X1 – 5 x2 + x3 = 2 - 3 x1 + x2 + 2 x3 = 9 - X1 – 7 x2 + 2 x3 = -1 Solve the system of linear equations by modifying it to REF and to RREF using equivalent elementary operations. Show REF and RREF of the system. Matrices may not be used. Show all your work, do not skip steps. Displaying only the final answer is not enough to get credit.

Answer: y+7=0 x(x-8)

Step-by-step explanation:

.

The correct expression which can be used to find AC is,

⇒ 7.8 (cos 23°)

We have to given that;

A triangle ABC shown in figure.

Now, We can formulate;

cos 23° = AC / AB

cos 23° = AC / 7.8

AC = 7.8 (cos 23°)

Thus, The correct expression which can be used to find AC is,

⇒ 7.8 (cos 23°)

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

648=7

Step-by-step explanation:

Answer:

The values included in a box plot are,

The third quartile

the second quartile

the smallest value

(the standard deviation can be approximated but it is not 'given' as such)

Step-by-step explanation:

In the box plot, The minimum, maximum, 1st and 3rd quartiles, and the median(2nd quartile) are included.

So we can answer the given question.

Answer:

so we know that we're starting with $2500. We know it's compound a continuous interest, and they tell us that the interest rate is 6% and we want to find the amount of time it's going to take for it to basically double because it says 5000. So we divide both sides by five Excuse me by 2500 and we end up with E to the 0.6 T is equal to two. We can take the natural log of both sides mhm, and we can use a log of a powers at this point. Oh, 60 can come down in front with log of a power and lo and behold Oh, my goodness, Ellen up e is one. So all we need to do to solve is divide both sides by 0.6, and that will give us our time. We need to round that off to the nearest 10th of a year. So Ln of two divided by 20.6 11.6 11.55 But to the nearest Tampa would be 11.6 years. And we are done. Mm hmm.

Step-by-step explanation:

The boat should travel 12 kilometers in 3 hours. The solution has been obtained by using unitary method.

What is a unitary method?

In the unitary approach, the value of a single unit is estimated before the value of the required number of units is established. Simply expressed, the unitary technique is used to calculate the value of a single unit given a multiple.

We are given that the boat covers total distance of 20 kilometers during the 5-hour tour.

This means that

Distance = 20 kilometers

Time taken = 5 hours

So, using unitary method,

Distance covered in 1 hour = 20/5 = 4km

Distance covered in 3 hours = 4*3 = 12 kilometers

Hence, the boat should travel 12 kilometers in 3 hours.

Learn more about unitary method from the given link

brainly.com/question/28731562

#SPJ1

The family of all linear equations that are parallel to y=-1/2x-2 is defined as:

y = (-1/2)*x + b

Such that b ≠ -2.

We know that a general linear equation is written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

We know that two linear equations are parallel if and only if the lines have the same slope and a different y-intercept.

So the family of lines parallel to:

y = (-1/2)*x - 2

Are of the form:

y = (-1/2)*x + b

Where b ≠ -2.

All these lines are parallel to the given ones.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

3/4 cups of sugar

Step-by-step explanation:

So we know that 1/8 cup of sugar is for 1/3 OF a recipe.

So if we want the full recipe we jsut have to multiply 1/8 by 3 since its only worth 1/3 of the recipe.

You’ll get 3/8 cups of sugar for a whole recipe. The question asks for 2 full recipes and since we already know it takes 3/8 cups for one we can multiply that by 2 to find the amount of sugar needed for 2 full recipes.

You’d get 6/8 cups of sugar.

Simplified: 3/4

Answer:

32/675x+65

Step-by-step explanation:

well set it up as 35 dividing all the other numbers. Then multiply 15 and 46 to get 675x+65

    1)    32                            2)     45 x 2^5              3)

          -----   x  45  +  65                ---------                        3^2-1  x  2^5+65

          15                                         3 x 5

     4)                                5)                        

           96+65                            161

The number of cans of cat food needed for different numbers of cats may vary based on factors such as the size of the cats, their dietary requirements, and the type of cat food being used.

However, as a general estimate, I can provide you with a rough guideline:

For 1-5 cats: It is typically recommended to provide approximately 1 can of cat food per cat per day. So, for 1-5 cats, the shelter would need around 7 cans per week (1 can x 5 cats x 7 days).

For 6-10 cats: Following the same guideline, the shelter would require around 42 cans per week (1 can x 8 cats x 7 days).

For 11-15 cats: The shelter would need approximately 77 cans per week (1 can x 13 cats x 7 days).

These estimates are based on a daily feeding of canned cat food. The specific dietary needs of the cats and the type of food being used may require adjustments to the quantities. It's always best to consult with a veterinarian or a professional shelter worker to determine the exact requirements for the cats in your care.

