Answer:
The statement that is NOT always true about matrices A, B, and C is:
C. If A is singular, then its transpose is also singular.
Step-by-step explanation:
A matrix A is singular if and only if its determinant is zero. However, the transpose of a matrix does not necessarily have the same determinant as the original matrix. So, it is possible for a matrix A to be singular while its transpose is non-singular. Therefore, statement C is not always true.
sin¹(x)-cos¹ (x)/sin²(x)-cos² (x) =1
....................................................................................
Answer: A 265100
Step-by-step explanation:
Given:
t=5 years
Formula:
V= 220000(1.038)⁵ >plug into the calc: 220000 * 1.038^5
V= 265100
Answer is A. 265100
Answer:
a) $265,100
Step-by-step explanation:
Given equation:
[tex]\boxed{V=220000(1.038)^x}[/tex]
where:
V is the value of the home after x years.x is the number years.The Lee family bought their home for $220,000 this year.
To find the value of the Lee family's home in 5 years, substitute x = 5 into the given equation and solve for V:
[tex]\begin{aligned}x=5 \implies V&=220000(1.038)^5\\&=220000(1.20499922...)\\&=265099.829...\\&=\$265,100\;\sf(nearest\;dollar)\end{aligned}[/tex]
Therefore, the value of the Lee's family home in 5 years is $265,100 to the nearest dollar.
A $8,300 loan at 13.05% compounded monthly is to be repaid by three equal payments due 3, 6, and 12 months after the date of the loan. Calculate the size of each payment. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Answer:
$2,856.71
Step-by-step explanation:
Factor [tex]x^{2}[/tex] + 64
The expression x^2 + 64 is a quadratic expression that cannot be factored using real numbers. However, it can be factored using complex numbers.
We know that i^2 = -1, so we can write:
x^2 + 64 = x^2 - (-64)
Now, we can use the difference of squares formula, which states that:
a^2 - b^2 = (a + b)(a - b)
Using this formula, we can write:
x^2 + 64 = (x + 8i)(x - 8i)
Therefore, the factored form of x^2 + 64 is (x + 8i)(x - 8i).
[tex]x^{2} + 64[/tex] can be factored into [tex](x + 8i)(x - 8i)[/tex], where [tex]i[/tex] is the imaginary unit.
Mr. Burst is speed eating spring rolls. He has eaten 8 and continues eat 4.5 rolls every minute. He needs to eat more than 44 to beat Mr. Bean's record. Write an inequality for the situation. Then solve and graph your solution to show how many more minutes it will take for Mr. Burst to beat Mr. Bean's record.
Mr. Burst needs to eat more than 8 minutes to beat Mr. Bean's record.
Let's define the variables:
x - the number of minutes Mr. Burst has been eating spring rolls
y - the total number of spring rolls Mr. Burst has eaten
Based on the given information, we can set up the following inequality:
y = 8 + 4.5x (equation representing the number of spring rolls Mr. Burst has eaten)
We want Mr. Burst to eat more than 44 spring rolls to beat Mr. Bean's record. Therefore, we can set up the inequality:
y > 44
Substituting the equation for y, we have:
8 + 4.5x > 44
To solve for x, we can isolate the variable:
4.5x > 44 - 8
4.5x > 36
x > 36 / 4.5
x > 8
Mr. Burst needs to eat more than 8 minutes to beat Mr. Bean's record.
To graph the solution, we plot the inequality on a number line, shading the region to the right of x = 8. This shows all the possible values of x that satisfy the inequality. The y-axis represents the number of minutes, and the x-axis represents the number of spring rolls.
|-----------------------|------------------>
0 8
Therefore, Mr. Burst needs to eat more than 8 minutes to beat Mr. Bean's record.
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list price: $6.40 dicount rate :15%. find the discount and find the sale price Emergency
The sale price is $5.44 while the discount is $0.96
What is an equation?An equation is an expression that is used to show how numbers and variables are related using mathematical operators
The list price of a goods is $6.40 and the discount rate is 15%, hence:
Discount = 15% of list price = 0.15 * $6.40 = $0.96
Sale price = List price - Discount = $6.40 - $0.96 = $5.44
The sale price is $5.44
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Why is FOQZ the odd one out in
these sets of letters?
