Answers
The size of matrix cM is given as follows:
9 x 10.
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant c.Matrix M of dimensions 9 x 10.Hence the size of matrix cM is given as follows:
9 x 10.
(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).
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Related Questions
The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
B(t) =
(
)t
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
Answers
a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]
b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.
a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:
B(t) = [tex]100(1 + 0.002)^t[/tex]
where t is the number of months.
b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.
For each month:
B(1) = 100(1 + 0.002) = $100.20
B(2) = 100(1 + 0.002)² = $100.40
B(2)/B(1) = $100.40/$100.20 = 1.001993
The amount in the account increases by a factor of approximately 1.002 every month.
For each year:
B(12) = 100(1 + 0.002)¹² = $102.44
B(24) = 100(1 + 0.002)²⁴ = $105.01
B(24)/B(12) = $105.01/$102.44 = 1.0249
The amount in the account increases by a factor of approximately 1.025 every year.
For every five years:
B(60) = 100(1 + 0.002)⁶⁰ = $110.41
B(120) = 100(1 + 0.002)¹²⁰ = $121.20
B(120)/B(60) = $121.20/$110.41 = 1.0991
The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.
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Hey folks help me out for some points :)
Answers
Answer:
C
Step-by-step explanation:
Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.
Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.
Would like some help with this question, please.
Answers
Answer:
i believe 67 its somewhat hard to tell but the line seems to be in the middle between 150 and 140
Step-by-step explanation:
since it heats up to 212 then the person lets it cool down for 10 mins the temp goes to 145 (Answer is 67)
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:
2,14,1,2,−6
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
What is Critical value ?
In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.
To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.
Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.
Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
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What integer values of x make the statement -3/x lesser than -x/3 true?
x=0
x=2
x=3
Any interger greater than -3
Any integer less than -3
x=1
You need to choose more than 1 answer
Answers
The integer values that make the statement true are x = -3, -2, -1, 1, 2, 3
We have,
We can start by multiplying both sides of the inequality by -3x to get rid of the denominators:
-3/x < -x/3
Multiplying by -3x on both sides.
-9 < -x²
Rearranging.
x² < 9
Taking the square root of both sides.
|x| < 3
This means that x can take any integer value between -3 and 3, excluding 0.
Thus,
The integer values are x = -3, -2, -1, 1, 2, 3
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Ayudenme a resolver esos 2 problemas, son inecuaciones, ya tengo la respuesta, falta solucion
Answers
The solution set for each rational inequality:
Case 1: - 9 ≤ x < - 5
Case 3: Every real number except x = 1.
How to solve a rational inequality
In this problem we find two cases of rational inequality, whose solution sets can be found by using algebra properties and sign laws. Now we proceed to solve on each case:
Case 1
(3 · x + 7) / (x + 5) ≥ 5
(3 · x + 7) / (x + 5) - 5 ≥ 0
[(3 · x + 7) - 5 · (x + 5)] / (x + 5) ≥ 0
(- 2 · x + 18) / (x + 5) ≥ 0
- 2 · (x - 9) / (x + 5) ≥ 0
The inequality is positive for - 9 ≤ x < - 5.
Case 3
(- x² - 1) / (- x² + 2 · x - 1) > 0
[(- 1) · (x² + 1)] / [(- 1) · (x² - 2 · x + 1)] > 0
(x² + 1) / (x² - 2 · x + 1) > 0
(x² + 1) / (x - 1)² > 0
The inequality is positive for all real number except x = 1.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)
How to find the half-life of a compound
The statement indicates the decay function of a particular compound, which is an exponential function of the form:
y = a · exp(- λ · t)
Where:
a - Initial mass of the compound.λ - Decay constant, in days⁻¹.t - Time, in days.The half-life of the particular compound is determined by the following expression:
t = ㏑ 2 / λ
Where t is the half-life.
If we know that λ = 0.0736, then the half-life of the particular compound is:
t = ㏑ 2 / 0.0736
t = 9.4 days
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Select the correct answer.
Simplify the expression so there is only one positive power for each base.
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
A. 2.7^(7) * 3.8^(5)
B. 2.7^(-7) * 3.8^(5)
C. 2.7 * 3.8^(5)
D. 2.7 * 3.8
E. 2.7^(7) * 3.8
Answers
The expression can be simplified to get:
2.7^(1)*3.8^(5)
The correct option is C.
How to simplify the expression?Remember that if we have the product of two powers with the same base, we only need to add the exponents.
Then we will get:
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
= (2.7^(-3)*2.7^(4)*3.8^(2)*3.8^(3))
= (2.7^(-3 + 4)*3.8^(2 + 3))
= 2.7^(1)*3.8^(5)
That is the expression simplified, we can see that the correct option is C.
