value of $75,000 using the formula:
z = (x - μ) / σ
where x is indeed the value we wish to standardise, is indeed the mean, and is the deviation.
z = (75,000 - 85,900) / 11,000
z = -0.99
Next, we look up the area to the right of z = -0.99 in the standard normal distribution table or by using a calculator. The area to the left of z = -0.99 is 0.1611, so the area to the right of z = -0.99 is:
1 - 0.1611 = 0.8389
Therefore, approximately 83.89% of professors make more than $75,000.
To know more about equation visit:
https://brainly.com/question/2972832
#SPJ1
20 points!! please help!!
To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.
What is area?Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure
Area of rectangle = length x width
= 20 ft x 8 ft
= 160 sq. ft
Area of triangle = 1/2 xbase xheight
= 1/2 x 8 ft x 10 ft
= 40 sq. ft
To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).
Using the Pythagorean theorem, we have:
12² = 10² + b²
144 = 100 + b²
44 = b²
b = √44
b ≈ 6.63 ft
Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:
Area of total figure = area of rectangle + area of triangle
= 160 sq. ft + 40 sq. ft
= 200 sq. ft
To know more about Pythagorean theorem visit:
https://brainly.com/question/15169173
#SPJ1
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
f(x) = 2x - 1 g(x) = 7x + 8 find (gof) (x)
Answer:
(gof)(x) = 14x + 1
Step-by-step explanation:
We can think of (gof)(x) as g(f(x)). Writing it in this form shows that we must start with the inner function and work our way to the outer function.
Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.
f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1
Now, this output becomes the input for g(x):
g(2x-1) = 7(2x - 1) + 8
14x -7 + 8
(gof)(x) = 14x + 1
PLEASE HELP???!!!!!!!
The quadratic equation on the graph can be written as:
y = x² + 6x + 8
Which function is represented byy the graph?Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:
y = a*(x - h)² + k
Here we can see that the vertex is at (-3, -1), replacing that we will get:
y = a*(x + 3)² - 1
Now we can also see that it passes through the point (-2, 0), replacing these values we will get:
0 = a*(-2 + 3)² - 1
0 = a - 1
1 = a
Then the quadratic is:
y = (x + 3)² - 1
Expanding that we get:
y = x² + 6x + 9 - 1
y = x² + 6x + 8
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
Wally Martin purchased an office chair for $167.87. He received a $19.95 rebate from the manufacturer and a $8.95 rebate from the store. What is the final price?
dose 2+2=4?.............................
Answer:
[tex]yeah \: 2 + 2 = 4[/tex]
Whats the the sum of x and 2
The sum of x and 2 is equal to x + 2.
What is value?Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.
This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.
To know more about value click-
https://brainly.com/question/843074
#SPJ1
Determine the order of the following matrix:
[9 6 -4 8]
The order of the matrix is 2 x 2.
What is a matrix and what is meant by its order?
In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.
The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.
Determine the order of the given matrix:
In the given problem, we are asked to find the order of the matrix:
[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]
we count the number of rows and columns.
This matrix has 2 rows and 2 columns, so its order is 2 x 2.
Therefore, the order of the matrix is 2 x 2.
To know more about matrix visit :
brainly.com/question/28180105
#SPJ1
Rewrite 1 + 2i in polar form.
A.√5
B.√5∠116.6°
C.[5√∠63.4°]
D.5√∠(63.4°)
1 + 2i in polar form is 5√2∠63.4°.
What is a polar form ?
In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).
D. 5√2∠63.4°
To convert a complex number from rectangular form to polar form, we use the following formulas:
r = √(a^2 + b^2)
θ = tan^-1 (b/a)
Where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 1 and b = 2, so:
r = √(1^2 + 2^2) = √5
θ = tan^-1 (2/1) = 63.4°
Therefore, 1 + 2i in polar form is 5√2∠63.4°.
To know more about polar form and given link below -
https://brainly.com/question/11741181
#SPJ1
Need help with the questions
1. Calculating the output when using -6 as the input, we have:
Rule 1: subtract 7 = -13
Rule 2: square the input = 36.
Rule 3: divide by 3 = 12
Rule 4: divide the input into 3 = -2
Rule 5: write π = -2π
Rule 6: volume of a cube = -216cm³
What is function rule?A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.