BCDEGPTV AJK FOQZ IY
The odd one out in the set is "FOQZ." It deviates from the pattern by the other sets, where the letters are arranged in Alphabetical order.
The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.
In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.
Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.
It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.
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What is the sum of the first 43 terms of the sequence?
−282,−277,−272,−267,...
The sum of the first 43 terms of the sequence given below is -7611.
What is the arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
The formula for it is:
[tex]\text{a}_\text{n}=\text{a}+\text{D}(\text{n}-1)[/tex]
Given Sequence:
[tex]\sf -282,-277,-272,-267, \ ...[/tex]It represent an A.P. with
first term [tex]\sf a=-282[/tex]common difference [tex]\sf d =5[/tex]So, sum of 43 terms.
[tex]\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[2\times(-282)+(43-1)5][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[-564+210][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[-354][/tex]
[tex]\text{S}_{43}={43}\times[-177][/tex]
[tex]\text{S}_{43}=\bold{-7611}[/tex]
Hence, the sum of the first 43 terms of the sequence given below is
-7611.
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Which describes the expression below? 7x + 4 A. a sum of 2 terms
B. a product of 2 factors C. a sum of 3 factors D. a product of 3 factors
The statement that best describes the expression that is given above would be a sum of 2 terms. That is option A.
What is a term in a mathematical expression?A term is defined as the major part of an algebraic expressions that contains a signed number, a variable, or a constant multiplied by a variable or variables.
The algebraic expression given is as follows;
= 7x + 4
Where;
7 = coefficient
X = variable
4 = Constant
But 7x = A Term
4 = A Term
Therefore, a sum of 2 terms is the best statement the explains the given expression.
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what is the answer to -4√14·2√8
Choose the most appropriate measures to describe the center and the variation. Dot plot, titled Prices of Games, shows the price in dollars with the following values that appear as dots above the line. One dot above 28. Two dots above 30. Four dots above 32. Three dots above 34. Two dots above 36. One dot above 38. The most appropriate measure to describe the center is the . The most appropriate measure to describe the variation is the .
The most appropriate measure to describe the center is the Median, and the most appropriate measure to describe the variation is the range.
The most appropriate measure to describe the center of the data in the dot plot is the median. The median represents the middle value when the data is arranged in ascending or descending order. In this case, the median is the value that divides the data into two equal halves. As there are 13 values in total, the median will be the seventh value, which corresponds to the value with two dots above it, which is 32 dollars. Therefore, the median accurately represents the center of the data in this case.
The most appropriate measure to describe the variation of the data in the dot plot is the range. The range represents the difference between the maximum and minimum values in a dataset. In this case, the minimum value is 28 dollars (one dot above it) and the maximum value is 38 dollars (one dot above it). Therefore, the range is 38 - 28 = 10 dollars, which indicates the spread or variation of the data.
Hence, the most appropriate measure to describe the center is the median, and the most appropriate measure to describe the variation is the range.
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The director of surgery at a local hospital is interested in understanding his unit’s costs. An assistant collected data for the past 36 months on unit cost (labor, supplies, and so on) along with the number of procedures performed in the unit. The assistant analyzed the data using a spreadsheet program, and the following output was generated.
Equation
Intercept $ 1,003,000
Coefficient on procedures $ 215
Statistical data
Correlation coefficient 0.503
R2 0.253
The unit is planning to perform an average 17,000 procedures per month for the coming year.
To make informed decisions about budget allocation and cost management, the director should consider this relationship between the number of procedures and unit cost.
The director of surgery at a local hospital aims to understand the unit's costs by analyzing data from the past 36 months, including unit cost (labor, supplies, etc.) and the number of procedures performed.
The assistant used a spreadsheet program to analyze this data and obtained an R2 value of 0.253.
This indicates that 25.3% of the variation in unit cost can be explained by the number of procedures performed. The unit plans to perform an average of 17,000 procedures per month in the upcoming year.
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Tell whether the data represent a linear, an exponential, or a quadratic function.
