The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).
Expanding the determinant using the first row, we get:
| a b c 7d + a 7e + b 7f + c g h i|
= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|
= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|
Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:
| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|
= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|
= -7e bi + gh - bhf + chi
|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|
= 7e ac - gci + chd - ahf
|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|
= -7e ab + ghi - bgd + aef
Substituting these expressions back into the expanded determinant and simplifying, we get:
| a b c 7d + a 7e + b 7f + c g h i|
= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)
= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi
= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)
Since |a b c d e f g h i| = 5, we have:
abe + bdf + cfg - aef = 5
Therefore, we can simplify the expression further:
| a b c 7d + a 7e + b 7f + c g h i|
= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)
= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)
Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).
Learn more about determinant
https://brainly.com/question/14083225
#SPJ4
The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.
First, factor out the 7 from the second row:
| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|
Expand the second row using the property of determinants that allows us to break up a row sum:
7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)
Now, use the property of determinants that allows us to switch rows and multiply by -1:
7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)
Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which
gives us:
7(| a b c d g h i| + | a b c e g h i| - 5)
Finally, multiply 7 by the expression inside the parentheses:
7| a b c d g h i| + 7| a b c e g h i| - 35
So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.
for such more question on expression
https://brainly.com/question/1859113
#SPJ11
The value of a painting rises from $120,000 to $192,000.
Work out the percentage increase in the value of the painting.
Step-by-step explanation:
Traders have invested $ 100,000 in the Peace Garden Center to boost the capital Mogadishu and make a profit. looga farm income to make people come to the door to take the free tickets for different values $ 0.8 adults and 0.6 children. As many as 150 tickets were sold on Friday for $ 102. produce more child tickets than adult tickets?
A scale drawing of a famous statue uses a scale factor of 260:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue? 261.2 feet 312.0 feet 216.7 feet 258.8 feet
A scale factor of 260:1, if the height of the scale drawing is 1.2 feet, the actual height of the statue is 312.0 feet. This is calculated by multiplying the height of the drawing by the scale factor.
The actual height of the statue, we need to scale up the height of the drawing using the given scale factor of 260:1.
The height of the drawing is 1.2 feet, we can calculate the actual height of the statue by multiplying the height of the drawing by the scale factor:
1.2 feet * 260 = 312 feet
Therefore, the actual height of the statue is 312.0 feet.
Learn more about scale:
https://brainly.com/question/32457165
#SPJ11
Ferdinand is playing golf. He hits a shot off the tee box that
has a height modeled by the function h(t) = –16t2 + 80t,
where h(t) is the height of the ball, in feet, and t is the time
in seconds it has been in the air. The graph that models
the golf ball's height over time is shown below.
When does the ball reach its maximum height?
What is the maximum height of the ball?
Answer:
Maximum height of the ball = 100 m
Time to reach the maximum height = 2.5 seconds
Step-by-step explanation:
Function that models the height h(t) of the ball and time 't',
h(t) = -16t² + 80t
Convert this equation into vertex form,
h(t) = -16(t²- 5t)
= -16[t² - 2(2.5t) + (2.5)² - (2.5)²]
= -16[[t² - 2(2.5t) + (2.5)²] + 16(2.5)²
= -16(t - 2.5)² + 16(6.25)
= -16(t - 2.5)² + 100
By comparing this equation with,
g(t) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola.
Vertex of the given parabola will be → (2.5, 100)
Therefore, maximum height of the ball = 100 m
Time taken by the ball to reach the maximum height = 2.5 seconds
Easy question!!! 1. Which statement is true?
All quadrilaterals are rectangles.
All quadrilaterals are squares.
All rectangles are quadrilaterals.
All quadrilaterals are parallelograms.
Answer:
All quadrilaterals are squares. All rectangles are quadrilaterals.
All quadrilaterals are parallelograms.
Step-by-step explanation:
A plot of corn is 8 1/2 yards wide. It is 9 1/4 times as long as it is wide. How long is the plot of corn?