2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.
b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.
c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.
Learn more about function rule on https://brainly.com/question/11356829
#SPJ1
what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).
How to obtain the coordinates of point P?The coordinates of point P are obtained applying the proportions in the context of the problem.
P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:
P - A = 2/3(B - A)
Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:
x - 9 = 2/3(-6 - 9)
x - 9 = -10
x = -1.
The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:
y + 8 = 2/3(7 + 8)
y + 8 = 10
y = 2.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
during last nights basketball game the number of points scored by the hornets was triple the number of points scored by the raiders the raiders scored 6 points how many points did the hornets score?
2
9
12
18?
Answer:
18
Step-by-step explanation:
siz times three is eighteen
i’m begging someone help please i’ll give brainlist
Answer:
a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.
b-yes- a triangle with angles 90, 50, and 40 is possible
c-yes. 65+45+70=180.
Step-by-step explanation:
OFFERING 70 POINTS AND BRAINLEST
Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.
The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
What is inequality?The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.
Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.
Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
Learn more about inequality here:
https://brainly.com/question/30228778
#SPJ1
Write a quadratic function in standard form to represent the data in the table.
Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To write a quadratic function in standard form, we need to use the general form of the quadratic equation:
y = ax²+ bx + c
where a, b, and c are constants. We can use the values in the table to find these constants.
When x = 2, y = 3
When x = 4, y = 1
When x = 6, y = 3
When x = 8, y = 9
When x = 10, y = 19
Substituting these values into the quadratic equation, we get:
3 = 4a + 2b + c
1 = 16a + 4b + c
3 = 36a + 6b + c
9 = 64a + 8b + c
19 = 100a + 10b + c
We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:
|16 4 1| |a| |1|
|36 6 1| |b| = |3|
|64 8 1| |c| |9|
Using a calculator or matrix software, we can solve for a, b, and c:
a = 1/2
b = -5/2
c = 5
To know more about function,
https://brainly.com/question/28193995
#SPJ1
Find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).
Answer:
The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:
[(x1 + x2) / 2, (y1 + y2) / 2]
In this case, A is located at (1, 4) and B is located at (3, -6). So the midpoint M of AB is:
[(1 + 3) / 2, (4 + (-6)) / 2]
= [2, -1]
Therefore, the midpoint of AB is at the point (2, -1).
The coordinates of the midpoint of the line AB is [2, -1]
What is section formula?Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.
It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.
Given that, we need to find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).
The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:
[(x1 + x2) / 2, (y1 + y2) / 2]
In this case, A is located at (1, 4) and B is located at (3, -6).
So the midpoint M of AB is:
= [(1 + 3) / 2, (4 + (-6)) / 2]
= [2, -1]
Hence, the midpoint of AB is at the point (2, -1).
Learn more about section formula click;
https://brainly.com/question/30242630
#SPJ2
Find the equation of the line containing the point
P(−2, 3)
and perpendicular to the graph of
3x + 9y = −2.
Answer:
Step-by-step explanation:
y = 3x + 9
It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
mentum
Copyright© 2022 Edmentum, Inc. All Rights Reserved
Privacy Policy California Priv
Mar 10
11:
Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
p=6t. what is the value of p when t= 14
Answer:
p=84
Step-by-step explanation:
p=6×14
p=84
answer: p=84
Which relationships describe angles 1 and 2? Select each correct answer. O complementary angles O adjacent angles O vertical angles O supplementary angles
Answer:2
Step-by-step explanation:Because the 2 is closest to the middle line
Answer:
relationship describes angles 1 and 2 is supplementary angles. From the given figure
it is concluded that
the relation ship between angle 1 and 2 is supplementary angles
because its is linear pair
and forms a line
therefore , the angles are supplementary angles
hence , relationship describes angles 1 and 2 is supplementary angle
Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))
Jaylen estimates the side of the square to be 8.5 inches long. The actual length of the side of the square is 8.3 inches long. What is the percent error of the area of the two squares?
Answer:
4.88%
Step-by-step explanation:
All sides of a square are equal
let x = length of a side
Area = x·x = x²
Estimated area = (8.5)² = 72.25 in²
Actual area = (8.3)² = 68.89 in²
percent error = (actual area - estimated area) / (estimated area) x 100
% error = (68.89 - 72.25) / (68.89) x 100 = -4.88% the negative sign means the estimate was higher than the actual.