(-1,0), (0, 12), (1, 16), (2, 12), (3, 0)
-Linear function
-Exponential function
-Quadratic function
Write the function. Use x as the variable.
y =
The solution is: the data (-1,0), (0, 12), (1, 16), (2, 12), (3, 0), represent a Quadratic function. and, the function is: where x as the variable: y = -4x² + 8x + 12.
Here, we have,
the data represent a function.
(-1,0), (0, 12), (1, 16), (2, 12), (3, 0)
now, we have,
when we plot the data in a graph
we get,
graph attached
it is a parabola,
so, we get,
the data (-1,0), (0, 12), (1, 16), (2, 12), (3, 0), represent a Quadratic function.
now, we get,
the function. where x as the variable:
y = -4x² + 8x + 12
Hence, The solution is: the data (-1,0), (0, 12), (1, 16), (2, 12), (3, 0), represent a Quadratic function. and, the function is: where x as the variable: y = -4x² + 8x + 12.
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Weekly wages at a certain factory are normally distributed with a mean of 400 dollars and a standard deviation of 50 dollars. Find the probability that a worker selected at random makes between 400 dollars and 550 dollars.
49.87% is the probability that a worker selected at random makes between 400 dollars and 550 dollars.
To find the probability that a worker selected at random makes between $400 and $550, we can use the properties of the normal distribution.
Given that the weekly wages are normally distributed with a mean (μ) of $400 and a standard deviation (σ) of $50, we can use these parameters to standardize the values and then find the corresponding probabilities.
To standardize the values, we use the z-score formula:
z = (x - μ) / σ
where x is the value we want to find the probability for.
For $400:
z1 = (400 - 400) / 50 = 0
For $550:
z2 = (550 - 400) / 50 = 3
Now, we can use the standard normal distribution table or a calculator to find the probabilities associated with these z-scores.
The probability of a worker making less than or equal to $400 is the same as the probability of z1 or less, which is P(z ≤ 0). From the standard normal distribution table, we find that P(z ≤ 0) is approximately 0.5.
The probability of a worker making less than or equal to $550 is the same as the probability of z2 or less, which is P(z ≤ 3). From the standard normal distribution table, we find that P(z ≤ 3) is approximately 0.9987.
Therefore, the probability that a worker selected at random makes between $400 and $550 is the difference between these two probabilities:
P(400 ≤ x ≤ 550) = P(z ≤ 3) - P(z ≤ 0) ≈ 0.9987 - 0.5 ≈ 0.4987
So, the probability is approximately 0.4987 or 49.87%.
Using the z-score, we transformed the values into a standard normal distribution, looked up the probabilities associated with the z-scores from a standard normal distribution table, and found the difference in probabilities to determine the probability of the worker's wage falling between $400 and $550.
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I really need help with this
Answer:
Step-by-step explanation:
Statement Reason
PR ≅ TR Given
<PQR≅<TSR Given
<PRQ≅<TRS Vertical Angles Theorem
PQR=TSR SAS Theorem (Side-Angle-Side)
Find the product of all integers between -11 and 13.
its 0
it's pretty long ngl
An isosceles triangle has equal sides where PQ = PR and base angles of 65⁰. QX = XR = 2.64 cm. Find a) PQ b) PX
Answer:
In an isosceles triangle, the sides opposite the equal angles are equal in length. Let's solve the given problem using the given information.
a) To find PQ, we need to find the length of the equal sides. Since QX = XR = 2.64 cm, we know that PQ = PR. Therefore, PQ = PR = 2.64 cm.
b) To find PX, we can use the concept of the Law of Cosines. In an isosceles triangle, the base angles are equal, so the angle at P is 65°, and the opposite side is PX.
Using the Law of Cosines formula:
c² = a² + b² - 2ab * cos(C)
Where c is the side opposite angle C, and a and b are the other two sides.
In our case, we have:
a = PQ = 2.64 cm
b = PR = 2.64 cm
C = 65°
We want to find PX, so c = PX.