Answer:
\(78 \frac{5}{8} \)
Step-by-step explanation:
\(for \: the \: width = 8 \tfrac{1}{2} \\ = \frac{17}{2} \\ sine \: the \: width \: is \: 9 \frac{1}{4} a \: long \\ 9 \ \frac{1}{4} = \frac{37}{4} \\ lenht \: of \: the \: plot = \ \frac{17}{2} \times \frac{37}{4} = \frac{629}{8} = 78 \ \frac{5}{8} \\ it \: will \: be78 \ \frac{5}{8}long \)
5) Please solve the following equation for x
5x2 +4= -41
Answer:
\(x= 3i, -3i\)
Step-by-step explanation:
please mark me brainliest :)
Given: g(x) = Vx – 4 and h(x) = 2x - 8.
What is g(h(10))?
2V2
VG
* V6 - 8
* 2V6 - 8
Answer:
\( 2\sqrt{2} \)
Step-by-step explanation:
\( g(x) = \sqrt{x - 4} \)
\( h(x) = 2x - 8 \)
\( h(10) = 2(10) - 8 = 12 \)
\( g(h(10)) = g(12) = \sqrt{12 - 4} \)
\( g(h(10)) = \sqrt{8} = 2\sqrt{2} \)
Answer: \( 2\sqrt{2} \)
Answer:
2 square root 2
Step-by-step explanation:
I really need help thank you so much
Jose invested $8,000 in an account paying an interest rate of 7 3 8 7 8 3 % compounded daily. Adam invested $8,000 in an account paying an interest rate of 7 7 8 7 8 7 % compounded annually. To the nearest dollar, how much money would Jose have in his account when Adam's money has tripled in value?
Answer:
Jose would have accumulated $23,325.21
Step-by-step explanation:
Giving the following information:
The interest rates are not clear. If they are not correct, replace them in the formulas.
Jose:
Initial investment= $8,000
Interest rate= 7.38 compounded daily.
Adam:
Initial investment= $8,000
Interest rate= 7.78% compounded annually.
Future value= 8,000*3= 24,000
First, we need to calculate the time required for Adam to triple its investment.
n= ln(FV/PV) / ln(1+i)
n= ln(24,000/8,000) / ln(1.0778)
n= 14.66 years
It will take Adam 14.66 years to triple the investment.
Now, the future value for Jose:
FV= PV*(1+i)^n
PV= 8,000
i= 0.0738/365= 0.0002
n= 14.66*365= 5,351 days
FV= 8,000*(1.0002^5,351)
FV= $23,325.21
Jose would have accumulated $23,325.21
Answer:
$23294
Step-by-step explanation:
im smart
deltamath gang
Mrs. Espinoza is renting an inflatable bounce house for her kids. The table shows the total amount she will be charged for a given number of hours it is rented. Which equation represents t, the amount of money Mrs. Espinoza will pay to rent the bounce house for h hours?
Answer: The equation that represents the amount of money Mrs. Espinoza will pay to rent the bounce house for h hours is:
t = 15 + 5h
Step-by-step explanation: From the table, it can be seen that the rental cost is $15 for the first hour and $5 for each additional hour.
The rental cost t can be represented by the equation t = 15 + 5h
The first term, 15, represents the fixed cost of $15 for the first hour.
The second term, 5h, represents the variable cost of $5 for each additional hour.
So if Mrs Espinoza rents the bounce house for h hour, the cost will be 15+5h.
Labeling:
t represents the total amount that Mrs. Espinoza will pay to rent the bounce house
h represents the number of hours that Mrs. Espinoza rents the bounce house.
15 is the fixed cost of renting the bounce house for the first hour.
5 is the variable cost for each additional hour.
The equation t = 15 + 5h represents the total cost of renting the bounce house for h hours.
How do you write three consecutive even numbers?.
Three consecutive even integers can be written with difference of two.
