Answer:
10, 8
Step-by-step explanation:
Let x be the number of salads and y be the number of burgers.
We know that:
x + y = 28 (the total number of people)
8x + 4y = 152 (the total cost in dollars)
We can use the first equation to solve for one variable in terms of the other.
x = 28 - y
Now we can substitute this expression into the second equation:
8(28 - y) + 4y = 152
224 - 8y + 4y = 152
224 = 12y
y = 18 (burgers)
We can then use this value to find the number of salads
x = 28 - y = 28 - 18 = 10 (salads)
So the manager bought 10 salads and 18 burgers
A square has sides that measure 8x + 5 inches. A rectangle has two sides that measure 4x - 5 inches and two sides that measure 12x + 15 inches.
For what value of x will the perimeters of the square and rectangle be the same?
Answer:
The perimeter of the square is 32x + 20 inches, and the perimeter of the rectangle is (4x - 5) + (4x - 5) + (12x + 15) + (12x + 15) = 32x + 20 inches.
So, to find the value of x that makes the perimeters the same, we set 32x + 20 = 32x + 20 and solve for x.
x = 0
Step-by-step explanation:
find the area of the shaded part given below where the diameter is 14 cm.
Answer:
area of sector = 49π/6 cm² ≈ 25.7 cm²
Step-by-step explanation:
area of sector = (n/360°)πr²
where n = central angle of sector, and r = radius of circle
Here, we have:
n = 60°
r = d/2 = 14 cm / 2 = 7 cm
area of sector = (60°/360°)π(7 cm)²
area of sector = (1/6)π(49 cm²)
area of sector = 49π/6 cm² ≈ 25.7 cm²
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3,0)
(5,-2)
the fed is most likely to use which tool(s) to conduct monetary policy? group of answer choices open market operations discount rate interest on reserves (ior) rate required reserve ratio
The Federal Reserve uses three main tools to conduct monetary policy: Open Market Operations, the Discount Rate, and Interest on Reserves (IOR).
Open Market Operations involve the buying and selling of government securities in the open market, which impacts the money supply and interest rates. The Discount Rate is the interest rate the Federal Reserve charges commercial banks to borrow from it. A lower Discount Rate encourages borrowing, while a higher Discount Rate discourages borrowing. Interest on Reserves (IOR) is the interest rate the Federal Reserve pays commercial banks on their excess reserves. A higher IOR rate encourages banks to keep more of their funds in the form of reserves, while a lower IOR rate encourages banks to lend out more of their funds. The Required Reserve Ratio is also used to affect the money supply, as it determines the amount of reserves banks must keep on hand. An increase in the Required Reserve Ratio reduces the money supply, while a decrease in the Required Reserve Ratio increases the money supply.
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section 7.5 substitution page 15 pdf answer key 7c i can solve a linear system of equations by substitution.
Yes, substitution can be used to solve a linear system of equations.
Linear System of Equations:
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.
The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.
Yes, a linear system of equations can be solved via substitution.
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Part 1
The graph shown is that of a function, f. Determine (a) f(); (b) the domain; (c) all x-values such that f(x); and (d) the range.
Question content area bottom left
Part 1
a) f()
enter your response here
Part 2
b) Find the domain. Select the correct choice below and fill in the answer box to complete your choice.
A.
The domain is the set
.
(Use a comma to separate answers as needed.)
B.
The domain is the interval
enter your response here.
(Type your answer in interval notation.)
Part 3
c) Find all x-values such that f(x). Select the correct choice below and fill in the answer box to complete your choice.
A.
f(x) only for the specific value(s) x
enter your response here.
(Use a comma to separate answers as needed.)
B.
f(x) for all values of x in the interval
enter your response here.
(Type your answer in interval notation.)
Part 4
d) Find the range. Select the correct choice below and fill in the answer box to complete your choice.
A.
The range is the set
.
(Use a comma to separate answers as needed.)
B.
The range is the interval
enter your response here.
(Type your answer in interval notation.)
.
.
.
Question content area right
Part 1
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
x
y
A coordinate system has a horizontal x-axis labeled from negative 12 to 12 in increments of 1 and a vertical y-axis labeled from negative 12 to 12 in increments of 1. From left to right, a curve starts at a closed dot at (negative 5, negative 7), rises at a decreasing rate, flattens out to pass through (negative 2, 2), and rises at an increasing rate until it ends at a closed dot at (2, 10). The curve also passes through the points left parenthesis negative 4 comma negative 2 right parenthesis and left parenthesis negative 3 comma 1 right parenthesis.
Answer:
Step-by-step explanation:
Part one is when you need to do area/perimiter.