Substituting the values into the formula:
PX² = (2.64)² + (2.64)² - 2(2.64)(2.64) * cos(65°)
PX² ≈ 6.9696 + 6.9696 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 11.1197
PX² ≈ 2.8195
Taking the square root of both sides, we get:
PX ≈ √2.8195
PX ≈ 1.678 cm
Therefore, a) PQ = PR = 2.64 cm, and b) PX ≈ 1.678 cm.
Step-by-step explanation:
evaluate 8x-4y when x=2 and y=3 (a)4 (b)28 (c)22 (d)18
Answer:
(a) 4
Step-by-step explanation:
Let's start with the equation:
8x-4y
Since we already have the values of x and y, we can solve out equation.
8(2)-4(3)
16-12=4
The answer is (a)4
an inventor is designing a machine that will have two gears. the first gear will complete one revolution every 8x squared y seconds. the second gear will complete one revolution every 6x to the third power y squared seconds. how often will both of the gears be in their starting positions at the same time
Answer:
every 24x^3y^2 seconds
Step-by-step explanation:
To determine how often both gears will be in their starting positions at the same time, we need to find a common multiple of the two revolution times.
The first gear completes one revolution every 8x^2y seconds, and the second gear completes one revolution every 6x^3y^2 seconds.
To find a common multiple, we need to factorize the revolution times:
8x^2y = (2^3)(x^2)(y)
6x^3y^2 = (2)(3)(x^3)(y^2)
The common multiple should include all the prime factors with their highest powers. Therefore, the common multiple would be:
(2^3)(3)(x^3)(y^2) = 24x^3y^2 seconds.
So, both gears will be in their starting positions at the same time every 24x^3y^2 seconds.
Emma and Lauren read a total of 47 books. Emma reads 17 more books than Lauren. Enter the number of books lauren read
Answer:30
Step-by-step explanation:47-17 = 30
The volume of a cylinder is 368 cubic inches and the radius of the cylinder is 4 inches. What is the height of the cylinder?
Answer: the answer is h=7.32in
A table is on sale for 68% off. The sale price is $147.20.
What is the regular price?
Answer:
Let's use "P" to represent the regular price of the table.
If the table is on sale for 68% off, then the sale price is 100% - 68% = 32% of the regular price.
We know that the sale price is $147.20, so we can write:
0.32P = $147.20
To find P, we need to divide both sides of the equation by 0.32:
P = $147.20 / 0.32
P = $460.00
Step-by-step explanation:
Answer:
$460 is the correct answer.
!
A washer and dryer cost a total of 928$. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer:
Cost of Washer = $696
Cost of Dryer = $232
Step-by-step explanation:
Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.
Put the equation together, so we can add the x variables together.
3x + x = 4x
The total cost will be what the '4x' is equal to.
4x = 928
Going back to algebra, we solve the equation by dividing both sides by 4.
x = 232
Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.
3x
3(232) = 696.
To check the answer, we can add them together to make sure we get the total cost.
696 + 232 = 928
Please help
21. What are the missing coordinates of point Q?
P(0, c)
A.
B.
C.
D.
Session 2-Calculator Allowed
(-2a, 0)
(2a, 0)
(-2a, c)
(2a, c)
Q(?, ?) O
N(2a, 0)
"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.
Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:
x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2
x-coordinate of Q = (0 + 2a) / 2 = a
So, we know that the x-coordinate of point Q is a.
To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:
y - c = (0 - c) / (2a - 0) * (x - 0)
Simplifying this equation gives:
y - c = -c/2a * xy = -c/2a * x + c
Substituting x = a in this equation gives:
y = -c/2a * a + cy = -c/2 + cy = c/2
So, we know that the y-coordinate of point Q is c/2.
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1. AD is tangent to the circle at point C. What is the measure of < BCA?
Circle B with radius B C. line tangent to chord C has points D A C in that order. segments are drawn from the center to each point.
Question 1 options:
180 degrees
40 degrees
90 degrees
50 degrees
2. What is the measurement of
3.What is the value of x? Round your answer to the nearest tenth
(hint: two secants)
4. What is the value of n?
5. Question 5 options:
In the picture, Line BC is an example of a
, segment DB is a
and line DB is a
Since AD is tangent to the circle at point C, we know that angle BCA is a right angle. Therefore, the measure of angle BCA is 90 degrees.
