Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has
$50 and she spends $3.25 every day. Write an inequality that shows when Sue's
account will be more than Troy's.
25 + 2.5d > 50 +
3.25d
25 - 2.5d > 50 -
3.25d
25 + 2,5d < 50+
3.25d
25 - 2.5d < 50-
3.25d

The gates diagram for the expression "(x AND y) NAND (w OR z)" consists of an AND gate, an OR gate, and a NAND gate. The inputs x, y, w, and z are connected to these gates, and the output is represented by O.

Here is the gate diagram for the expression "(x AND y) NAND (w OR z)":

  x       y         w       z

  │       │         │       │

  └───────┼─────────┼───────┘

          │         │

        ┌─┴─┐     ┌─┴─┐

        │AND│     │OR │

        └─┬─┘     └─┬─┘

          │         │

         ┌┴┐       ┌┴┐

         │NAND│    │NAND│

         └┬┘       └┬┘

          │         │

          │         │

          │         │

         ─┴─       ─┴─

          │         │

          Y         O

          │         │

          │         │

          │         │

In the gate diagram, the inputs x, y, w, and z are connected to their respective gates. The gates used in the diagram are:

AND gate: Performs a logical AND operation on the inputs x and y.

OR gate: Performs a logical OR operation on the inputs w and z.

NAND gate: Performs a logical NAND operation on the outputs of the AND gate and the OR gate.

The output of the entire expression is represented by the letter O. The gate diagram illustrates the logical structure of the expression and how the inputs are combined to produce the final output using the specified logic gates.

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In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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Answer:

Step-by-step explanation:

Because the first marble was returned before the second was chosen, there are always 4+5+3 = 12 marbles.

Probability of picking 1 red marble = number of red marbles / total number of marbles

= 4/12

= 1/3

Probability of picking 1 red marble two times in a row = Probability of picking 1 red marble * Probability of picking 1 red marble

= 1/3 * 1/3

= 1/9

Answer:

  f(-1) = 3

  f(5) = 20

Step-by-step explanation:

When evaluating a piecewise-defined function, the first step is to locate the argument value in the correct domain. Then the corresponding function is evaluated in the usual way.

__

For x=-1, the relevant piece is the one defined for x < 4:

  f(x) = x² +2

  f(-1) = (-1)² +2 = 3

__

For x=5, the relevant piece is the one defined for x > 4:

  f(x) = 2x +10

  f(5) = 2(5) +10 = 20

_____

Additional comment

The function written in this problem statement is "undefined" at x=4, so the graph would ordinarily show a "hole" there. We're not sure whether that is intentional.

The level of measurement is required of the independent variable (iv) and dependent variable (dv) to conduct a chi-square analysis is "the chi-squared test for independence."

A chi-square (X²) statistic is a test which compares a model to real observed data. A chi-square statistic requires data that is random, raw, mutually exclusive, obtained from independent variables, & drawn from a large enough sample. Tossing a fair coin, for example, meets these criteria.

Some key features regarding chi-square test are-

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To evaluate which of a set of curves fits the data best, you can use the option "c. R2", also known as the coefficient of determination.

R2 is a statistical measure that helps determine the proportion of variance in the dependent variable explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the curve to the data.

To evaluate which of a set of curves fits the data best, we can use the R2 (coefficient of determination) metric. R2 is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.

                                         A higher R2 value indicates a better fit of the curve to the data. APE (absolute percentage error), MAPE (mean absolute percentage error), and NPV (net present value) are not appropriate metrics for evaluating the fit of a curve to data. APE and MAPE are typically used to measure forecasting accuracy, while NPV is a financial metric used to determine the present value of future cash flows.

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Answer:

No.

Step-by-step explanation:

\(10^{4} =(10)(10)(10)(10)\\10^{4} =10000\\\)

\((10)(4)=40\)

\(10000\neq 40\). Therefore, \(10^{4} \neq\)10x4.

**Exponents expresses how many times the number it multiplied by it's own value. Such as \(x^{2}\) is the same as (x)(x) since it is times by itself 2 times. Or, \(6^{8}\) is the same as (6)(6)(6)(6)(6)(6)(6)(6) since it is times by itself 8 times.

Answer:

A =7  B=14

Step-by-step explanation:

AREA OF RING

PERIMETER OF RING

Answer:

78

Step-by-step explanation:

The median in a stem-and-leaf diagram is the number that is repeated the most. In this case, the number 78 is repeated 4 times (7 | 8 8 8 8). No other number in the diagram is repeated as much or more than the number 78.

Do not make the mistake of writing the answer as 8 instead of 78.You also want to make sure you don't accidently count 68 which is repeated twice (by looking at the 8's at the end and thinking it's part of the all/rest of the 8's in the diagram).