DO
what’s the domain of this function please help
Express the formula v=pie r^2 • H in terms of height, H. Use that formula to find the height when the volume is 45pid and the radius is 3
Option (b) is the correct option i.e. The height is 5 units.
What precisely are volume and height?The height of an object is determined by measuring the distance between its base and its top.
As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."
Given, V = πr².H
V/πr² = H
So, It can be written in terms of height, H as V/πr².
Now, If r = 3 units and V= 45π then,
H = V/πr² = 45π / π(3)²
= 45π/9π
= 5 units.
Hence, height is 5 units.
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six hundred six and two thousand, three hundred seventy-one ten-thousandths in numerical form
Answer:606.02371
Step-by-step explanation:
The numerical representation of "six hundred six and two thousand, three hundred seventy-one ten-thousandths" is 606.02371.
Consider f(x) = 3x. Describe how the graph of each function compares to f.
The graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.
How to describe the transformation?The parent function for this problem is defined as follows:
f(x) = x.
The transformed function is given as follows:
f(x) = 3x.
The only transformation is a multiplication by the constant 3. As the constant has an absolute value greater than 1, the graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.
Missing InformationThe problem asks for how the graph of f(x) = 3x compares to the graph of f(x) = x.
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An airplane travels 150 miles in 3/4 hour. What is the average speed of the airplane?
Answer:
200mph
Step-by-step explanation:
hich of the following expressions is never a prime number when p is a prime number? (a. p2 16, b. p2 24, c. p2 26, d. p2 46, e. p2 96)
From the given expressions of prime numbers, the following are never a prime number:
Option b. p²+ 24
Option c. p²+ 26
Prime number is represented by 'p'
The expressions which can never be a prime number is given by :
Let us consider value of p = 1
a. p²+ 16
⇒1² + 16
⇒17 a prime number
b. p²+ 24
⇒1² + 24
⇒25 is not a prime number.
c. p²+ 26
⇒1² + 26
⇒27 is not a prime number.
d. p²+ 46
⇒1² + 46
⇒47 a prime number.
e. p²+ 96
⇒1² + 96
⇒97 a prime number.
Therefore, the expression represented by option b. p²+ 24 and option c. p²+ 26 can never be a prime number.
The above question is incomplete , the complete question is :
Which of the following expressions is never a prime number when p is a prime number?
a. p²+ 16 b. p²+ 24 c. p²+ 26 d. p²+ 46 e. p²+ 96
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A city has a population of 310,000 people. Suppose that each year the population grows by 8%. What will the population be after 14 years?
round your answer to the nearest whole number.
The longer leg of a right triangle is 3cm longer than the shorter leg. The hypotenuse is 6cm longer than the shorter leg. Find the side lengths of the triangle.
In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is 9 inches.
How can the lenght be calculated?The concept that will be used is pythagoras theorem.
We can make s = the length of the shorter leg.
Where the longer leg can be expressedas (s + 3),
Then the hypotenuse is( s + 6).
From pythagoras theorem, a^2 + b^2 = c^2.
then we have s^2 + (s + 3)^2 = (s + 6)^2
[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]
s^2 + s^2 + 6s + 9 = s^2 + 12s + 36
If we collect like terms we have
s^2 - 6s - 27 = 0
Then if we factorize we have
(x - 9)(x + 3) = 0
then
we can set the whole left side to equal 0.
x - 9 = 0, then x = 9
x + 3 = 0, then x = -3.
But we can only have positive value which sis 9, hence shortest side is 9 inches.
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What type of triangle and are they congruent
Answer: AAS and both triangles are congruent
Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate. The way you tell the difference between the two is by how the congruent angles and the congruent side is shown. In ASA, the congruent side would be the included side between both congruent angles. Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS. This means that the triangles are congruent.
Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles. If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.
I hope this helps you!
Recall that lim f(x) = L means: For all € > 0 there is a 6 > 0 such that for all x satisfying 0 < Ix ~ cl < & we have that |f(x) - Ll < € What if the limit does not equal L? Think about what the means in €, 6 language. Consider the following phrases: 1.€ > 0 2.6 > 0 3.0 < Ix - cl < 6 4. Wf(x) - Ll > e 5. but 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form rigorous assertion that lim flx) + L and enter their reference numbers in the appropriate sequence in these boxes:
As per the given limit, the rigorous assertion of the function is a − δ < x < a + δ
In math term function is called as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
Here we have given that the distance between two points a and b on a number line is given by |a−b|.
And we need to find the rigorous assertion of the function.
Then the statement is written as
=> |f(x)−L|<ε
And it can be be interpreted as the distance between f(x) and L is less than ε.
