As the exponent on the base 10 increases, does
the standard notation number get larger or
smaller in value? Explain why.

Help Please

Step-by-step explanation:

use substitution method so it will now look like

8x + 5(-4x) = 24

8x + (-20x) = 24

-12x = 24 (divide both sides by 12)

-x = 2 (multiply both sides by negative 1)

x = -2

substitute to find y

y= -4(-2)

=8

Answer:

\(x=-2\\y=8\)

Step-by-step explanation:

\(8x+5y=24\\y=-4x\)

We already have y in terms of, so the easiest way to do is by plugging that value in the first equation.

\(8x+5y=24\\8x+5(-4x)=24\\8x-20x=24\\-12x=24\\x=\frac{24}{-12} \\x=-2\)

After having found the value of x, replace it in the second equation to find y.

\(y=-4(-2)\\y=8\)

A person weighing 173 pounds can burn 10.7 calories per minute.

The given equation is ŷ=2.2+0.05x.

To solve this question, we can use the equation given, ŷ=2.2+0.05x. We can insert the known weight value, 173 pounds, to calculate the anticipated calories burned per minute.

y = 2.2 + 0.05x

y = 2.2 + 0.05 × 173

y = 10.7

Therefore, a person weighing 173 pounds can burn 10.7 calories per minute.

Learn more about the least-squares here:

https://brainly.com/question/30176124.

#SPJ4

"Your question is incomplete, probably the complete question/missing part is:"

By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ=2.2+0.05x

Based on the information gathered by Thomas, select the statement that is true.

a) A person weighing 149 pounds can burn 9.8 calories per minute.

b) A person weighing 134 pounds can burn 8.9 calories per minute.

c) A person weighing 125 pounds can burn 8.3 calories per minute.

d) A person weighing 173 pounds can burn 10.7 calories per minute.

Answer:

A person weighing 134 pounds can burn 8.9 calories a minute.

Step-by-step explanation:

Answer:

y=2/7 x+38/7

Step-by-step explanation:

equation of the line y =ax+b;

a = 4-6/ -5-2

Answer:

0

Step-by-step explanation:

The answer would be -3/4

Answer:

d= 0.65 or 13/20

Step-by-step explanation:

-4(3d - 2) = 8d -5

-12d +8 = 8d -5

arrange like terms on the same side of the equation

8 +5 = 8d +12d

13 = 20d

13/20 = d

Answer:

GCF = 2 :)

Step-by-step explanation:

The greatest common factor is the biggest number that each number is divisible by.

There is no number greater than 2 that 14, 4 and 42 are all divisible by! :)

Answer:

y=-2x

Step-by-step explanation:

The y-intercept is 0 so b is 0

and it is going down   2 right 1 so it is -2/1  -2/1 =-2 so it is y= -2x

Answer:

y = -2x + 0

Step-by-step explanation:

y = mx + c

m = gradient and c = y intercept ( the point where the line intercepts the y axis)

Firstly, we can tell the gradient is negative because it has a negative slope (sorta like down a hill) where as x increases y decreases.

To calculate the gradient you use the equation y/x

Pick anywhere on you graph and measure. I have taken from (0,0) to (0,-4) for y and (0,-4) to (2,-4) for x.

Next subtract them (0,-4) - (0,0) = 0,-4. Then take that - 4 for y

Next subtract for them for x (0,-4) - (2,-4) = 0- 2 and -4 -(-4)

                                                                    = -2 and -4 + 4 = 0

                                                                    = -2

So y = -4 and x = -2

y/x = 4/2 = 2

Because we know our gradient is negative add a minus and we get our gradient as -2

For y intercept simply find where the line crosses through the y axis, which in this question happens to be 0

answer = -2x + 0

Answer:  " 3x²  + 19x + 20 " .