Hope this helps :)

Answer:

  1.4×10¹⁸ m³

Step-by-step explanation:

You want 1.4×10⁹ km³ expressed in terms of m³.

1 km = 10³ m. Substituting that value for km in the given expression, we find the volume is ...

  1.4×10⁹ km³ = 1.4×10⁹×(10³ m)³ = 1.4×10¹⁸ m³

<95141404393>

Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

The given value is 1.4 × 109 km3 to be converted into

m3.1 km = 1000 m.

Hence,

1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, 1.4 × 109 km3 is equal to

1.4 × 1018 m3.

To convert

1.4 × 109 km3

into m3, the given value is multiplied by

(109 m3/km3), as 1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, the conversion factor from km3 to m3 is 109, and this factor is multiplied by the given value. In the final answer, the value is expressed as 1.4 × 1018 m3.

Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

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All of 4x+8 is under a cube root sign.

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

Work Shown:

To find the inverse, we swap x and y, then solve for y.

\(y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\\)

------------

Side note:

If \(f(x) = \frac{1}{4}x^3 - 2\) and \(g(x) = \sqrt[3]{4x+8}\), then \(f(g(x)) = x\) and \(g(f(x)) = x\)for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.

Answer:

see explanation

Step-by-step explanation:

(a)

x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides

0 = x² - 2x - 3 ← in standard form

0 = (x - 3)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

-----------------------------------

(b)

\(\frac{x+2}{3}\) - \(\frac{2}{15}\) = \(\frac{x-2}{5}\) ( multiply through by 15 to clear the fractions )

5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides

5x + 10 - 2 = 3x - 6

5x + 8 = 3x - 6 ( subtract 3x from both sides )

2x + 8 = - 6 ( subtract 8 from both sides )

2x = - 14 ( divide both sides by 2 )

x = - 7

--------------------------------------------

(c) Assuming lg means log then using the rules of logarithms

log \(x^{n}\) ⇔ nlogx

log x = log y ⇒ x = y

Given

log(2x + 3) = 2logx

log(2x + 3) = log x² , so

x² = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 , x = - 1

x > 0 then x = 3

1 . Price of car 8 years later is $4305.

The price of a car that was bought for $10,000 and has depreciated 10% yearly can be calculated by multiplying the original price of the car ($10,000) by (1 - 0.10) raised to the power of the number of years (8). It means the car will lose 10% of its value each year for 8 years. Therefore, the price of the car 8 years later would be $4304.67. This is the final amount after 8 years of deprecation on the original price of the car.

2. The yearly value of the card 25 years later is $16.93 and equation of price is given by 5 * (1 + 0.05)^t where t is time.

The formula used to calculate the future value of an item that appreciates at a certain annual rate is called compounding. In this case, the baseball card was bought for $5 and has appreciated at a rate of 5% per year. The formula used to find the value of the card 25 years later is "Price = initial value * (1 + interest rate)^number of years". Plugging in the given values, we get: "Price = 5 * (1 + 0.05)^25"

Price=5(1+0.05)^25

Price=5(1.05)^25

Price=16.93

so the final price of baseball is $16.93

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The expected percentage of their offspring that would produce pink flowers would be 0%. This is because both the parents that are involved in the cross produce only white flowers and therefore the offspring produced as a result of the cross are expected to only produce white flowers.

However, if the offspring from the cross between the two white flower producing wildflowers were to be crossed with another wildflower population that has pink flowers, there is a chance that some of the offspring from that cross would produce pink flowers. In the given scenario, the cross is being made between two white flower producing wildflowers. Since both the parents involved in the cross produce only white flowers, there is no chance of their offspring producing pink flowers.

The color of the flowers in the offspring is determined by the genetic makeup of the parents that are involved in the cross.In the case of the given wildflowers, the fact that 77% of the offspring produced by a cross between two pink wildflowers produced pink flowers while 23% produced white flowers indicates that the gene for pink flowers is dominant over the gene for white flowers. This is because the gene for pink flowers was passed down to more than three-quarters of the offspring in the cross between the two pink wildflowers. The gene for white flowers, on the other hand, was passed down to only a quarter of the offspring.Hence, if the offspring from the cross between the two white flower producing wildflowers were to be crossed with another wildflower population that has pink flowers, there is a chance that some of the offspring from that cross would produce pink flowers.