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Josh is looking for the best deal on a refrigerator that has a wholesale price of $549. Help him compare the price of the
refrigerator at two different stores by completing the following.
(a)
(b)
Josh then looks at the refrigerator in a department store that marks up the refrigerator's wholesale price 50%. But
because of a customer loyalty program, he would receive a 10% discount off the in-store price. Ignoring tax, how
much would he pay for the refrigerator at this store?
(c)
Josh goes to a superstore that marks up the refrigerator's wholesale price 40%. Ignoring tax, how much would he
pay for the refrigerator at this store?
$0
Check
Select the true statement.
O Josh would pay more for the refrigerator at the superstore.
O Josh would pay more for the refrigerator at the department store.
O Josh would pay the same amount for the refrigerator at the department store and at the superstore.
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Answers
b) Josh would pay $741.15 for the refrigerator at the department store with 10% discount.
c) The true statement is: Josh would pay more for the refrigerator at the superstore.
(b) If the department store marks up the wholesale price of the refrigerator by 50%, then the price at the store would be:
Wholesale price + (50% x Wholesale price) = $549 + (0.5 x $549) = $823.50
If Josh would receive a 10% discount off the in-store price, then the price he would pay would be:
In-store price - (10% x In-store price) = $823.50 - (0.1 x $823.50) = $741.15
(c) If the superstore marks up the wholesale price of the refrigerator by 40%, then the price at the store would be:
Wholesale price + (40% x Wholesale price) = $549 + (0.4 x $549) = $768.60
Therefore, Josh would pay $768.60 for the refrigerator at the superstore.
Comparing the prices, we can see that Josh would pay less for the refrigerator at the department store after factoring in the discount:
Price at department store = $741.15
Price at superstore = $768.60
So the true statement is: Josh would pay more for the refrigerator at the superstore.
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Write an equation (any form) for the quadratic graphed below
Answers
Answer:
[tex]y = -2(x - 1)^2 + 3[/tex]
Step-by-step explanation:
The given figure which is a quadratic is the shape of a parabola
The general vertex form equation of a parabola is
[tex]y = a(x - h)^2 + k[/tex]
where,
( h, k ) is the vertex and a is a constant
Looking at the figure we see the vertex is at [tex](1, 3)[/tex]
So the equation of the parabola is
[tex]y = a(x - 1)^2 + 3[/tex]
To compute the constant [tex]a[/tex] take a point (x, y) through which the parabola passes, plug in these x, y values into the above equation and solve
The parabola passes through point [tex](3, -5)[/tex]
Plugging
[tex]x = 3, y = -5[/tex]
gives
[tex]- 5 = a(3-1)^2 + 3\\\\-5 = a\cdot 2^2 + 3\\\\-5 = 4a + 3\\\\-5-3=4a\\\\-8 = 4a\\\\a = -8/4 = -2\\\\[/tex]
Therefore the equation of the given quadratic(parabola) is
[tex]y = -2(x - 1)^2 + 3[/tex]
4cos45°-2sin45°. Please let me know the answer with thorough steps.
Answers
We know that cos(45) = sin(45) = √2/2.
Substituting these values, we can simplify the expression as follows:
4cos(45) - 2sin(45)
= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)
= 2√2 - √2
= √2
Therefore, the answer is √2.
Write the following Babylonian numeral as a Hindu-Arabic numeral.
<|| <<||||
Answers
Answer:
The Babylonian numeral <|| <<|||| represents the number 51 in the Babylonian numeral system.
To convert it to the Hindu-Arabic numeral system, we first need to determine the place values of the symbols. The symbol <|| represents 50 and <<|||| represents 1.
So, we can write the number as:
50 + 1 = 51
Therefore, the Hindu-Arabic numeral equivalent of the Babylonian numeral <|| <<|||| is 51.
On the axes below sketch the graph of y = 4x² + 8x +3
Label all points of intersection and the turning point in your sketch.
Answers
1. Find the vertex (turning point) of the parabola by using the formula x = -b/2a, where a = 4 and b = 8. This gives x = -1, which is the x-coordinate of the vertex. To find the y-coordinate, substitute x = -1 into the equation: y = 4(-1)² + 8(-1) + 3 = -1.
2. Plot the vertex at the point (-1, -1).
3. To find the x-intercepts, set y = 0 in the equation and solve for x. This gives x = (-8 ± √(8² - 4(4)(3)))/(2(4)) = (-8 ± √16)/8 = -1/2 or -3. Plot these points on the x-axis.