To learn more about factors

https://brainly.com/question/28230573

#SPJ11

Answer:

D) (9 , 5)

Step-by-step explanation:

y = x - 4

Substitute x = 9 value in the equation

y = 9 - 4 = 5

We got the y value as 5

So, (9,5) is the pair generated by the equation

Answer:

D. (9, 5)

Step-by-step explanation:

y = x - 4

A. (9, 13)

B. (11, 44)

C. (11, 15)

D. (9, 5)

If you plot this on a graphing calculator, such as Desmos, you'll see that only D. (9, 5) is on the line of y=x-4

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probability is expressed as

Number of favorable outcomes/total number of possible outcomes

From the information given,

Total number of outcomes = 16

Starting from 1, the multiples of 3 between 1 and 16 are 3, 6, 9, 12 and 15

This means that the number of favorable outcomes is 5

Therefore, the probability that the card has a multiple of 3 on it is

5/16 = 0.3125

The inverse demand function of the given demand function is p = 50 - q/2.

A graph that depicts the relationship between a product's price and demand is called a demand curve. On a demand graph, the horizontal axis represents the amount desired, while the vertical axis represents the product's price.

The price is a function of the quantity required when there is an inverse demand curve. The inverse of a demand curve indicates that variations in the amount required cause changes in price levels. The formula for calculating the demand curve for a product yields the graph of an inverse demand curve.

Given demand function: q = 100 - 2p.

To find the inverse demand function, we find the inverse of the equation, by isolating p, to get:

q = 100 - 2p,

or, 2p = 100 - q,

or, p = 100/2 - q/2,

or, p = 50 - q/2.

Thus, the inverse demand function of the given demand function is p = 50 - q/2.

Learn more about inverse functions at

https://brainly.com/question/3831584

#SPJ4

To calculate the linear demand function, we need to determine the values of "a" and "b" in the equation Q(P) = a - bP, where Q(P) represents the quantity demanded at a given price.

First, let's find the value of "a." We know that when the price was $17, the average quantity sold was 2,108 mugs. Substituting these values into the equation, we have:

2,108 = a - b(17)

Next, let's find the value of "b." We now have a second data point: when the price increased to $24, the average quantity sold dropped to 1,632 mugs. Substituting these values into the equation, we have:

1,632 = a - b(24)

Now, we have a system of two equations:

2,108 = a - 17b
1,632 = a - 24b

We can solve this system of equations to find the values of "a" and "b." Subtracting the second equation from the first, we get:

476 = 7b

Dividing both sides by 7, we find:

b = 68

Now, we can substitute the value of "b" into either equation to solve for "a." Let's use the first equation:

2,108 = a - 17(68)

2,108 = a - 1,156

Adding 1,156 to both sides, we find:

a = 3,264

Therefore, the linear demand function for the pumpkin shaped coffee mugs is:

Q(P) = 3,264 - 68P

To learn more about demand function, visit here:

https://brainly.com/question/28198225

#SPJ11

Answer:

Step-by-step explanation:

54 equals 9 more than a number

So if we do this, we get

54 = x+9

x+9 = 54

54-9=x

54-x = 9

Answer:

Step-by-step explanation:

You have to do the opposite of the firs t one. You are going to add 5 to the four to get

p = 9. There is your answer!  Add on both sides!

Answer:

add 5 to both sides of the equal sign

Step-by-step explanation:

the answer will be p=9

If Chris bought 5 tacos and 2 burritos for $13. 25 and  Brett bought 3 tacos and 2 burritos for $10. 75, the price of one taco is $1.25, and the price of one burrito is $3.50.

Let the price of one taco be T and the price of one burrito be B. We have the following equations:

5T + 2B = $13.25
3T + 2B = $10.75

To find the prices of the taco and the burrito, we can use the system of equations. First, subtract the second equation from the first equation:

(5T + 2B) - (3T + 2B) = $13.25 - $10.75
2T = $2.50

Now, divide by 2 to find the price of one taco:

T = $1.25

Next, plug the value of T back into one of the equations (let's use the second equation):

3($1.25) + 2B = $10.75
$3.75 + 2B = $10.75

Now, subtract $3.75 from both sides:

2B = $7.00

Finally, divide by 2 to find the price of one burrito:

B = $3.50

So, the price of one taco is $1.25, and the price of one burrito is $3.50.

More on price: https://brainly.com/question/23747357

#SPJ11

If a scatterplot shows a non-linear relationship between the response and explanatory variable, several options can be considered depending on the purpose of the analysis and the nature of the data.