_____________________

Step-by-step explanation:

Note:  "ax + bx = (a+b)x " ;

_____________________

Given:  " 1x(3x + 4) + 5(3x + 4) " ;

Let: "a = 1x " ;  "b = 5 " ; "x" = "(3x +4) " ;

           → 1x(3x + 4) + 5(3x + 4)  =

                 " (1x + 5) (3x + 4) " ;

_____________________

      Note:  " (a + b)(c + d) = ac + ad + bc + bd " ;

           → (1x + 5) (3x + 4)  = (1x*3x) + (1x* 4) + (5*3x) + (5*4) ;

                                         =  3x²  +   4x   +    15x   + 20 ;

                                              → Combine the "like terms" :

                                                       + 4x + 15x = + 19x ;

                                              →  and rewrite:

                                         =   3x²  + 19x + 20 .

_____________________

Hope this is helpful!

 Wishing you the best!

_____________________

Answer:

120

Step-by-step explanation:

All the interior angles in a regular hexagon are 120 degrees.

Answer: \(|x| \leq 5\) (the last option)

Step-by-step explanation: When you plug in values from the given solution set, the number is positive because of the absolute value symbol. This causes the range of possible values to be from 0 to 5, which are all less than or equal to 5.

THIS IS EASY?? OH HELL NO-

\(\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}\)

\(\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}\)

\(\\ \rm\dashrightarrow B=10log10^5\)

\(\\ \rm\dashrightarrow B=10\times 5log10\)

\(\\ \rm\dashrightarrow B=10(5)\)

\(\\ \rm\dashrightarrow B=50dB\)

Answer:

50 Db

Step-by-step explanation:

Given:

\(L=10 \log \dfrac{I}{I_0}\)

\(I_0=10^{-12}\)

where:

To find the approximate loudness of a dinner conversation with a sound intensity of \(I=10^{-7}\), substitute the values of I and I₀ into the given equation and solve for L:

\(\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}\)

\(\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:\)

\(\implies L=10 \log 10^{-7-(-12)\)

\(\implies L=10 \log 10^5\)

\(\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax\)

\(\implies L=5 \cdot 10 \log 10\)

\(\implies L=50 \log 10\)

As the given log does not have a specified base, assume the base is 10.

\(\implies L=50 \log_{10} 10\)

\(\textsf{Apply log law}: \quad \log_aa=1\)

\(\implies L=50 (1)\)

\(\implies L=50\:\:\sf Db\)

Learn more about log laws here:

https://brainly.com/question/27963321

https://brainly.com/question/28016999

Answer:

\(\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }\)

Step-by-step explanation:

Hello,

let's solve

\(x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\\)

\(\Delta=b^2-4ac=9+4*2*2=9+16=25\)

There are two solutions

\(x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}\)

And

\(x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}\)

So we can write

\(x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer: 24 pages

Step-by-step explanation:

10 times 24 equals 240

Answer:

Janet has to read 24 pages.

Hallie has to read 240 pages.

Step-by-step explanation:

If Janet has to read n pages, then Hallie has to read 10×n.

Together they have to read 11 × n = 264 pages, so: n=264÷11=24.

Hope this helps

The two values of the expression 5x - 6 are -6 and 9 when x takes the values of 0 and 3, respectively.

We have,

To find two values of the expression 5x - 6, we need to assign different values to x and evaluate the expression.

Let's choose two arbitrary values for x and calculate the corresponding values of 5x - 6:

If we let x = 0:

5x - 6 = 5(0) - 6 = -6

If we let x = 3:

5x - 6 = 5(3) - 6 = 15 - 6 = 9

Therefore,

The two values of 5x - 6 are -6 and 9 when x takes the values of 0 and 3, respectively.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Chess is not a static game of complete information for several reasons. Firstly, the game is dynamic, meaning that the position of the pieces on the board changes constantly throughout the game.

Unlike in games like Tic Tac Toe or Connect Four, the state of the game at any given point is not fixed, and there are a vast number of possible outcomes. This means that players cannot simply memorize the best moves and outcomes for every situation, as they would in a game of complete information.

Secondly, chess is a game of imperfect information, as both players do not know what moves their opponent will make. Even with a complete understanding of the game's rules, players cannot predict with certainty the moves of their opponent, and must instead make strategic decisions based on their best assessment of their opponent's likely choices.

Finally, chess is a game of hidden information, as players do not know what their opponent is thinking or planning. A player may be able to predict their opponent's next move, but cannot know for sure what their long-term strategy is, making it difficult to make optimal decisions.