The even integers are defined as the numbers that are completely divisible by two. The complete division means that the result of division will be zero. The even integers are always present after a gap of one number in between.
This means that there is a difference of two numbers between integers. Firstly of all, the first even number is two. Following it four. There is a gap of number that is three. Hence, to find the consecutive even integers, add number two to the number.
Learn more about even integers -
https://brainly.com/question/28185835
#SPJ4
the marks on a statistics midterm are normally distributed with a mean of 78 and a standard deviation of 6. what proportion of the class has a midterm grade of less than 75?
The proportion of the class with a midterm grade less than 75 is approximately 0.3085, or 30.85%. This means that 30.85% of the class is expected to have a midterm grade lower than 75.
We can use the cumulative distribution function (CDF) of the normal distribution to find the proportion of the class with a midterm grade less than 75.
The CDF of a normal distribution with mean μ and standard deviation σ evaluated at a point x is given by the formula:
CDF(x) = 0.5 * [1 + erf((x - μ) / (σ * √2))]
where erf is the error function.
For this problem, μ = 78 and σ = 6, and x = 75, so the CDF can be calculated as follows:
CDF(75) = 0.5 * [1 + erf((75 - 78) / (6 * √2))]
= 0.5 * [1 + erf(-0.3536)]
The value of erf(-0.3536) can be looked up in a table or calculated using a software package. The result is approximately -0.383.
CDF(75) = 0.5 * [1 + -0.383] = 0.5 * [0.617] = 0.3085
To know more on cumulative distribution function
https://brainly.com/question/15353924
#SPJ4
I don't get this question can some one please help me solve it
Answer:
3, 2
Step-by-step explanation:
In order for the equation to be equal to zero, the following must be true:
x-3 = 0 or,
x-2 = 0
Therefore the 2 solutions are x=3, x=2
What are the opposites of 7, −2.8, 3.35, and 6
1
5
? Enter the answers in respective order, each separated by comma.
Answer: your mom
Step-by-step explanation: just cause
Simplify 9/16 + 1/16 • (2_3)-1
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
9/16 + 1/16 * (2/3)^(-1)
Step 02:
we must apply the algebraic rules to find the solution
\(\frac{9}{16}+\frac{1}{16}\cdot(\frac{2}{3})^{-1}=\frac{9}{16}+\frac{1}{16}\cdot\frac{3}{2}=\frac{9}{16}+\frac{3}{32}\)\(\frac{9\cdot2+3\cdot1}{32}=\frac{21}{32}\)The answer is:
21 / 32
let the random variables x and y have a joint pdf which is uniform over the triangle with vertices at (0,0) , (0,1) , and (1,0).
The joint PDF which is uniform over the triangle with vertices is:
f(x,y) = 2, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x.
How to find x and y have a joint pdf which is uniform over the triangle with vertices?Since the joint PDF is uniform over the triangle with vertices at (0,0), (0,1), and (1,0), the joint PDF can be expressed as:
f(x,y) = c, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x,
where c is a constant that ensures that the total probability over the entire region is equal to 1. To find c, we can integrate the joint PDF over the entire region:
\(\int \int f(x,y)dydx = \int ^1_0 \int _0^{(1-x)} c dydx\)
\(= \int ^1_0 cx - cx^2/2 dx\)
= c/2
Since the total probability over the entire region must be equal to 1, we have:
∫∫f(x,y)dydx = 1
Thus, we have:
c/2 = 1
c = 2
Therefore, the joint PDF is:
f(x,y) = 2, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x.
Learn more about joint PDF
brainly.com/question/31472458
#SPJ11
Find the measure of each missing angle.
The measure of angles are:
3. <1 = 63, <2= 49, <3= 87, <4= 44
4. <1= 52, <2= 79, <3= 38
What is Angle Sum property?The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments. When the values of the other two angles are known, one can utilise the angle sum property to determine the measure of an unknown interior angle.
