What is the product of the binomials (4a – 1) and (2b + 3)?

The estimated multiple regression equation is ŷ = 1,304 + 113x1 - 237x2 + 30x3.

In the estimated multiple regression equation, ŷ represents the predicted or estimated value of the dependent variable. The equation includes three independent variables: x1, x2, and x3, with respective coefficients of 113, -237, and 30.

The constant term is 1,304. The equation can be used to estimate the value of the dependent variable (ŷ) based on the values of the independent variables (x1, x2, x3).

The coefficients indicate the effect of each independent variable on the dependent variable, with positive coefficients indicating a positive relationship and negative coefficients indicating a negative relationship.

For more questions like Value click the link below:

https://brainly.com/question/30145972

#SPJ11

The probability of getting 5 face cards when taken without replacement is 0.00030473728.

There are 12 face cards in the deck overall.

When six cards are dealt, 12C5 equals 792.

without a replacement

P (5 face cards) = 12/5

P(5)=792 / 2598960 for five face cards.

P(5)=0.00030473728 for five face cards.

When 6 cards are picked from a deck without replacement, the likelihood of getting 6 face cards (a king, queen, or jack) is therefore 0.00030473728.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a claim is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 indicates the event's impossibility and 1 indicates its certainty.

To learn more  about probability

brainly.com/question/24756209

#SPJ4

Answer:

1/4

Step-by-step explanation:

answer key lang sakalam

#carry learning

Since the information about variable 'q' is not provided, it is not possible to determine the remainder when q is divided by 6 based on the given context.

The question states that x is a positive integer such that x ≥ 75, but it does not provide any information about the variable 'q'. Without knowledge of the value or any relationship between 'q' and 'x', we cannot determine the remainder when 'q' is divided by 6.

The remainder will depend on the specific value of 'q' and how it relates to the number 6. Therefore, without further information, it is not possible to determine the remainder when 'q' is divided by 6.

To learn more about division click here: brainly.com/question/2684764
#SPJ11

Answer:

y = 5x

Step-by-step explanation:

Use the direct variation equation y = kx

Plug in 30 as y and 6 as x, then solve for k

y = kx

30 = k(6)

5 = k

Plug in 5 as k into y = kx

y = 5x

So, the equation relating x and y is y = 5x

Answer:

y=5x

Step-by-step explanation:

30 divide by 6 = 5 so y = 5x

The total propagated uncertainty for the equation P = mgh is calculated to be approximately 9.6 ± 1.03 N. The largest source of uncertainty in this equation arises from the uncertainty in the value of g, which contributes ±1.86 N to the total uncertainty.

To find the total propagated uncertainty for P = mgh, we need to consider the individual uncertainties of the variables m, g, and h, and then combine them using the rules of error propagation.

The equation for P = mgh involves multiplication, so we use the rule that states the fractional uncertainties add in quadrature. The fractional uncertainties for m, g, and h are calculated by dividing their respective absolute uncertainties by their measured values.

For m = 5 ± 0.2 kg, the fractional uncertainty is 0.04, and for g = 9.8 ± 1.9 m/(s^2), it is 0.194. For h = 3 ± 0.1 m, the fractional uncertainty is 0.033.

Next, we multiply these fractional uncertainties by the values of mgh to obtain the individual propagated uncertainties for each variable. Multiplying mgh by the fractional uncertainties of m, g, and h gives us ±0.2 N, ±1.91 N, and ±0.1 N, respectively. To find the total propagated uncertainty, we add these individual uncertainties in quadrature: ±√((0.2 N)^2 + (1.91 N)^2 + (0.1 N)^2) = ±1.03 N.

The largest source of uncertainty in this equation is the uncertainty in the value of g, which contributes ±1.91 N to the total propagated uncertainty. This is because the uncertainty in g has the largest fractional uncertainty among the variables involved in the equation.

Therefore, the total propagated uncertainty for P = mgh is approximately 9.6 ± 1.03 N, with the largest source of uncertainty arising from the uncertainty in g, contributing ±1.86 N to the total uncertainty.

Learn more about equation here:

https://brainly.com/question/649785

#SPJ11

The coefficient of determination is 1.

Given

Total Sum of squares (SST) = 90

Sum of squares due to error (SSE) = 0

We have to find coefficient of determination.

The correlation of determination is the ratio of the explained variation to the total variation.

The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.

The coefficient of determination is also called r-squared or r-square.

Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.

Coefficient of determination can be found with the following formula:

Formula of coefficient of determination :

\(R^{2} = 1 - \frac{SSE}{SST}\)

= 1 - \(\frac{0}{90}\)

= 1 - 0

= 1

\(R^{2}\) = 1

Therefore,

The coefficient of determination is 1.