Here are some possible actions:

Transform the data: One common approach is to transform the data to make the relationship linear. For example, if the relationship appears to be exponential, taking the logarithm of the response variable might make it linear. Similarly, taking the square root, cube root, or inverse of one or both variables might also help.

Use a non-linear model: Another option is to fit a non-linear model that can capture the curvature in the relationship. There are many types of non-linear models, such as quadratic, cubic, exponential, logistic, or spline models. The choice of model depends on the shape of the curve and the underlying theory or hypothesis.

Resample or subset the data: If the non-linear relationship is driven by outliers, influential points, or a subset of the data, it might be helpful to resample or subset the data to remove them. For example, trimming the extreme values, bootstrapping the data, or stratifying the data by a third variable might help.

Explore alternative variables or interactions: If the non-linear relationship is due to an unobserved or omitted variable, it might be useful to explore alternative variables or interactions that could explain the pattern. For example, if the response is sales and the explanatory variable is price, adding a competitor's price or a marketing variable might improve the fit.

Use caution in interpretation: Finally, if the non-linear relationship persists after exploring the above options, it might be necessary to acknowledge the non-linearity and use caution in interpreting the results. Non-linear relationships can be more difficult to interpret and extrapolate, and the statistical inference might be more uncertain or sensitive to assumptions.

for such more question on scatterplot

https://brainly.com/question/28605735

#SPJ11

Answer:

Step-by-step explanation:

2)f(x) = 2x² +4x - 3    

a = 2 ; b = 4 ; c = -3

1) Put x = -1 in the equation

f(x) = 2*(-1)² + 4*(-1) -3 = 2 - 4 -3 = -5

Vertex = (-1,-5)

2) Upward

3) Minimum

4) axis of symmetry = -b/2a = -4/2*2=-4/4= -1

x = -1

5) domain: all real numbers  (-∞ ,∞)

Range : y ≥ -5 ; [-5 , ∞)

3) f(x) = 3x² - 6x + 4

Vertex : (1,1)

Opening : upward

Minimum

Axis of symmetry: x = 1

Domain: all real numbers

Range: y ≥ 1 ; [1, ∞)

4)f(x) = -x² - 2x - 3

a) Vertex:  f(x) = -(-1)² - 2*(-1) - 3 = -1 + 2 - 3 = -2

Vertex( -1,-2)

b) downward

c) Maximum

d) Axis of symmetry: x = 2/-2 = -1  

x = -1

e) Domain: all real numbers

Range: y ≤ -2 ; (-∞ , -2]

5)f(x) = 2(x -2)²

a) Vertex: (2, 0)

b) Opening: upward

c) Minimum

d) x = 2

e)Domain: all real numbers

Range: y ≥ 0 ; [0,∞)

Answer:

C. -3/4, -2/3, 1/5

Step-by-step explanation:

Just from observation, you can tell the 1/5 will be the greatest because all the other fractions are negative. Then, I converted them to decimal form to make it easier.

-2/3 = -0.6666666 (the 6 goes on forever)

-3/4 = -0.75

1/5= 0.20

Then, you put them in order.

-3/4 would be the least .

Followed by, -2/3

Finally, 1/5

the probability that fewer than three of the selected adults watch prime-time live is  0.004672

Let X denote the mumber of adults watching prime-time TV inve.

Then X olows a Binomial with n=7 and p= 08.

. P(X=x)-nC.p"(1-p)* = 7c, (0.8y (0.2)**, (x =0,12,3,..7)

(a) PX=2) =7C,(0.8(02) =0.0043008

() P(X-1)-7C,(0.3) (0.2) =00003584

(c) P(X <3)- P(X =0)+P(X =1)+P(X -2)

- 7C,(0.8 (0.2) -0.0003584-0.0043008

= 0.004672

(d) Noe that P(X =2)=0.0043008 <0.05.

Thus, it is unusually low.

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

Answer:

25

Step-by-step explanation:

25 students total.

3/5 = 15 (Girls)

2/5 = 10 (Boys)

Answer:

25 students in total..........

1. Change both numbers to common base.

2. Use quotient rule \(a^x \div a^y = a^{x-y}\)

e)

You can write 9 as 3², then both numbers have the same base.

\(9^x = (3^2)^x = 3^{2x}\), where x is the exponent

I cannot really see the exponents because picture is bad quality.

\(9^x \div 3^y =\)

\(= (3^2)^x \div 3^y =\)

\(=3^{2x} \div 3^y =\)

\(= 3^{2x-y}\)

You want to replace x and y with actual numbers, but as I said the picture is too bad.

f)

Convert to base 4, then quotient rule.

g)

Use the quotient rule, you already have same base.

h)

Convert to base \(\frac{2}{3}\), then quotient rule.