Overall, chess is a highly dynamic and complex game that is not static or complete in terms of information. Players must make strategic decisions based on incomplete and uncertain information, making it a challenging and rewarding game for those who play it.

Chess is a strategic board game played between two players, with each player starting with 16 pieces on a 64-square board. The game has been around for centuries and is considered one of the most popular and complex games in the world.

Know more about "chess":-

https://brainly.com/question/9389753#

#SPJ11

If a many-to-many-to-many relationship is created when it is not appropriate to do so, the problem can be corrected by re-designing the database schema to remove the unnecessary relationship.

Here are some steps you can follow to correct the problem:

Analyze the existing database schema to identify the many-to-many-to-many relationship and the tables involved in it.

Evaluate the relationship to determine whether it is necessary or not. If it is not, remove it from the schema.

If the relationship is necessary, analyze the tables and their attributes to identify the primary keys and foreign keys involved in the relationship.

Create a new table to serve as an intermediary between the tables involved in the relationship.

Update the foreign keys in the related tables to point to the primary keys in the new intermediary table.

Migrate the data from the existing tables to the new intermediary table.

Test the new database schema to ensure that it functions correctly and that all data is correctly retrieved and stored.

Overall, the process of correcting a many-to-many-to-many relationship involves re-evaluating the database schema and modifying it as necessary to ensure that it is properly designed to store and retrieve data efficiently and accurately.

for such more question on database schema

https://brainly.com/question/12125305

#SPJ11

Step-by-step explanation:

a)Perimeter of a Rectangle = \(2 (l+w)=2(24+15)=78\)

Circumference of a circle = \(\frac{\pi d}{2}\)

= \(\frac{3.14X24}{2} \\= \frac{75.36}{2} \\= 37.68\)

Perimeter of the whole figure = \(15 + 15 + 24 + 37.68= 91.68cm\)

b) Area of the rectangle =\(wl=15X24=360\)

Area of a semi circle = \(\frac{\pi }{2} Xr^{2}\)

= \(1.57\) x \(12X12\)

=\(226.08\)

Area of the whole figure = \(360 + 226.08\)

= \(586.08\)\(cm^{2}\)

Hope it helps

Pls Mark me Brainliest

Throwing a dart at a stationary dart board can be classified as a projectile motion.

:

When a dart is thrown at a stationary dartboard, it follows a curved path known as projectile motion. Projectile motion occurs when an object is launched into the air and moves along a curved trajectory under the influence of gravity, with no other external forces acting on it. In this case, the dart is subjected to the force of gravity but doesn't experience any significant air resistance or external forces once it leaves the hand of the thrower.

The motion of the dart can be described using principles of kinematics. The dart moves in two dimensions: horizontally and vertically. The horizontal motion is uniform and unaffected by gravity, while the vertical motion is influenced by the force of gravity acting in the downward direction. The dart follows a parabolic path, with its maximum height reached at the peak of the trajectory.

To determine the distance and accuracy of the dart throw, various factors need to be considered, such as the initial velocity, launch angle, and the height of the dartboard. These factors can be used to calculate the range, time of flight, and maximum height of the dart.

Throwing a dart at a stationary dartboard involves projectile motion, where the dart follows a curved path influenced by gravity. Understanding the principles of projectile motion can help improve accuracy and distance in dart throwing by considering factors like initial velocity and launch angle. By mastering the art of projectile motion, dart players can enhance their skills and aim for higher scores on the dartboard.

To know more about Projectile Motion, visit

https://brainly.com/question/10680035

#SPJ11

Answer:

\(\circ\ \ 36\sqrt{3}\)

Step-by-step explanation:

\(CD=12\times \sin(60) =12\times \frac{\sqrt{3} }{2}\)

Important Note:………………………………………………………………………………………

ABC is an equilateral triangle because it has 2 angles of measure 60

===========================================================

According to the note AB = 12

Final answer :

\(\text{Area of triangle ABC} =\frac{AB\times CD}{2}\)

                                  \(=\frac{12\times 6\sqrt{3} }{2}\)

                                  \(=\frac{72\sqrt{3} }{2}\)

                                  \(=36\sqrt{3}\)

Thus, the rate per period (i) is 1.5%, and the number of periods (n) is 24 periods (6 years x 4 quarters per year).