3. <3 + 93=1 80 (linear pair)
<3 = 87
<2 = 49 (Vertical opposite angle)
<3 + <4 + 49= 180 (Angle sum property)
87 + <4 + 49= 180
<4 = 44
and, <2 + <1 + 68= 180 (Angle sum property)
49+ <1 + 68= 180
<1 = 63
4. <3 = 38 (alternate interior angle)
<2 + <3 + 63= 180 (Angle sum property)
38+ <2 + 63= 180
<2 = 79
and, <1 + 90 + 38= 180 (Angle sum property)
<1= 52
Learn more about Angle sum property here:
https://brainly.com/question/4316040
#SPJ5
Can someone please help me with these pleaseeeee
Nesesito ayudaaaaa ¿Cuanto es (-6)+4=
What Is 1+1
Whats Is Pie divided by 6 times 48 + 1400 divided by 1300 = what????
Prty please help me! WILL MARK BRAINLIEST IF ANSWERED CORRECTLY!
Answer:
Volume of prism: 5,400 cubic feet
Volume of pyramid: 1,800 cubic feet
Volume of composite figure:
3,600 cubic feet
Step-by-step explanation:
Volume of prism:
\(30 \times 12 \times 15 = 5400\)
Volume of pyramid:
Area of base: 30 × 12 = 360 square feet
Height: 15 feet
\( \frac{1}{3} (30 \times 12 \times 15) \)
\( \frac{1}{3} \times 5400 = 1800\)
Volume of composite figure:
\(5400 - 1800 = 3600\)
3,600 cubic feet
3/5 divided by 2 1/2
Step-by-step explanation: To divide mixed numbers, first rewrite the mixed numbers as improper fractions.
So here, 3/5 is already a fraction and 2 and 1/2 can be written as 5/2.
Remember that dividing by a fractions means the same thing
as multiplying by the reciprocal of that fraction.
In other words, 3/5 ÷ 5/2 can be rewritten as 3/5 · 2/5.
Finally, multiplying across the numerators and the
denominators, we have 6/25.
The result of the division of 3/5 divided by 2 1/2 is: 6/25.
Here, we have,
given that,
3/5 divided by 2 1/2
To divide mixed numbers, first rewrite the mixed numbers as improper fractions.
So here, 3/5 is already a fraction and 2 and 1/2 can be written as 5/2.
Remember that dividing by a fractions means the same thing
as multiplying by the reciprocal of that fraction.
In other words, 3/5 ÷ 5/2 can be rewritten as 3/5 · 2/5.
Finally, multiplying across the numerators and the
denominators,
we have 6/25.
To learn more on division click:
brainly.com/question/21416852
#SPJ6
How many 4 - digit numbers can be made by using digits 1 to 7 (repetition is not allowed), if the digit 4 will always be there in the number? a) 272 b) 480 c) 289 d) 270
None of the options (a) 272, (b) 480, (c) 289, or (d) 270 is the correct answer in the repetition.
What is Repetition?Repetition is a figure of speech that allows a word to be used several times in the same sentence, verse, paragraph, or stanza.
To solve this problem, we need to determine the number of possibilities for the other three digits of the 4-digit number, given that the digit 4 must be included.
First, let's consider the possibilities for the thousands digit (the leftmost digit) of the 4-digit number. Since the digit 4 must be included, we are left with 6 digits (1, 2, 3, 5, 6, 7) to choose from for this position.
Next, let's consider the possibilities for the hundreds digit (the second leftmost digit) of the 4-digit number. Since we have used one digit (4) for the thousands digit, we are left with 5 digits (1, 2, 3, 5, 6, 7) to choose from for this position.
Similarly, for the tens digit (the second rightmost digit), we have 5 remaining digits to choose from.
Finally, for the units digit (the rightmost digit), we have 4 remaining digits to choose from.
Since we are multiplying the number of possibilities for each position, the total number of 4-digit numbers that can be made using the digits 1 to 7, with the digit 4 included, is:
6 * 5 * 5 * 4 = 600
Therefore, the correct option is not among the given choices. None of the options (a) 272, (b) 480, (c) 289, or (d) 270 is the correct answer.
