Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water, in inches, t
minutes after Tyler began to fill the bathtub.
These statements describe how the water level in the tub was changing over time. Use the statements to sketch an
approximate graph of function.
B (0) = 0
. B (1) < B (7)
B (9) = 11
• B (10) = B (23)
.
.
.
.
• B (20) > B (40)
You may want to use the following graph as a starting point for your sketch. Then fill it in with the information listed above.

Answer:

w

Step-by-step explanation:

Monday = 4

Tuesday = 1/3 w  (where w is the miles walked on Wednesday)

Wednesday = w

Total = 24

4 + 1/3 w + w = 24

Combine like terms

4 + 4/3 w = 24

Subtract 4 from each side

4/3 w = 20

Multiply each side by 3/4

w = 20 *3/4

w = 15

In the equation when we start, we need to put the variable, not the solution

At the end we have the solution

Part A

start by naming the variables you will be using in the system of equation

x= number of two-point baskets

y= number of three-point baskets

since she did 23 baskets the first equation representing the number of baskets she made will be

the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.

Part B

Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.

However both methods could be used.

Part C

The formula C = 5(F - 32), is misspelled.

The formula °C = 5/9 (°F - 32), is the formula to convert degrees Fahrenheit to degrees Celsius. Therefore it is True.

Let's first find the class width. The formula for finding class width is:Class width = (Maximum value - Minimum value) / Number of classes Given:Minimum = 12Maximum = 79Number of classes = 6Class width = (79 - 12) / 6 = 11.16667 ≈ 11.17 ≈ 11 (rounded off to the nearest whole number)Now, we can find the lower class limits.

The lower class limit for the first class will be the minimum value, which is 12.Lower class limit for the first class = 12The lower class limit for the second class will be the lower class limit of the first class plus the class width.Lower class limit for the second class = 12 + 11 = 23 Lower class limit for the third class = 23 + 11 = 34Lower class limit for the fourth class = 34 + 11 = 45Lower class limit for the fifth class = 45 + 11 = 56 Lower class limit for the sixth class = 56 + 11 = 67Thus, the correct lower class limits are 12, 23, 34, 45, 56, and 67.Next, we can find the upper class limits. The upper class limit for the first class will be the lower class limit of the second class minus 1.Upper class limit for the first class = 23 - 1 = 22Upper class limit for the second class = 34 - 1 = 33Upper class limit for the third class = 45 - 1 = 44Upper class limit for the fourth class = 56 - 1 = 55Upper class limit for the fifth class = 67 - 1 = 66Upper class limit for the sixth class = 79Thus, the correct upper class limits are 22, 33, 44, 55, 66, and 79. In statistics, a class is a range of data that is grouped together. In a frequency distribution, classes are used to organize the data into groups and display how many times each group occurs. To create classes, we need to find the class width, lower class limits, and upper class limits. To find the class width, we use the formula: Class width = (Maximum value - Minimum value) / Number of classes. Once we have the class width, we can find the lower class limits by adding the class width to the lower class limit of the previous class. The lower class limit of the first class is equal to the minimum value. To find the upper class limits, we subtract 1 from the lower class limit of the next class. The upper class limit of the last class is equal to the maximum value. In this problem, the minimum value is 12, the maximum value is 79, and the number of classes is 6. Therefore, the class width is (79 - 12) / 6 = 11.17, which is rounded off to 11. The lower class limits are 12, 23, 34, 45, 56, and 67. The upper class limits are 22, 33, 44, 55, 66, and 79.

The class width, the lower class limits, and the upper class limits have been found using the given minimum and maximum data entries and the number of classes. The class width is 11. The lower class limits are 12, 23, 34, 45, 56, and 67. The upper class limits are 22, 33, 44, 55, 66, and 79.

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Answer:

area = length*width ...

length = area/width

l = (x2+8x+15)/(x+3)

l = [(x+5)(x+3)]/(x+3) = x+5

The length is x+5

Step-by-step explanation:

Answer:

3x+4=7x-8

Step-by-step explanation:

hoped it helped..

You have the following expression:

2.5 x 10⁴ - 1.5 x 10³

in order to simplify the previous expression, consider that the factors with base 10 have to have the same exponent. You can write the second term as a factor with 10⁴ if you write 1.5 as 0.15 (if you increase the exponent you move the decimal point to the left). Then, you can subtract the coefficients of the term and put the same factor x 10⁴:

Then, you have:

1.5 x 10³ = 0.15 x 10⁴

2.5 x 10⁴ - 0.15 x 10⁴ = 2.35 x 10⁴

Hence, the asnwer is:

2.35 x 10⁴

Answer:

the money left is $487.50

Step-by-step explanation:

The computation of the money left is shown below:

= Total money - spent money

= $750 - $750 × 35%

= $750 - $262.50

= $487.50

Hence, the money left is $487.50

We simply deduct the spent money from the total money

Answer:

7. r = -5

8. x = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

r + 2 - 8r = -3 - 8r

Step 2: Solve for r

Step 3: Check

Plug in r into the original equation to verify it's a solution.

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

Step 4: Define equation

-4x = x + 5

Step 5: Solve for x

Step 6: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

The limiting value of the sequence will be the same even if a different value is assigned to x0.

The limiting value of the sequence is determined by the recursive equation xn = √(1996x\(n^{-1}\)). As n grows infinitely large, the value of xn will approach the same limiting value regardless of the initial value assigned to x0. This is because the recursive equation will continue to generate values that are closer and closer to the limiting value, regardless of the starting point.