Given: Quarterly deposits of $700 are made for 6 years into an annuity that pays 6% compounded quarterly.

To find: The rate per period (i) and the number of periods (n).

To find the rate per period (i) and the number of periods (n), we use the formula for the future value of an annuity.FV = PMT [((1 + i)^n - 1) / i]

Here, PMT = $700,

i = rate per period,

n = number of periods, and

FV = ?

We know that $700 is deposited quarterly, so in a year, the number of deposits made will be 4.

Thus, the total number of periods (n) will be 4 times the number of years (6).

Therefore,

n = 4 × 6

= 24

The rate per period (i) can be calculated by substituting the given values in the formula for the future value of an annuity.

FV = PMT [((1 + i)^n - 1) / i]

FV = 700 [((1 + i)^24 - 1) / i]

If the annuity pays 6% compounded quarterly, then the rate per period will be 6% / 4 = 1.5%.

Therefore, the equation becomes:

FV = 700 [((1 + 0.015)^24 - 1) / 0.015]

= 700 [((1.015)^24 - 1) / 0.015]

= 700 [(1.4322 - 1) / 0.015]

= 700 [28.81]

= 20167.19

Rate per period (i) is 1.5%, and the number of periods (n) is 24.

To know more about compounded quarterly visit:

https://brainly.com/question/31793584

#SPJ11

Answer:

7.5 kg

Step-by-step explanation:

Ratio of sand to cement = 24kg : 5kg

Today he needs to make the same type of mortar mix, but he will use 36kg of sand.

Let

x = quantity of cement used

Ratio of sand to cement = 36 kg : x kg

Equate both ratios

24 kg : 5 kg = 36 kg : x kg

24/5 = 36/x

Cross product

24 * x = 5 * 36

24x = 180

x = 180/24

x = 7.5

x = quantity of cement used = 7.5 kg

Answer:

\(13-6x=2\left(8+3x\right)\)

\(13-6x=16+6x\)

\(13-6x-13=16+6x-13\)

\(-6x=6x+3\)

\(-6x-6x=6x+3-6x\)

\(-12x=3\)

\(\frac{-12x}{-12}=\frac{3}{-12}\)

\(x=-\frac{1}{4}\)

or

\(x=-0.25\)

Answer:

-1/4 = x

Step-by-step explanation:

first, we distribute the 2 into the parenthesis

13 - 6x = 2(8 + 3x)

13 - 6x = 16 + 6x

then, we add 6x to both sides to move all of the x terms onto one side

13 - 6x = 16 + 6x

13 = 16 + 12x

next, we subtract 16 on both sides

13 = 16 + 12x

-3 = 12x

next, we divide both sides by 12 to isolate x

-3 = 12x

-3/12 = x

finally, we simplify the fraction

-3/12 = x

-1/4 = x

Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

To know more about Distance visit,

https://brainly.com/question/26550516

#SPJ4

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

To learn more about eigenvalues click here: brainly.com/question/29861415

#SPJ11

Standard form equation of given circle.

The standard form of the equation of a circle is (x - h)² + (y - k)²= r², where (h,k) is the center of the circle and r is the radius. To find the standard form of the equation of the circle in the graph, we need to first determine its center and radius.

We can see that the center of the circle is (-3,1) and its radius is the square root of 2. Using this information, we can plug these values into the standard form equation and simplify to get (x + 3)² + (y - 1)² = 2 as the standard form of the equation of the circle.

This means that any point (x,y) that satisfies this equation will lie on the circle with center (-3,1) and radius square root of 2.

Learn more about standard form

brainly.com/question/29000730

#SPJ11

Answer:

7.5 × 10\( {}^{2} \) (scientific notation)

Step-by-step explanation:

➟ 750 = 7.5 × 10\( {}^{2} \) (scientific notation)

Answer:

x<8

Step-by-step explanation:

i don't think the question was complete, i cannot make an inequality with just the information given.