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The perimeter and the area of each composite figure are, respectively:

Case 10: Perimeter: p = 16 + 8√2, Area: A = 24

Case 12: Perimeter: p = 28, Area: A = 32

Case 14: Perimeter: p = 6√2 + 64 + 3π , Area: A = 13 + 9π

In this question we find three composite figures, whose perimeter and area must be found. The perimeter is the sum of all side lengths, while the area is the sum of the areas of simple figures. The length of each line is found by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

The perimeter of the semicircle is given by following formula:

s = π · r

And the area formulas needed are:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Semicircle

A = 0.5π · r²

Where:

Now we proceed to determine the perimeter and the area of each figure:

Case 10

Perimeter: p = 2 · 8 + 4 · √(2² + 2²) = 16 + 8√2

Area: A = 4 · 0.5 · 2² + 4² = 8 + 16 = 24

Case 12

Perimeter: p = 2 · 4 + 4 · 2 + 4 · 2 + 2 · 2 = 8 + 8 + 8 + 4 = 28

Area: A = 4 · 6 + 2 · 2² = 24 + 8 = 32

Case 14

Perimeter: p = 2√(3² + 3²) + 2 · 2 + 2 · 2 + 2 · 2 + π · 3 = 6√2 + 64 + 3π

Area: A = 2 · 0.5 · 3² + 2² + π · 3² = 9 + 4 + 9π = 13 + 9π

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Answer:

The possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Step-by-step explanation:

Let;

Length of Rectangle A be a

Width of Rectangle A be b

Length of Rectangle B be c

Width of Rectangle B be d

Thus;

Area of Rectangle A = a × b

Area of Rectangle B = c × d

We are told that the area of Rectangle A is twice the area of Rectangle B:

Thus;

2cd = ab - - - - - eq. 1

perimeter of Rectangle A = 2a + 2b

perimeter of Rectangle B = 2c + 2d

We are told that the perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B. Thus, we now have;

20 + 2c + 2d = 2a + 2b - - - - eq. 2

We have 4 unknowns which are (a, b, c and d) but only 2 equations, so we need to reduce to 2 unknown variables and calculate the other ones. In this way, one of the infinite solutions is obtained.

Let's assume that c = 1 and d = 2, we obtain:

From eq 1, we have;

2 * 1 * 2 = a*b

ab = 4 or a = 4/b

From eq 2, we have;

20 + 2(1) + 2(2) = 2a + 2b

26 = 2a + 2b

Putting a = 4/b into this, we have;

26 = 2(4/b) + 2b

Multiply through by b to get;

26b = 8 + 2b²

So,we have;

2b² -26b + 8 = 0

Using quadratic formula for this,

b = 0.315 or 12.685

When, b = 12.685, a = 4/12.685 = 0.315

When, b = 0.315, a = 4/0.315 = 12.685

So, the possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Answer:

m∠a = 60° ; m∠b = 30°

Step-by-step explanation:

They are complementary angles meaning they have a sum of 90°.

2x + x = 90

3x = 90

x = 30

2(30) = 60

Answer:

240 copies in 30 minutes

Step-by-step explanation:

they gave us the info that it makes 40 copies in 5 minutes, divide 40/5 and you get 8, which tells us that it makes 8 copies per minute.

multiply the 8 copies that it can make in a minute by the 30 minutes, 30*8 and you get 240 copies

hope this helps :)

a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

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Answer:

The total percentage loss would be 67%.

Step-by-step explanation:

Since we have given that

Rate of decline each year = 20%

Number of years = 5

We need to find the total percentage loss in value of the house at the end of 5 years.

So, Total percentage loss would be

Answer:

The large box weighs 18.75 and the small box weights 15.75

Step-by-step explanation:

We are looking to find 2 variables so we will need two equations.

Let l = the large box weight

Let s = the small box weight

7l + 9s + 273                   5l +3s = 141

I want to add these two equations together and have one of the variables be eliminated.  The way both equations are written now, neither variable will drop out.  I see that 9 is a multiple of 3.  If I multiply the second equation all the way through by - 3, the s variable will be eliminated.

-3(5l +3s) -3(141)  Multiple everything by -3

-15l -9s = -423  Now I will add this to the original equation 7l + 9s = 273

7l + 9s = 273

-8l = -150  Divide both sides by -8

l = 18.75  This is the weight of the large box.

Plug in 18.75 to either of the ordinal equations to find the weight of the small box.

5l + 3s = 141

5(18.75) + 3s = 141  Distribute the 5

93.75 + 3s = 141  Subtract 93.75 from both sides

3s = 47.25  Divide both sides by 3

s = 15.75

Check:

Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.

7l + 9s = 273

7(18.75) + 9(15.75) =273

131.25 + 141.75 = 273  Checks

5l + 3s = 141

5(18.75) + 3(15.75) = 141

93.75 + 47.25 = 141

141 = 141 Checks

Answer:

A

Step-by-step explanation:

dont know just trust me

Answer:

science is not made but it exists by its self normally

Answer:

A

Step-by-step explanation:

she already has 100 dollars (100)

and is saving 20 dollars a week (20x)

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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