Therefore in recursive equations, the limiting value of the sequence will be the same even if a different value is assigned to x0.

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Noelia has 216 cards after buying part of the set with her friends.

Combining items and counting them as a single, large group is done through addition.

Given that, Noelia has 144 role-playing cards.

Now, she bought 72 cards more, therefore, the number of cards Noelia has is:

144 + 72

= 216

Hence, Noelia has 216 cards after buying part of the set with her friends.

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multiply 144 times 27 which is 3,888

3888

-     9                      

-----------

3,879     3,879

              -      72

           --------------

          3,807

Answer:

4√5

Step-by-step explanation:

Let's call it x

According to Euclidean theorem x^2 = 5×16

x^2= 80 and

x = 4√5

The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Answer:

0

Step-by-step explanation:

-5 + 7 - 6 - (-4)

-11 + 7 - (-4)

-11 + 7 +4

-11 + 11

= 0

Answer: 0

Step-by-step explanation:

-5 + 7 -6-(-4)    

-5 + 7 -2

-5+ 5 = 0

Modifying Above p with caret minus Upper E less than p less than ModifyingAbove p with caret plus Upper E

where p is the point estimate, and Upper E is the margin of error.


To express the confidence interval (0.008, 0.096) in the form of ModifyingAbove p with caret minus Upper E less than p less than ModifyingAbove p with caret plus Upper E, we first need to find the point estimate (p) and the margin of error (Upper E).

The point estimate is the midpoint of the interval, which is:

p = (0.008 + 0.096) / 2 = 0.052

The margin of error is half the width of the interval, which is:

Upper E = (0.096 - 0.008) / 2 = 0.044

Therefore, the confidence interval can be expressed as:

ModifyingAbove 0.052 with caret minus 0.044 less than p less than ModifyingAbove 0.052 with caret plus 0.044

This means that we are 95% confident that the true population proportion (p) falls within the range of 0.008 to 0.096.

the confidence interval (0.008, 0.096) can be expressed in the form of Modifying Above p with caret minus Upper E less than p less than Modifying Above p with caret plus Upper E as Modifying Above 0.052 with caret minus 0.044 less than p less than Modifying Above 0.052 with caret plus 0.044. This means that we are 95% confident that the true population proportion falls within this range.

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Answer:

20 Plates

Step-by-step explanation:

Given that :

Sally's kitchen :

Setup cost = $60

Cost per plate = $12

Jimmy's BBQ :

Setup cost = $100

Cost per plate = $10

Let number of plates = x

Equate both and solve for x :

Sally's kitchen = Jimmy's BBQ

60 + 12x = 100 + 10x

12x - 10x = 100 - 60

2x = 40

x = 40/2

x = 20

20 plates

Answer:

D

Step-by-step explanation:

Given

- (x + 3) - 2(4x - 3) ← distribute both parenthesis

step 1

= - x - 3 - 8x + 6 ← collect like terms

step 2

= - 9x + 3

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:

There are a total of 2500 cups

Step-by-step explanation:

10% of the cups are green

you can set up a equation for this

x = total cups

.10x = 250

multiply both sides by 10 to make x a whole number

x = 2500

Answer: 73.9

Step-by-step explanation:

Answer:

2 hours

Step-by-step explanation:

variable x = hours

fix it fast: 25 + 50x

do it right: 35 + 45x

25 + 50x = 35 + 45x

subtract 45x from both sides

subtract 25 from both sides

(this action cancels out 45x on the right side and 25 on the left side so you can combine like terms)

50x - 45x = 35 - 25

5x = 10

divide by 5 on both sides

x = 2

Answer:

I want to say it's 60...because if you add up 150 and 90 (the right angle) you get 240 which when subtracted from 360 gives you 120...with both E & G being created with equal lengths you would divide 120 by 2 which gives you 60. Hope this helps :)

Answer:

12

Step-by-step explanation:

5x4=20

3x4=12

Answer:

12 Parts Red

Step-by-step explanation:

5*4=20

3*4=12

12 Parts Red

Answer:

Y= 14x+5

Step-by-step explanation:

Answer:

≤

Step-by-step explanation:

First we solve 5(x + 2) ≥ 2(x + 8).

5x + 10 ≥ 2x + 16

3x ≥ 6

x ≥ 2.

Now we place an equal sign into the box:

4(x - 6) = 2(x - 10)

4x - 24 = 2x - 20

2x = 4

x = 2.

For the solution to only have 1 value, the solution must be x = 2.

Therefore we must have x ≥ 2 and x ≤ 2.

Answer:

Answer: A. The contrapositive of the statement will be :

Step-by-step explanation:

The contrapositive of an if-then statement "p then q' is given by :

"If not q then not p".

The given statement is

Then the contrapositive of the statement will be :

Hence, A is the right option.

Answer:

(1) Reuse;  (2) Recycle ;  (3) Reduce

Step-by-step explanation:

The ideal sequence would be:

1) Use it again (reuse) if the object still serves its intended purpose/s

2) If not possible to the used again, send it to a recycling plant to extract from it items/parts/substance of utility for other new products

3) if it cannot be reused or recycled, the last option will be to reduce it completely.

Answer:

x = 2.

Step-by-step explanation:

First convert to vertex form:

f(x) = 5x^2 - 20x + 3

= 5(x^2 - 4x) + 3

= 5 [(x - 2)^2 - 4] + 3

= 5(x - 2)^2 -20 + 3

= 5(x - 2)^2 - 17.

The line of symmetry  is x = 2.