Find out more information about coefficient of determination here

https://brainly.com/question/28046641

#SPJ4

Answer:

Step-by-step explanation:

7/25 28%

0.24 6/25 24%

0.31818 7/22 31.818%

0.30435 7/23 30.435%

Answer:

7/25 (simplified) OR 28/100.

‎‎‎‎‎‎

The relation 1 is not a function, while the relation 2 is a function

For a relation to be a function, the following must be true:

Each y value in the function must have a unique x value

i.e. Each y value must have exactly one x value

Using the above as a guide, we have

Relation 1: This relation is not a function, because the x value 5 has two y values 2 and 4

Relation 2: This relation is a function, because each y value must have exactly one x value

Read more about functions and relations at:

https://brainly.com/question/10283950

#SPJ1

Answer:

$8.50

Step-by-step explanation:

10 pounds of bananas

Answer:

100 Meters

Step-by-step explanation:

10X5X2=100m.

Hope This Helps :)

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

To learn more on trigonometric functions: https://brainly.com/question/25618616

#SPJ1

The property which is used in the given expression is:

Additive property.

The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

There are two distinct identity qualities of numbers: additive identity and multiplicative identity. The original number is returned when additive identity is added to a number. Similar to this, multiplicative identity returns the original number when multiplied by any number.

Hence we get the required answer.

Learn more about Additive property here:

https://brainly.com/question/778086

#SPJ9

Answer:

3

Step-by-step explanation:

Factors of 15 are 1, 3, 5, 15

Factors or 6 are 1, 2, 3, 6

HCF = 3

The item which is closest in size to one mole of gas at STP is C) A microwave

A mole is the quantity of matter contained in a body.

We know that at STP the volume of gas occupied by one mole of a gas at STP is 22.4 dm³.

Now, we have 4 items.

Let us assume that each item is a cube. Also, since 22.4 dm³ is the volume of the cube, its length is

L = ∛22.4 dm³

=  ∛(22.4 × 10³) cm³

= 28.2 cm

So, ithe item that is comparable to this length is the microwave.

So, the item is C. A microwave

Learn more about mole of gas here:

https://brainly.com/question/24274266

#SPJ1

g(4) = 1 * g(4), which means that q(4) is equal to g(4). y(-4) = f(-4) * h(-4) = 1 * (-4) = -4. Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.

For the first part of the problem, we are given f(t) = u(t), g(t) = 2tu(t), and g(t) = f(t - 1) * g(t). To determine q(4), we need to substitute t = 4 into the equation g(t) = f(t - 1) * g(t). This gives us g(4) = f(3) * g(4). Since f(t) = u(t), we know that f(3) = u(3) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Therefore, we have g(4) = 1 * g(4), which means that q(4) is equal to g(4).

For the second part of the problem, we are given f(t) = u(-t), h(t) = tu(-t), and y(t) = f(t) * h(t). To determine y(-4) and y(4), we substitute t = -4 and t = 4 into the equation y(t) = f(t) * h(t). For y(-4), we have y(-4) = f(-4) * h(-4). Since f(t) = u(-t), we have f(-4) = u(4) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Similarly, h(-4) = -4u(4) = -4. Therefore, y(-4) = f(-4) * h(-4) = 1 * (-4) = -4.

Similarly, for y(4), we have y(4) = f(4) * h(4). Since f(t) = u(-t), we have f(4) = u(-4) = 0 because u(t) is a unit step function that equals 0 for t < 0. Thus, y(4) = f(4) * h(4) = 0 * h(4) = 0.

Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ11

Answer:

2

Step-by-step explanation:

(1/2)(6x-2) - 3(x-1)

take the (1/2) and distribute it to the 6x and the 2

(3x-1) - 3(x-1)

next, distribute the 3 to the x and the 1

(3x-1) - (3x-3)

then you simplify

3x-3x cancels

-1 - -3 is the same as -1 +3

so you get 2

Answer:

7 = n is greater than 9

9=m is less than or equal to 55

Step-by-step explanation:

Answer:

7. −2 < n < 0

8. Not sure about this one

9. m ≤ 55

10. 55 all the way to -40 on the inequalities graph

One reason why this condition may hold is because students who live closer to campus may be more likely to attend class since they don't have to travel as far

Part (i) Yes, this model uncovers the ceteris parabus effect of PC ownership on GPA.

There is, however, a possible correlation between PC ownership and the error term, which could be resolved by including it in the model.

There may be an unobserved factor that is correlated with both GPA and PC ownership.

It's possible that individuals who own PCs are more technologically savvy than those who don't, and that this technical proficiency is linked to higher GPAs.

Part (ii) PC is likely to be linked to parental annual income because high-income families can afford computers for their children, whereas low-income families may not.

Parental income would be a reasonable IV for PC since it is associated with the student's ability to afford a PC.