According to the statement the simplest pos expression of f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15)  = wxyz + wxy'z + wx'yz + wx'y'z

To find the simplest pos expression of f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15) using K-maps, we first need to create the K-map for f. The K-map for this function has four variables, w, x, y, and z, with each variable representing one column or row in the K-map. We then fill in the cells corresponding to the eight minterms given in the question, as shown below:
   z\wy 00 01 11 10
   0    1  1  1  1
   1    1  1  1  1
Next, we group the adjacent cells with the value 1 to form groups of 2, 4, or 8 cells. In this case, we have one group of 8 cells, two groups of 4 cells, and one group of 2 cells. These groups correspond to the following pos expression:
f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15) = wxyz + wxy'z + wx'yz + wx'y'z
This is the simplest pos expression for the given function, as it uses only four terms, which is the minimum number required to represent all eight minterms. In other words, any further simplification would result in a longer expression that does not provide any additional benefit.

To know more about expression visit :

https://brainly.com/question/20314344

#SPJ11

Therefore, the value of q(α) is 0.

Let p(x) = x³ + ax² + bx + c be a polynomials with distinct roots α, β, and γ, where α, β, and γ are real numbers and α, β, and γ are also roots of another polynomial q(x)

.To find: the value of q(α).

Given:p(x) = x³ + ax² + bx + c

has three distinct roots α, β, and γ such that α, β, and γ are real numbers and α, β, and γ are also roots of q(x).

The root of p(x) are:

α, β, and γThe root of q(x)

are:α, β, and γ

Since α, β, and γ are the roots of q(x),

we have:q(x) = (x - α) (x - β) (x - γ) ... (1)

Let's evaluate q(α) using equation (1)

q(α) = (α - α) (α - β) (α - γ)q(α) = 0

(Since α, β, and γ are distinct)

Therefore, the value of q(α) is 0. Hence, the correct option is (D).

for more such question on polynomials

https://brainly.com/question/4142886

#SPJ11

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

The value of circumferences of both circles to the nearest hundredth are 28.27 ft and 44ft.

Since, We know that;

The circumference of a form is the space surrounding its edge. Find the circumference of various forms by summing the lengths of their sides.

Given two coincide circles, the Radius of the smaller circle is 4.5ft.

Since the diameter is 9 ft.

Since, the bigger circle is 2.5 ft wider than the smaller circle,

Thus, the radius of the bigger circle = 4.5 + 2.5

Hence, the radius of the bigger circle = 7

From the formula for the circumference of a circle:

Circumference = 2π × radius

Thus,

The circumference of the yellow(bigger) circle is about = 2 x pi x 7

The circumference of the yellow(bigger)  circle is about = 44 ft

The circumference of the purple(smaller) circle is about = 2 x pi x 4.5

The circumference of the purple(smaller) circle is about = 28.274 ft

therefore, The circumference of the yellow circle is about 44 ft. The circumference of the purple circle is about 28.27ft.

Learn more about circumference here:

brainly.com/question/6465134

#SPJ1

The Circumference of the yellow circle is about 44 ft.

The circumference of the purple circle is about 28.27ft.

We have,

Radius of the smaller circle is 4.5ft

and radius of the bigger circle = 4.5 + 2.5 = 7 ft

Now, Circumference of Bigger circle (yellow) = 2 x π x r

= 2(3.14)(7)

= 44 ft

and, Circumference of Smaller circle (Purple) = 2 x π x r

= 2(3.14)(4.5)

= 28.274 ft

Learn more about circumference here:

brainly.com/question/6465134

#SPJ1

Yes, the wait time significantly decreased after implementing the new system, based on hypothesis testing.

To determine if the wait time has significantly decreased, we can conduct a hypothesis test using the one-sample t-test. The null hypothesis, denoted as H0, is that the population mean waiting time is still 84.3 seconds, while the alternative hypothesis, denoted as Ha, is that the population mean waiting time has decreased to less than 84.3 seconds.

Let's set the significance level at α = 0.05. Since the sample size is large (n = 45), we can use the t-distribution to conduct the hypothesis test. The test statistic can be calculated as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (79.1 - 84.3) / (17.3 / sqrt(45))

t = -2.16

Using a t-distribution table or calculator with 44 degrees of freedom

(df = n - 1), the p-value for this test is found to be approximately 0.018.

Since the p-value (0.018) is less than the significance level (0.05), we reject the null hypothesis. This means we have evidence to suggest that the wait time has significantly decreased after implementing the new drive-through system.

Therefore, based on the given data, we can conclude that the wait time has significantly decreased at the fast-food restaurant after implementing the new drive-through system.

Learn more about significantly decreased

brainly.com/question/3612236

#SPJ11