The function h(t) = 1,000(0.95)' models the = size of a mold culture t hours after being treated. What is the most appropriate domain for this function?

The correct answer is option (B) 0.276. At x = 0.276, the slope of the line tangent to the f graph at (x,f(x)) = 3 is obtained.

The derivative of f can be used to determine the value of x for which the slope of the line perpendicular to the f graph at (x, f(x)) equals 3. (x). F(x) derivative is provided by:

f'(x) = 8e4x2

Now, we set the derivative f'(x) equal to 3 and solve for x:

3= 8e4x2

1/8 = e4x2

ln(1/8) = 4x2

x2 = ln(1/8)/4

x = ±√(ln(1/8)/4)

We take the positive root since we are trying to get the positive value of x:

x = √(ln(1/8)/4)

We now change this x value into our equation and find x:

x = √(ln(1/8)/4)

≈ 0.276

Therefore, the value of x for which the slope of the line tangent to the graph of f at (x,f(x)) is equal to 3 is 0.276.

Complete Question:

Let f be the function given by f(x)=2e4x2 For what value of x is the slope of the line tangent to the graph of f at (x,f(x)) equal to 3?

(A) 0.168

(B) 0.276

(C) 0.318

(D) 0.342

(E) 0.551

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your monthly payment for borrowing $15,000 over 5 years with an annual interest rate of 5.9% and monthly payments will be approximately $283.89.

To calculate the number of months required to pay off the loan, we can use the loan repayment formula:

n = -log(1 - (r * PV) / PMT) / log(1 + r)

Where:

n = Number of months

PV = Loan amount (purchase price of the car)

PMT = Monthly payment

r = Monthly interest rate (APR divided by 12)

Substituting the given values, the formula becomes:

n = -log(1 - (0.04/12 * 12000) / 300) / log(1 + 0.04/12)

Simplifying this expression, we find:

n ≈ 40

Therefore, it will take approximately 40 months to pay off the loan for the used car.

Moving on to the second question, to calculate the monthly payment for borrowing $15,000 over 5 years with an annual interest rate of 5.9% and monthly payments, we can use the loan payment formula:

PMT = PV * (r *\((1 + r)^n\)) / (\((1 + r)^n\) - 1)

Where:

PMT = Monthly payment

PV = Loan amount

r = Monthly interest rate (annual interest rate divided by 12)

n = Number of months (5 years * 12 months per year)

Substituting the given values, the formula becomes:

PMT = 15000 * (0.059/12 * (\((1 + 0.059/12)^(5*12)\))) / (\((1 + 0.059/12)^(5*12)\) - 1)

Calculating this expression, we find:

PMT ≈ $283.89

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Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.

Here,

Given : Ria purchases 19 books for £6.82 apiece.

Thus,

Total cost of book = 19 * 6.82

=> 129.58

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

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Julianna had a new carpet installed in her apartment and had a rectangular piece left over that measured 60 square feet. To solve for the length of the carpet piece, we need to use the formula for the area of a rectangle, which is length times width. We know the width is 2 feet, so we can set up the equation:

2(x² - 19) = 60 Simplifying this equation, we get: x² - 19 = 30 x² = 49 Taking the square root of both sides, we get:
x = 7 or x = -7 Since we are looking for a length, we can ignore the negative solution and choose x = 7. Plugging this value back into the equation, we get: 2(7² - 19) = 60 2(49 - 19) = 60 2(30) = 60
Therefore, the length of the carpet measured in feet is 30. The answer is G x = 7, and the carpet is 30 feet in length.
When it comes to carpet installation, it's important to accurately measure the space to ensure you purchase the right amount of carpet. It's also important to account for any odd spaces or corners that may require extra carpet. When you have leftover carpet, you can use it to create a cozy area rug or donate it to a local charity. Remember to always dispose of carpet properly by recycling or disposing of it in a landfill.

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Answer:

Together, they have 12 + 2(12) = 12 + 24 = 36 toys.

Answer:

so in total they have 36 toys

Step-by-step explanation:

True. Nonsampling errors refer to errors that occur during the data collection process that are not related to the sampling method used. These errors can occur in any type of data collection method, whether it be through surveys, experiments, or observational studies.

Nonsampling errors can arise due to a variety of reasons, such as poor survey design, biased sampling methods, inadequate training of surveyors, errors in data entry or processing, or even deliberate fraud.

Nonsampling errors can have a significant impact on the quality of the data collected, as they can introduce biases and inaccuracies into the results. These errors can result in incorrect conclusions and decisions based on the data, which can have serious consequences. Therefore, it is important to take steps to minimize nonsampling errors during the data collection process, such as carefully designing surveys, ensuring proper training of surveyors, and conducting thorough quality checks on the data collected.