4. To find the y-intercept, set x = 0 in the equation and solve for y. This gives y = 3, so the y-intercept is at the point (0, 3).
5. Since the coefficient of x² is positive, the parabola opens upwards. Sketch the curve passing through the points found above.
6. Label the points of intersection and the turning point on the graph.
Mrs. Hopkins gives her students a math quiz every 8 and a science quiz every 6 days. If she gives math and science quizzes today, how many days will it be before both quizzes are given on the same day again?
Answers
Therefore , the solution of the given problem of unitary method comes out to be once more administer maths and science quizzes on the same day.
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
List the multiples of each integer until we discover a common multiple as one method to determine the least common multiple:
=> 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are all multiples of 8.
=> 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60 are multiples of 6.
As an alternative, we can use the prime factorization technique to identify the smallest common multiple:
=> 8's prime factors are 2 x 2 x 2
=> 6's prime factors are 2 x 3
=> 2 x 2 x 2 x 3 = 24
We can see that 24 is the smallest common multiple once more, and in 24 days,
Mrs Hopkins will once more administer maths and science quizzes on the same day.
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With workings, please help
Answers
Answer:
it's 4 cm
Step-by-step explanation:
A. Square = 50 cm²
A. Square = s × s
50 = s²
s = √50
SP = hypotenuse (c) = s
c = s = √50
b = √34
a = PT = ...?
use Pythagorean theorem to find PT
a² + b² = c²
a² + (√34)² = (√50)²
a² + 34 = 50
a² = 50 - 34
a² = 16
a = √16
a = 4 cm
#CMIIWHow much money should Be deposited today in an account that earns 10.5 percent compounded monthly so that it will accumulate to $22,000 in four years
Answers
Answer:
$12,276.24
Step-by-step explanation:
22000 / (1 + 0.105/12)^4*12
12276.24
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we want to find the present value P that will accumulate to $22,000 in four years at an annual interest rate of 10.5% compounded monthly (i.e., n = 12). Therefore, we have:
A = $22,000
r = 0.105/12 (monthly interest rate)
n = 12
t = 4
Substituting these values into the formula and solving for P, we get:
P = A/(1 + r/n)^(nt) = $22,000/(1 + 0.105/12)^(12*4) ≈ $14,005.70
Therefore, the amount that should be deposited today in the account is approximately $14,005.70.
3^-1/2 x^1/2
express with radical signs instead of fractional exponents. rationalize the denominator.
please help
Answers
Answer:
[tex]\sqrt{x/3}[/tex]----------------------
Use the following identities:
[tex]a^{-b}=1/a^b[/tex][tex]a^{1/2}=\sqrt{a}[/tex][tex]a^bc^b=(ac)^b[/tex]Apply the identities to the given expression:
[tex]3^{-1/2}x^{1/2}=(3^{-1}x)^{1/2}=(x/3)^{1/2}=\sqrt{x/3}[/tex]Use mathematical induction to prove 2^n>=2n is true for all positive integers.
Answers
By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
The given inequality is 2ⁿ≥2n.
Let n = 1
2^1 ≥ 2^1
2 ≥ 2 which is true
Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.
We need to prove that 2^(k+1) ≥ 2^(k+1)
2^(k+1) ≥ 2*2^k (by the inductive hypothesis)
2^(k+1) ≥ 2*2^(k+1)
2^(k+1) ≥ 2^(k+1) which is true
Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
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Which fraction is a multiple of 1/9?
Answers
Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
Here, we have,
To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.
We have,
Multiple of fraction is the number which is n times of the original function. Here can be any whole or fraction number.
The given number in the problem is the fraction number which is,
The above number is the unit fraction.
Unit fraction-
Unit fractions are the fraction in which the value of numerator is 1.
The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,
1/9 = 2/9, 3/9, 4/9,5/9 .......so on.
Hence the multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
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Describe the graph proportional relationship represented by the equation y=5.5x
Answers
A box in the shape of a right rectangular prism has a length of 8.5 inches, a width of 4.5 inches, and a height of 3.75 inches, What is the volume, in cubic inches, of the box?
Answers
The volume of the prism is 143.44 in³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces.
The general formula for the volume of a prism is expressed as;
V = base area × height
The prism is a rectangular prism, therefore the volume will be calculated as
V = l× w × h
where l is the length of the base and w is the width of the base
V = 8.5× 4.5 × 3.75
V = 143.44 in³
therefore the volume of the rectangular prism is 143.44 in³
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A subscription to a live streaming program normally costs $29 but is on sale for 25% off. An 8% tax is added at checkout. What is the total cost?