Here we have another statement that is written as
=> 0<|x−a|<δ
And it ma be interpreted as the value of x≠a and the distance between x and a is less than δ.
Here we have also important to look at the following equivalences for absolute value that the statement |f(x)−L|<ε is equivalent to the statement L−ε<f(x)<L+ε.
And the statement 0<|x−a|<δ is also equivalent to the statement a−δ<x<a+δ here we know that x≠a.
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I just need help with number 2 on box A. I can record the coordinates of the triangle.
The coordinates of the ends of the image are J'(x, y) = (- 7, 7), K'(x, y) = (- 5, 2) and L'(x, y) = (- 2, 3), whose transformation formula is P'(x, y) = P(x, y) + (0, - 2 · p). A representation of the figures is in the image shown below.
How to derive the reflection formula of a figure
In this problem we find a geometric locus generated by three points on Cartesian plane that is reflected over the x-axis, whose formula is shown below:
P'(x, y) = P(x, y) + (0, - 2 · p)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointp - y-Coordinate of the original point.If we know that J(x, y) = (- 7, - 7), K(x, y) = (- 5, - 2) and L(x, y) = (- 2, - 3), then the coordinates of the image are:
J'(x, y) = (- 7, - 7) + (0, 14)
J'(x, y) = (- 7, 7)
K'(x, y) = (- 5, - 2) + (0, 4)
K'(x, y) = (- 5, 2)
L'(x, y) = (- 2, - 3) + (0, 6)
L'(x, y) = (- 2, 3)
Now we proceed to graph both the geometric locus and its image.
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which of the following is true of a scientific theory? view available hint(s)for part a which of the following is true of a scientific theory? it generates testable hypotheses, is supported by a large body of evidence, and is broad in scope. it is only accepted after the person who formulated it has died. it is formulated by many scientists over drinks at a convention. it is a method or device that applies scientific knowledge for some specific purpose. it must demonstrate the effect of one variable by testing control groups and experimental groups.
Out of the following, the statement is It generates testable hypotheses, is supported by a large body of evidence, and is broad in scope is true of a scientific theory.
A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. A scientific theory is not just an idea or speculation. It is a systematic way of organizing and interpreting observations that are based on facts and evidence. It is also open to being tested and disproved if new evidence arises.
A scientific theory must be supported by a large body of evidence from multiple sources to be considered valid. Furthermore, a scientific theory must be broad in scope and explain a wide range of phenomena. It must also generate testable hypotheses that can be tested and verified through experimentation and observation.
A scientific theory is not accepted until it is thoroughly tested and confirmed through numerous experiments and observations. Therefore, it is not accepted after the person who formulated it has died.
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Find the value of k for which each equation has the following: a real double root two different double roots imagenary roots k^2x^2-8x 4
The value of k for which the equation has imaginary roots is k > ±2.
Function value of x intervalFor a quadratic equation of the form k²x²-8x+4 to have a real double root, the discriminant (b²-4ac) must be equal to zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².
For the discriminant to be equal to zero, 64 - 16k² = 0 and k² = 4. Therefore, the value of k for which the equation has a real double root is k = ±2.
For a quadratic equation of the form k²x²-8x+4 to have two different double roots, the discriminant (b²-4ac) must be greater than zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².
For the discriminant to be greater than zero, 64 - 16k² > 0 and k² < 4. Therefore, the value of k for which the equation has two different double roots is k < ±2.
For a quadratic equation of the form k²x²-8x+4 to have imaginary roots, the discriminant (b²-4ac) must be less than zero. For this equation, the discriminant is (-8)² - 4 * k^2 * 4 = 64 - 16k².
For the discriminant to be less than zero, 64 - 16k² < 0 and k² > 4. Therefore, the value of k for which the equation has imaginary roots is k > ±2.
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Alexandra invested 40% of his money in mutual funds, 40% in real estate, and 20% in stocks. If the value of the money that he invested in mutual funds, real estate, and stocks grew by 2%, 7%, and 11% respectively, what was the average growth on his total investment?
Answer:
To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.
First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.
So the amount invested in mutual funds is 40/100 * $100 = $40
The amount invested in real estate is 40/100 * $100 = $40
The amount invested in stocks is 20/100 * $100 = $20
Then we can calculate the growth of each investment using the percentages provided:
The growth of mutual funds is 2/100 * $40 = $0.80
The growth of real estate is 7/100 * $40 = $2.80
The growth of stocks is 11/100 * $20 = $2.20
Now we can add up the growth of each investment and divide it by the total investment to find the average growth:
($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%
So the average growth on Alexandra's total investment is 5.8%.