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Answer: x = 12, ∠B = 45°

Step-by-step explanation:

Angle A and Angle B are alternate exterior angles meaning that they are equal

5x - 15 = 2x + 21

3x - 15 = 21

3x = 36

x = 12

B = 2(12) + 21

B = 24 + 21

B = 45

Answer:

  D.  36 units

Step-by-step explanation:

You want the perimeter of the given isosceles triangle.

The Pythagorean theorem tells you the relationship between the side lengths of a right triangle. An altitude of an isosceles triangle divides it into two congruent right triangles. We can use this fact to find the lengths of the sides of the triangle that are not aligned with the grid.

By counting grid squares, or by finding the difference of coordinates, we can determine the lengths of the sides of each right triangle to be 12 units (horizontally) and 5 units (vertically). Then the slant length s is ...

  s² = 12² + 5²

  s² = 144 +25 = 169

  s = √169 = 13

The two congruent side lengths of the red triangle are 13 units each, and its "base" is 10 units. The perimeter is the sum of these lengths:

  P = 13 +13 +10 = 36 . . . . units

__

Additional comment

The integer side lengths of the right triangle can be written as a triple: {5, 12, 13}. This is known as a "Pythagorean triple." Perhaps the most famous of these is {3, 4, 5}. Others you will encounter in algebra, trig, and geometry problems are {7, 24, 25}, {8, 15, 17}.

It can be time-saving to learn to recognize such ratios of side lengths, so you don't have to go through the whole Pythagorean theorem calculation when you want to find a missing side.

You can also find the perimeter of the given triangle by considering the red sides of the right triangle: 5 + 13 = 18. They match corresponding lengths on the other half of the red triangle, so its perimeter is 2×18 = 36.

Answer:

Independent variable: Time studying

Dependent variable: Score

Step-by-step explanation:

Independent variable is what you change, dependent variable is the result. So if changing how much time you spend studying changes your math test results,  the independent variable is time. Have a nice day!

y = (-11/55)x + 11  is the linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb.

To write a linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb, we need to use the slope-intercept form of a linear equation: y = mx + b.

We know that the ramp is 11 inches off the ground at the curb, which means that the y-intercept (where the ramp meets the curb) is 11 inches:

y = mx + 11

To find the slope (m), we need to use the information that the other end of the ramp rests on the street 55 inches from the curb. We can use the formula for slope:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) are the coordinates of the curb (0, 11) and (x2, y2) are the coordinates of the other end of the ramp (55, 0).

m = (0 - 11) / (55 - 0) = -11/55

Now we can substitute the slope and the y-intercept into the equation:

y = (-11/55)x + 11

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Answer:

f(g(-1)) = -10

Step-by-step explanation:

f(-1) = -2(-1) -3

f(-1) = -5

g(-5) = (5^2) + 5(-5)

g(-5) = -10

Answer:

start by plotting number 5 on the y-axis, and from that point move up 3 and to the left 4

Step-by-step explanation:

The area of the whole shape is approximately 391.98 m² (rounded to 1 decimal place).

To calculate the area of the shape formed by a right-angled triangle and a quarter circle, we can find the area of each component and then sum them together.

Area of the right-angled triangle:

The area of a triangle can be calculated using the formula A = (base × height) / 2. In this case, the base and height are the two sides of the right-angled triangle.

Area of the triangle = (22 m × 15 m) / 2 = 165 m²

Area of the quarter circle:

The formula to calculate the area of a quarter circle is A = (π × r²) / 4, where r is the radius of the quarter circle. In this case, the radius is half the length of the hypotenuse of the right-angled triangle, which is (22² + 15²)^(1/2) = 26.907 m.

Area of the quarter circle = (π × (26.907 m)²) / 4 = 226.98 m²

Total area of the shape:

To find the total area, we sum the area of the triangle and the area of the quarter circle.

Total area = Area of the triangle + Area of the quarter circle

Total area = 165 m² + 226.98 m² = 391.98 m²

Therefore, the area of the whole shape is approximately 391.98 m² (rounded to 1 decimal place).

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There are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit using combinations.

To determine how many phone numbers can be made with 10 digits, where any single digit number (0-9) can be used for any digit, follow these steps:

1. Understand that there are 10 possible digits (0-9) for each digit in the phone number.
2. Since there are 10 digits in the phone number, you need to calculate the total number of combinations by multiplying the number of possibilities for each digit.

To calculate this, simply raise the number of possible digits (10) to the power of the number of digits in the phone number (10):

10^10 = 10,000,000,000

So, there are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit.