The measurement of what is not specified, please provide more information.
The value of x cannot be determined without additional information about the diagram.
The value of n cannot be determined without additional information about the diagram.
In the picture, Line BC is an example of a line, segment DB is a line segment, and line DB is also a line.
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7.343 degrees North of your position is a tall object. Call the phone number you wrote down earlier do get the height of the object. Use the ILevel app to estimate the angle of elevation to the top of this object by holding the phone up to your eye and pointing it at the top of the object. If the object is a right cylindrical cone whose radius equals its height, use trigonometry to estimate the horizontal distance, in meters, to the base of the object from your current position. (1 meter is about 3.28 feet)
The horizontal distance to the base of the object from our current position is approximately 50 meters.
Let's assume that we find out that the height of the object is 50 meters.
Since the object is a right cylindrical cone whose radius equals its height, we know that the angle between PR and QR is 45 degrees (half of 90 degrees).
We can use this information to set up a right triangle with PR as the hypotenuse, PQ as one leg, and QR as the other leg.
We can use trigonometry to solve for PQ, which represents the horizontal distance to the base of the object from our current position.
We know that tan(45) = PQ/50, where PQ is in meters.
Solving for PQ, we get:
PQ = 50 meters x tan(45°) = 50 meters x 1 = 50 meters.
Therefore, the horizontal distance to the base of the object from our current position is approximately 50 meters.
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Calculate the total cost of an item bought at a negotiated price of $21,980 with 7.6 percent sales tax and a $82 registration fee.
$22,473.18
$22,962
$23,656.71
$23,732.48
The total cost of the item 23, 732.48 dollars.
How to find the total cost of the item?The item was negotiated at a price of $21,980 with 7.6 percent sales tax
and a $82 registration fee.
Therefore, let's find the total cost of the item.
Hence,
The sales tax is a consumption tax on the sale of goods and services. Therefore,
sales tax = 7.6 % of 21980
sales tax = 7.6 / 100 × 21980
sales tax = 167048 / 100
sales tax = 1670.48 dollars
Therefore,
total cost of items = 21980 + 1670.48 + 82
total cost of items = 23, 732.48 dollars
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Find the area between the curves y=e^-0.3x and y=2.2x+1 from x=0 to x=2
From x = 0 to x = 2, the area of the region between the curves [tex]y = e^{-0.3x[/tex] and y = 2.2x + 1 is roughly 2.496 square units.
To determine the area, the intersection points of two curves must be identified, and the difference between the curves must be integrated over the provided time interval.
Finding the points of intersection by setting the two equations equal to each other:
[tex]e^{-0.3x[/tex] = 2.2x + 1
After graphing the two equations, we find that they intersect at approximately (0.380, 1.836) and (1.847, 5.080).
We can now find the area by integrating the difference between the curves across the given range [0, 2].
To get the area between two curves, use the following formula:
Area = ∫(upper curve - lower curve) dx
Area = ∫(2.2x + 1 - [tex]e^{-0.3x[/tex] ) dx
Solving,
Area ≈ 2.496
Hence the area between the curves y = [tex]e^{-0.3x[/tex] and y = 2.2x + 1 from x = 0 to x = 2 is approximately 2.496 square units.
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Can someone help with measuring mass
the question is
1 . Compare the following measurements and insert <,> or = symbol.
4.5 kg ______ 150 cm
Answer: 4.5 km>150 cm
Step-by-step explanation:
I think you meant km, because kilograms are not compatible with cm, unless it's kg/m to g/cm.
Kilometers are units of measurement, and so are centimeters, so It'd be accurate only then.
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The exact value of the expression is -05
How to determine the valueTo determine the value, we need to know the conversion formula for radians to degrees
We have that;
1 radian = 57.2958 degrees
If the value of the radian is in terms of pie, we have that;
π radians = 180 degrees
Then, from the information given, we have that;
if π radians = 180 degrees
-10π/3 = x
x = -1800π/3 × 1/π
Divide the values, we get;
x = -600
Now, substitute the value into the cosine identity, we have;
cos(-600)
determine the value, we get;
-0.5
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