$7.25
$21.75
$23.49
$39.15
Answers
A subscription to a live streaming program normally costs $29 but is on sale for 25% off. An 8% tax is added at checkout then the total cost is $23.49.
To calculate the total cost, first, we find the discounted price of the subscription. A 25% discount on $29 is calculated by multiplying $29 by 0.25 (25% as a decimal), which gives us a discount of $7.25. Subtracting the discount from the original price, we get the discounted price of $29 - $7.25 = $21.75.
Next, we need to add the 8% tax to the discounted price. To calculate the tax amount, we multiply $21.75 by 0.08 (8% as a decimal), which gives us $1.74. Adding this tax amount to the discounted price, we get the total cost as $21.75 + $1.74 = $23.49.
Step 1: Calculate the discount amount:
Discount = 25% of $29
Discount = 0.25 * $29
Discount = $7.25
Step 2: Find the discounted price:
Discounted Price = Original Price - Discount
Discounted Price = $29 - $7.25
Discounted Price = $21.75
Step 3: Calculate the tax amount:
Tax Amount = 8% of Discounted Price
Tax Amount = 0.08 * $21.75
Tax Amount = $1.74
Step 4: Calculate the total cost:
Total Cost = Discounted Price + Tax Amount
Total Cost = $21.75 + $1.74
Total Cost = $23.49
So, the total cost after applying the 25% discount and adding an 8% tax at checkout is $23.49.
- Discount = 0.25 * $29 = $7.25
- Discounted Price = $29 - $7.25 = $21.75
- Tax Amount = 0.08 * $21.75 = $1.74
- Total Cost = $21.75 + $1.74 = $23.49
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What is the equation of the line that passes through the point ( 4 , 0 ) and has a slope of − 2?
Answers
Step-by-step explanation:
y=m(x-x1)+y1
y=-2(x-4)+0
y=2x-8+0
y=2x-8
In ΔFGH, g = 910 cm,
m∠G=98° and
m∠H=51°. Find the length of h, to the nearest 10th of a centimeter.
Answers
In ΔFGH, the length of h is 714.2 cm
Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G, and h represents the opposite side to angle H.
Consider the following figure.
Using sine rule for triangle FGH,
sin F/f = sin G/g = sin H/h
Consider equation sin G/g = sin H/h
sin(98°) / 910 = sin(51°) / h
We solve this equation for h.
h = (sin(51°) × 910)/ sin(98°)
h = (0.777 × 910)/ 0.99
h = 714.21
h = 714.2 cm
This is the required length of h.
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Who can help me with this?
Answers
The original price of this car is equal to $6,600.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
Assuming the original price is represented by the variable x, we have the following:
12.5/100 × x = x - 5,775
0.125x = x - 5,775
5,775 = (x - 0.125x)
5,775 = 0.875x
x = 5,775/0.875
x = $6,600.
In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.
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Asynchronous activity
Answers
In the triangles given the analysis for same is given below
What is the analysis of the two triangles given above?1) the corresponding vertices are
R ~ C and
E ~ 0
2) The corresponding angle are
∠E ~∠O and
∠ R ~ ∠C
3)
The corresponding sides are;
ER ~ CO;
MO ~ EM
CM ~ RM
4) the congruent angles are:
∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR
5) the congruent sides are:
ER ≅ CO;
MO ≅ EM
CM ≅ RM
6) the congruent triangles are;
ΔMER ≅ ΔMOC
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In our chapter on inverse functions, we discussed several charcteristics related to inverse functions. Asumme that you were given information that the points P(2, 4) was on the graph of a function, y. Therefore, the point Q, (___, ___) would be on the graph of y-1, the inverse function of y.
Write at least three sentences to explain how you can identify the point Q. Explain how you would find the coordinates and be sure to include the actual coordinates of point Q.
Answers
Answer: you could reflect the points (2, 4) to both axisis to find the inverse, add a negative in front of both numbers, or multiply the function by -1.
Step-by-step explanation:
Have a great night.
what is 9v+–3v+–4v–2+1 simplified
Answers
Answer:
2v-1
Step-by-step explanation:
9v+-3v+-4v-2+1
=9v-3v-4v-1
=6v-4v-1
=2v-1
A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.
Answers
Answer:
mt1= 995
mt2=975
Step-by-step explanation:
the line inside the box plot shows where the median is.
surface area of a square prism 3ft 3ft 15ft
Answers
Answer:
198 ft^2
Step-by-step explanation:
l = 3
w = 3
h = 15
2(3*3) + 4(3*15) = 18 + 180
18 + 180 = 198 ft^2