Sally opens a savings account with $9,000 that earns 7% interest per year, not compounded How much interest, to the nearest penny, will Sally earn in 7 years?
Answer: Sally will earn $4,830.00 in interest over 7 years.
Step-by-step explanation:
If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:
I = P * r * t
where:
I = the interest earned
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time period, in years
In this case, we have:
P = $9,000 (the initial deposit)
r = 7% = 0.07 (the annual interest rate)
t = 7 (the number of years)
So, plugging in the values:
I = $9,000 * 0.07 * 7
I = $4,830.00
Therefore, Sally will earn $4,830.00 in interest over 7 years.
Out of 144 children who have school dinners, 1/3 chose pasta, 1/4 chose jacket potatoes and the rest chose curry. How many chose curry?
Answer:
A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us
Step-by-step explanation:
i may be wrong but I tried
What is the volume of this cone?
The volume of the cone is 2119. 5 cubic centimeters
How to determine the volume of the coneThe formula used for calculating the volume of a cone is expressed as;
V = πr² h/3
Given that the parameters are namely;
V is the volume of the cone.π takes the constant value of 3.14h is the height of the cone.r is the radius of the cone.Now, substitute the values, we have;
Volume , V = 3.14 × 15² × 9/3
Divide the values, we have;
Volume = 3.14 × 225 × 3
Multiply the values, we get;
Volume, V = 2119. 5 cubic centimeters
Learn about volume at: https://brainly.com/question/1972490
#SPJ1
(HELP PLEASE)A school track is pictured
below. The straightaway on
each side measures/100 yards.
The curves are semicircles with
diameter 36 yards. What is the
distance, in yards, around the
entire track? Use the button
on your calculator and express
your answer to the nearest
hundredth.
Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.
What's the easiest way to define distance?The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.
Describe a distance example.As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.
The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].
The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.
Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]
[tex]= 200 yards + 36pi yards[/tex]
[tex]= 312.57 yards[/tex] (rounded to two decimal places)
Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.
To know more about distance visit:
https://brainly.com/question/30123904
#SPJ1
Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
I will mark you brainiest!
What is the value of x in the figure below
A) 4.5
B) 10
C) 5
D) None of the choices are correct
Answer:
I will not show you the process it is easy the answer is 4.5 or 6 ≈
SOLVE THIS BUT I DON'T WANT ANSWER I WANT SOLVING AND ANSWER
50PTS
WILL MARK AS BRAINLIEST
50/1.428
Answer:
Alright
Step-by-step explanation:
50/1.428
Multiply the numerator by the denominator to get 50000/1428
Set equation up in long division format
Divide 50000 by 1428 to get 3
Divide 7160 by 1428 to get 5
Divide 200 by 1428 to get 0
Divide 2000 by 1428 to get 1
Divide 5720 by 1428 to get 4
Divide 80 by 1428 to get 0
Divide 800 by 1428 to get 0
35.014
D) what is the domain and range of the graphed function?
E) Isabel’s competition, who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0.
F) graph the function in part e
G) is your graph discrete or continuous? Explain.
The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.
What is a Continuous Function?A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.
We can express the total cost of an order as a function of the number of books sold, x, using the formula:
f(x) = 1.99x + 3
This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.
For example, if we sold 3 books, we can use the function to find the total cost:
f(3) = 1.99(3) + 3 = 9.97
This means that selling 3 books would cost $9.97 in total.
The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.
The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.
In contrast, a discrete function can only take on specific values, usually whole numbers or integers.
Read more about domain and range here:
https://brainly.com/question/26098895
#SPJ1
A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nall
Number
of Nails
67
18
10
Abundance
(%)
[7]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
Med Nail % Abund.
Enter
According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.
Explain medium?Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.
To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:
Total number of nails = 67 + 18 + 10 = 95
Next, we can calculate the percent abundance of the medium nails using the formula:
Percent abundance = (number of medium nails / total number of nails) x 100%
Using the values from of the table as inputs, we obtain:
Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%
As a result, the sample's average percentage of medium nails is roughly 18.95%.
To know more about medium visit:
https://brainly.com/question/16408033
#SPJ1