To learn more about Repetition from the given link
https://brainly.com/question/29008533
#SPJ4
ILL GIVE BRAINLIEST #20 please, how do I know if it’s similar or not? Is it similar
Answer:
Step-by-step explanation:
20.
itis not similar as ratio of corresponding sides is not equal.
4/2=2
6/4=3/2
8/6=4/3
2≠3/2≠4/3
Compute the distance between the two points. (3, 7) and (0, 0)
Answer: √58 or about 7.6
Step-by-step explanation:
use the distance formula: √((x1 - x2)² + (y1 - y2)²)
√((3 - 0)² + (7 - 0)²)
√((3)² + (7)²)
√(9 + 49)
√58
hope this helps!
Answer:
about 7.6
Step-by-step explanation:
right on edge 2021
in testing a hypothesis from a random sample involving three or more means, the appropriate test would be a one-way anova. True or false?
A stock just paid a dividend of $1.55. The dividend is expected to grow at 26.56% for three years and then grow at 3.42% thereafter. The required return on the stock is 14.40%. What is the value of the stock?
Here, we are supposed to find the value of the stock. Let's begin by determining the expected dividends: Expected dividends1st year dividend (D1)
= $1.55(1 + 26.56%)
= $1.96Second-year dividend (D2) = $1.96(1 + 26.56%) = $2.48Third-year dividend (D3)
= $2.48(1 + 26.56%)
= $3.
= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4...∞Where r
= required rate of return Let us substitute the values now PV of the future dividends
= $1.96/(1 + 14.40%)^1 + $2.48/(1 + 14.40%)^2 + $3.14/(1 + 14.40%)^3 + $3.25/(1 + 14.40%)^4...∞PV of the future dividends = $1.96/1.1440^1 + $2.48/1.1440^2 + $3.14/1.1440^3 + $3.25/1.1440^4...∞PV of the future dividends
= $1.72 + $1.92 + $2.04 + $1.86...∞PV of the future dividends
= $7.54We know that the value of the stock is the present value of the expected dividends, so we can calculate it as follows: Value of the stock
= PV of the future dividends Value of the stock
= $7.54
To know more about future visit:
https://brainly.com/question/1621783
#SPJ11
we can extend our defintion of the average value over a continous function to an infinite interval by defining the average value f on the interval [0, infinity) to be
We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\) .
The definition of the average value of a continuous function f(x) can be expanded to include the infinitely long interval [a,∞] as follows:
\(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)
Let's assume that f(x) is any continuous function. Assume that the integral \(\int\limits^i_0 {f(x)} \, dx\) is divergent and that f(x)≥0 in the range [a,∞].
Show that, if this limit exists, \(f_{ave} = \lim_{x \to \infty} f(x)\) .
Hence, We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\) .
To learn more about continuous function here:
https://brainly.com/question/21447009
#SPJ4
based on the graph below, what is the total number of solutions
Answer: Three
Step-by-step explanation: The equations touch each other 3 times on the graph, therefore there are three solutions
Do larger sample sizes increase the certainty of the statistical test? why or why not?
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results.
larger sample sizes generally increase the certainty of the statistical test. This is because larger samples provide more information and reduce the likelihood of chance variations affecting the results. The estimated parameter becomes more stable and accurate with a larger sample size. Additionally, larger sample sizes allow for the detection of smaller effect sizes and greater statistical power. However, it is important to note that sample size alone does not guarantee the validity of the statistical test. Other factors such as sampling methods, data quality, and appropriate statistical analysis must also be considered.
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results. Additionally, larger sample sizes decrease the margin of error and increase the statistical test's power, allowing for better detection of true differences or relationships in the population. Overall, larger sample sizes lead to more reliable and valid conclusions in statistical tests.
To know more about statistics visit :
https://brainly.com/question/15525560
#SPJ11