QUESTION; 01. A sarveyor standing 25°SW of a tower measure the angle of elevation of the top of the tower as 46°30' from a position 23°SE from the tower the elevation of the top is 37°15'. Determine the height of the tower if the distance between the two observations is 75m.
When you know the tower's height, you may calculate your distance from it.The answer is 92.54 feet .
Determine the height of the tower ?When you know the tower's height, you may calculate your distance from it.The tangent of the angle of elevation multiplied by the horizontal distance, or doing the calculation, is all that is required to manually determine the height.
30° vertical angle from A to the tower's summit
50 + x is the horizontal separation between A and the tower's base.
Call h to get the tower's height.
tan 30 = h / (50 + x) => 50 + x = h / tan 30 => x = h / tan 30 - 50 (1)
40° vertical angle from B to the tower's summit
The tower's base is x feet away from B in a horizontal direction.
ratio: x = h / tan40; tan40 = h / tan40 (2)
Consequently, (1) and (2) are equivalent.
Tan40 = Tan30 - 50 =
30 - 40 = 50 h/tan
1,7321h - 1,1918h = 50
0.5403h = 50
h = 50/0.5403 = 92.54
Response: 92.54 feet
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Why do you think insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage?
We can actually think that insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage because the risk of a claim is typically lower for uninsured/underinsured coverage.
What is insurance?An agreement to provide compensation to another party in the event of a certain loss, damage, or injury is known as insurance, and it is a way to safeguard against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.
Collision coverage is for damage to the policyholder's own vehicle, while uninsured/underinsured coverage is for damage caused by another driver who does not have enough insurance to cover the costs of an accident. Since fewer drivers are uninsured or underinsured, the likelihood of a claim being made under that coverage is lower, and thus the cost is less.
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A Sulfa drug is to be given to a 130-pound patient at the rate of 2.5 mg per pound of body weight.
How many mL are necessary if the concentration of the drug is 200 mg per mL?
Answer:
1.625 mL
Step-by-step explanation:
2.5 mg per lb
For 130 lb, 130 × 2.5 mg = 325 mg are needed.
1 mL has 200 mg
1 mL is to 200 mg as x ml is to 325 mg
1/200 = x/325
200x = 325
x = 1.625
Answer 1.625 mL
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours | Total Number of Students
0 | 1
1 | 8
2 | 2
3 | 5
4 | 9
5 | 7
6 | 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for exactly 1 hour is 0.23
How to determine the probability that a student studied for exactly 1 hour?Probability is a measure of the likelihood of a particular event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
From the given table, you need notice that the number of students who study for 1 hour is 8.
In order to determine the probability that a student studied for exactly 1 hour, we need to find total number of students. That is:
Total number of student = 1 + 8 + 2 + 5 + 9 + 7 + 3 = 35
probability (exactly 1 hour) = number of exactly 1 hour/Total number
probability (exactly 1 hour) = 8/35 = 0.23
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Answer:
B
Step-by-step explanation:
Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, the y increases by a common difference of 3.
For each x increase of 1, the y increases by a common factor of 3.
For each x increase of 1, the y increases by 4 more than the previous increase.
For each x increase of 1, the y increases by doubling and then adding 1.
The correct option regarding the growth rate of the exponential function is given as follows:
For each x increase of 1, the y increases by a common factor of 3.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
As the function in this problem is exponential, the increase of the output y must be a common factor, purely.
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The data set, {+3, -1, -2, +1} shows the moves a player made. Explain the meaning of zero in this situation.
The meaning of a zero in this situation shows that there was a time the player was in a steady position or without movement.
What is a data set?A data set is defined as the number of variables that makes up the data of an event, research or an experiment.
The data sets that was given are {+3, -1, -2, +1} which represent the number of moves that was made by a player.
But when a zero is included in that data set, this means that the player didn't make a move at the particular point in time.
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x=8+27y by substitution
The expression can be rewritten as -
y = (1/27)x - (8/27)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
x = 8 + 27y
We can rewrite the expression as -
x = 8 + 27y
27y = x - 8
y = (1/27)x - (8/27)
Therefore, the expression can be rewritten as -
y = (1/27)x - (8/27)
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For a particular company the salaries of five employees are: $45,000 $52,000 $67,000 $42,000 $56,000 A new employee is hired and her salary is $280,000. What word best describes this data set with the new employee included?
Need help with questions 12!
Answer:
So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
Step-by-step explanation:
We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
solve it to find the value of X. also find the actual length of each square[tex]perimeter of square 40cm,(x+2)cm[/tex]
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
What is the perimeter of the square?The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
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