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The work done by the constant force of 6 N in moving an object from x = 0 to x = 4 meters is equal to 24 J.

Work is the dot product of force and displacement, which in this case is the product of the constant force of 6 N and the displacement of 4 meters in the x-direction.

Work is calculated as W = F * d * cos(Θ), where Θ is the angle between the force and displacement vectors, and in this case, it is 0° as the force and displacement are in the same direction.

Therefore, W = 6 N * 4 m * cos(0°) = 6 N * 4 m = 24 Nm = 24 J. The unit of joule (J) can also be expressed as Newton-meter (Nm).

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The product of 20  x  9  x  5 is calculated to be 900

The property used is the commutative property of multiplication

Data given in the question include

product of 20 x 9 x 5

The commutative property of multiplication is the property of multiplication that is used as follows

a * b * c = c * b * a

Applying the commutative property of multiplication to the given problem we have

= 20 * 9 * 5

= 180 * 5

= 900

also

= 5 * 9 * 20

= 45 * 20

= 900

The product of 20 * 9 *  5 = 900

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We can use a priority queue to keep track of the k most frequent strings. The priority queue should be sorted by the frequency of the strings, and in case of ties, we should sort by lexicographical order.

Here's the step-by-step algorithm to solve the problem:

1. Create a hash map to count the frequency of each string in the array.
2. Create a priority queue and define a custom comparator function that compares strings based on their frequency and lexicographical order.
3. Iterate over the keys of the hash map and add each string to the priority queue.
4. Pop the top k strings from the priority queue and add them to the result array.
5. Return the result array sorted in descending order of frequency.

Here's the Python code that implements this algorithm:

```
import heapq
from collections import defaultdict

def topKFrequent(words, k):
   freq = defaultdict(int)
   for word in words:
       freq[word] += 1
   
   pq = []
   for word, count in freq.items():
       heapq.heappush(pq, (-count, word))
   
   res = []
   for i in range(k):
       res.append(heapq.heappop(pq)[1])
   
   return sorted(res, key=lambda x: (-freq[x], x))
```

In this code, we use a defaultdict from the collections module to count the frequency of each string. We then use a heap (implemented as a list) to keep track of the k most frequent strings. The -count value is used as the first element of each tuple in the heap, so that we can sort the strings by frequency in descending order. The second element of each tuple is the string itself, which is used to break ties in case of equal frequency. Finally, we sort the result array based on the frequency and lexicographical order using the sorted function and a lambda function.

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Answer:

I just need the points sry, not sry reesesTM

Step-by-step explanation:

Answer:

So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.

Step-by-step explanation:

Let x be the amount invested in the mutual fund that earned a 5% profit, and let y be the amount invested in the mutual fund that earned a 2% profit. We know that the total investment was $1,200, so:

x + y = 1200

We also know that the total profit was $39, which can be expressed as a decimal as 0.39 (since profit is calculated as a percentage of the initial investment). The amount of profit earned on the first fund is 5% of x, or 0.05x, and the amount of profit earned on the second fund is 2% of y, or 0.02y. So:

0.05x + 0.02y = 0.39

We now have two equations with two variables:

x + y = 1200

0.05x + 0.02y = 0.39

We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:

x = 1200 - y

0.05(1200 - y) + 0.02y = 0.39

Simplifying and solving for y:

60 - 0.05y + 0.02y = 0.39

0.03y = 0.39 - 60

0.03y = -59.61

y = -59.61 / 0.03

y = 1987

This tells us that $1,987 was invested in the mutual fund that earned a 2% profit. To find the amount invested in the mutual fund that earned a 5% profit, we can substitute into the first equation:

x + y = 1200

x + 1987 = 1200

x = 1200 - 1987

x = -787

This doesn't make sense, since we can't have a negative investment amount. It means that we made a mistake somewhere. Checking our work, we can see that the equation 0.05x + 0.02y = 0.39 should actually be:

0.05x + 0.02y = 39

(without the decimal point). With this correction, we can solve as before:

x + y = 1200

0.05x + 0.02y = 39

x = 1200 - y

0.05(1200 - y) + 0.02y = 39

60 - 0.05y + 0.02y = 39

0.03y = 21

y = 700

So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.

Given parameters:

 The coordinates are:

                 P1 (8, -4) and P2 (-3, 9)

Unknown:

The midpoint of the endpoints = ?

Solution:

     x₁  =  8

     y₁  = -4

     x₂  = -3

     y₂  = 9

  midpoints;     x\(_{m}\) , y\(_{m}\)  = \(\frac{x_{1} + x_{2} }{2} ,\) \(\frac{y_{1} + y_{2} }{2}\)

                                       = \(\frac{8 +(-3)}{2}\) , \(\frac{-4 + 9}{2}\)

                                       = \(\frac{5}{2}\) , \(\frac{5}{2}\)

   The coordinate of the x-axis is \(\frac{5}{2}\)

Answer:

The ball will hit the floor after 3 seconds.