Part (iii) An potential IV for PC is the grant that students received for the purpose of purchasing a computer.

Since this grant was randomly assigned, it is exogenous and relevant.

Part (iv) In this scenario, the IV for PC would be whether or not the student received a grant to purchase a computer. This is a valid IV because the students' data was not used to determine who got the grant, and it is relevant since it is related to whether or not they owned a computer.

Part (i) Attendance rate (attrate) may be endogenous in this model, since there may be an unobserved factor that affects both attendance rate and student performance.

Part (ii) Distance from a student's living quarters to campus could be linked to the error term (u) because students who live closer to campus may have an easier time attending class and may be less susceptible to factors outside of their control that could impact their performance.

Part (iii) In order for dist to be a valid IV for attrate, it must be uncorrelated with u and must be correlated with attendance rate (attrate).

One reason why this condition may hold is that students who live closer to campus may be more likely to attend class since they don't have to travel as far.

Learn more about ceteris parabus from the given link;

https://brainly.com/question/13242876

#SPJ11

\(3x + 20 = (5 \times 1095) - 14 \\ 3x + 20 = 5475 - 14 \\ 3x = 5461 - 20 \\ 3x = 5441 \\ x = \frac{5441}{3} \)

Answer:

27.25 Years Old

Step-by-step explanation:

Find the total age of the 17 golfers.

52(17) = 884

Find total age of the 9 golfers.

9(74) = 666

Subtract.

884 - 666 = 218

Divide by the 8 golfers.

218/8 = 27.25

Answer:

Hey there!

Solving for a:

a=x-b

Solving for x:

x=a+b

Solving for b

a+b=x

b=x-a

Let me know if this helps :)

Given:

The distance traveled in 10 seconds is 450 feet.

To find the distance traveled in 1 minute:

In 10 seconds, the distance is 450 feet.

In 20 seconds the distance will be,

In 30 seconds the distance will be,

In 40 seconds the distance will be,

In 50 seconds the distance will be,

In 60 seconds the distance will be,

Hence, the distance traveled in 1 minute is 2700 feet.

So, the table becomes,

Answer:

.15 × $154,500 = $23,175 down payment

a) The solution of equation \(4^{x+1} = 5^{3x}\) is x = log4/(3log5 - log4).

b) The extraneous roots of equation \(\log_{2}x + \log_{2} (x+2) = 3\) is -4 and 2.

a) The first equation is \(4^{x+1} = 5^{3x}\).

Now solving the equation.

To solve the equation we take log on both side.

\(\log(4^{x+1}) = \log(5^{3x})\)

Using the formula \(\log m^n = n\log m\).

Now the equation is

(x+1) log4 = 3x log5

x log4 + log4 = 3x log5

Subtract x log4 on both side, we get

3x log5 - x log4 = log4

Taking common x

x(3log5 - log4) = log4

Divide by (3log5 - log4) on both side, we get

x = log4/(3log5 - log4)

b) The second equation is \(\log_{2}x + \log_{2} (x+2) = 3\)

Now solving the equation.

We can write the equation as

\(\log_{2}(x(x+2)) = 3\)

Now eliminating the log

x(x+2) = (2)^3

x(x+2) = 8

Now simplify the bracket

x^2 + 2x = 8

Subtract 8 on both side, we get

x^2 + 2x - 8 = 0

Now factor the equation

x^2 + (4-2)x - 8 = 0

x^2 + 4x - 2x - 8 = 0

x(x + 4) -2(x + 4) = 0

Now the factor of the equation is

(x + 4)(x - 2) = 0

Now equating the factor equal to zero.

x + 4 = 0                                 x - 2 = 0

x = -4                                      x = 2

Now the solution of equation is -4 and 2.

To learn more about extraneous roots of equation link is here

brainly.com/question/26751713

#SPJ4

Answer:

4 :)

Step-by-step explanation:

The area of the rectangular base of his friend's tank is 468.75 square inches. So, Option D is correct.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

One of Julian's friends also has a rectangular aquarium.

The dimensions of his friend's tank are each exactly 1 1/4 times the dimensions of Julian's tank.

Let x be the length of Julian's tank.

Let y be the width of Julian's tank.

So, the Area of Julian's tank = length × Width

                                               = xy

Since we are given

300 = xy

Now we are given that the dimensions of his friend's tank are each exactly times the dimensions of Julian's tank.

So, the length of his friend's tank = 5/4 x

So, the width of his friend's tank = 5/4 y

So, Area of his friend's tank = ( 5/4 x) (5/4 y)

                                           = 25 / 16 xy

                                           = 25 / 16 (300)

                                           = 468.75

Hence the area of the rectangular base of his friend's tank is 468.75 square inches.

So, Option D is correct.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1