Step-by-step explanation:

Answer:

the range is the set of possible output of values

Step-by-step explanation:

The range is the set of y-values (OUTPUT) that map to the set of x-values (INPUT).

Answer:

the answer is c or 35x^2 + 210x +315

Step-by-step explanation:

The area of the square is "d" and since it asks for the combined area of the triangle and square it has to be more than that, hope that helps.

The second option has the best value for money. It is $0.014 cheaper.

First we know that a 80 ml bottle is priced at  £55, then the price per ml will be given by the quotient:

p = 55/80 = 0.689

In the other case a 50ml bottle costs  £45 and a second one of 50ml comes by half of that at £22.5

Then the price for 100ml is £67.5

Then the value for money here is:

q = 67.5/100 = 0.675

Then the second option has the best value for money by $0.014. Being cheaper.

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The number of days Super Sally and Lazy Petunia work are illustrations of simultaneous equations

(a) Super Sally and Lazy Petunia

Represent their earnings with the first letters.

So, we have:

\(\mathbf{L = \frac 12S}\) -- number of days

\(\mathbf{20L + 57S= 7733}\) --- the total earnings

Make S the subject in \(\mathbf{L = \frac 12S}\)

\(\mathbf{S = 2L}\)

Substitute 2L for S in \(\mathbf{20L + 57S = 7733}\)

\(\mathbf{20L + 57 \times 2L = 7733}\)

Expand

\(\mathbf{20L + 114L = 7733}\)

Add

\(\mathbf{134L = 7733}\)

Divide both sides by 134

\(\mathbf{L = 57.7}\)

From the options, the closest to 57.7 is 60.

Hence, the number of days that Petunia worked is closest is 60

(b) 4 digit even numbers

The digits are given as: 0, 1, 5, 6, 7, 8 and 9

To create a 4-digit number, the first digit cannot be 0.

So, the first digit can be any of the remaining 6

Because, it is an even number, the number can only end with 0, 6 or 8

So, the last digit can be any of the 3

Since there is no repetition, the second and the third digits can be any of the remaining 5 and 4 digits, respectively.

So, the number of digits is:

\(\mathbf{n =6 \times 3 \times 5 \times 4}\)

\(\mathbf{n =360}\)

Hence, the number of digits is (d) 360

(c) The value of 28^983 x 98^984/14^2948

Rewrite the expression as:

\(\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}\)

Express all number as a base of 14

\(\mathbf{\frac{14^{2 \times 983} \times 14^{7 \times 984}}{14^{2948}} }\)

Apply law of indices

\(\mathbf{14^{2 \times 983+7 \times 984-2948}}\)

Evaluate all products

\(\mathbf{14^{1966+6888-2948}}\)

Evaluate the exponent

\(\mathbf{14^{5906}}\)

Hence, the result of \(\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}\) is \(\mathbf{14^{5906}}\)

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Answer:

68

Step-by-step explanation:

\(4+\left(11-3\right)^2\\(11-3)=8\\=4+8^2\\=4+64\\=68\)

A bell-shaped probability distribution that is symmetrical about its mean is the student's t-distribution. In the following situations, it is thought to be the distribution that should be used to build confidence intervals when working with little samples that have fewer than 30 components if it is unclear what the population variance is.

When the involved distribution is either normal or nearly normal.

A t-distribution is used to test the following in addition to being used to build confidence intervals:

Individual population mean

The variations in two population means.

The average variation among paired (dependent) populations.

The correlation coefficient for the populace.

If the sample size is high enough for the central limit, a t-distribution may still be viable for usage even in the absence of explicit normality for a specific distribution theorem that must be used. In this scenario, the distribution is regarded as roughly normal.

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The quadratic equation we  use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0

What is Quadratic equation?

The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.

What is Rectangle?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.

Let W be the width of rectangle.

then, length of the rectangle is W + 6 .

and the Area, A = 16 inches^2

And the area of recatngle is A = L x W

Hence, A = (W+6)W

So, 16 = W^2 + 6W

Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;

W^2 + 6W - 16 = 0

By the quadratic formula we have

\(w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}\)

\(w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}\)

\(w = \frac{-6 \pm \sqrt{36 + 64} }{2}\)

\(w = \frac{-6 \pm 10 }{2}\)'

Hence, we take width as a positive because width never be negative .

so,the value of width is ;

w = 2

and length o rectangle is ;

l = w + 6 = 2 + 6 = 8

l = 8

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