Virginia needed some batteries for her flashlights. She bought 4 batteries for $6.80. At that rate, how much would 10 batteries cost?

Answer:

48

Step-by-step explanation:

a² - 16

a = 8

8² - 16 = 64 - 16 = 48

So, the answer is 48

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

The dimensions of the rectangle, obtained using Pythagorean Theorem are;

The length of the rectangle = 4·√5 units

The width of the rectangle = 2·√5 units

Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side.

Let x represent the width of the rectangle, we get;

The length = 2·x

Therefore, according to Pythagorean Theorem, we get;

√((x² + (2·x)²) = 10

((x² + (2·x)²) = 10² = 100

5·x² = 100

x² = 100 ÷ 5 = 20

x = √(20) = ±2·√5

Whereby the dimensions of a rectangle are natural numbers, we get;

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To send the frequency distribution data to Excel, you can follow these steps:

1. Open Excel on your computer.

2. Create a new worksheet or open an existing one where you want to import the data.

3. Label the first column as "Number of Tests Performed" and the second column as "Number of Patients".

4. In the first column, enter the values 0, 1, 2, 3, and 4 or more in separate cells, corresponding to the number of tests performed.

5. In the second column, enter the corresponding values 14, 8, 4, 4, and 2, which represent the number of patients for each category of tests.

6. Select both columns by clicking and dragging over the cells.

7. Go to the "Copy" option in the Excel toolbar or use the Ctrl+C keyboard shortcut to copy the selected data.

8. Switch to the Excel worksheet where you want to paste the data.

9. Select the first cell where you want to paste the data.

10. Right-click on the cell and choose the "Paste" option or use the Ctrl+V keyboard shortcut to paste the data.

Now, the frequency distribution data from the emergency room tests should be successfully transferred to Excel.

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After 4000 years, only about 52.5 mg of Radium-226 remains in the original sample containing 300 mg of Radium-226

So if a sample contains 300mg of Radium-226 and 4000 years have passed since its creation, we can calculate the remaining amount of Radium-226 using the following formula:

Remainder= Initial value * (1/2) ^ (time / half-life)

where the Initial amount is the initial amount of Radium-226 in milligrams, time is the time in years, and the half-life is the half-life of Radium-226 in years.

Putting the values given into the formula, we get

Amount remaining = 300 * (1/2)^(4000/1590)

= 300 * (1/2)^2.5

= 300 * 0.1755

≈ 52.5 mg

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 The radius of convergence,  R, is 1

To find the radius of convergence, R, of the series, we can use the formula:

R = 1 / lim(n→∞) |(aₙ₊₁ / aₙ)|

In this case, we have the series [∑ from n = 0 to ∞] (x - 8)^n(n^8 + 1).

To apply the ratio test, let's compute the limit of |(aₙ₊₁ / aₙ)| as n approaches infinity:

lim(n→∞) |[(x - 8)^(n + 1)(n^8 + 1)] / [(x - 8)^n(n^8 + 1)]|

Simplifying, we can cancel out (n^8 + 1) terms:

lim(n→∞) |x - 8|

For the series to converge, the limit above must be less than 1. Therefore, we have:

|x - 8| < 1

This inequality implies that x must be within a distance of 1 from 8. Hence, we have:

7 < x < 9

Therefore, the interval of convergence, I, is (7, 9), and the radius of convergence, R, is half the length of the interval:

R = (9 - 7) / 2 = 2 / 2 = 1

Thus, the radius of convergence, R, is 1.

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Based on fractional values, if Susan originally has 7 yards of fabric, after making 3 aprons consuming 5⁵/₈ yards, the quantity of fabric left is 1³/₈ yards.

Fractional values are the results of fractional computations.

Fractions may be proper, improper, and complex fractions, depending on the values of the denominators and the numerators.

Algebraic expressions that have fractions are stated as fractional values.

The original quantity of fabric that Susan has = 7 yards

The quantity of fabric used for the front of each apron = 1¹/₄ yards

The quantity of fabric used for the tie of each apron = ⁵/₈ yards

The total quantity of fabric used for each apron = 1⁷/₈ yards (1¹/₄ + ⁵/₈)

The total quantity of fabric used for the 3 aprons made = 5⁵/₈ yards (1⁷/₈ x 3)

Therefore, the remaining quantity of fabric that Susan has after making the 3 aprons = 1³/₈ yards (7 - 5⁵/₈).

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Susan first made 3 aprons using 1¹/₄ yards for the front and ⁵/₈ yards for the tie.

Answer:

900

Step-by-step explanation:

Answer:

Ernest is wrong, because the sandwich can be made in 6 different ways (lunch > sandwich: white bread > cheese, pickles, mayonnaise ; wheat bread > cheese, pickles, mayonnaise) and the lunch can be made in 8 different ways.

Answer:

n > 8/3

Step-by-step explanation:

Divide both sides of the equation by 3 to make n the only variable left, n> 8/3

a. the distribution of X ~ N(15,5)

b.  the probability that it lasted at least 12 days = 0·72575

c.  the probability that it lasted between 17 and 22 days  = 0.30567

d. 72% of all of these types of trials are completed within  13 days

(a)

The x follow normal distribution with mean standard deviation

X ~ N(15,5)

(b)

probability at least 12 days.

P(X≥12) = 1 - P(X ≤12)

            = 1 - P((X - μ)/б ≤ (12-15)/5 ]]

            = 1 - P[Z  < -0.6]

            = 1 - 0·27425

            = 0·72575

(c)

Probability at least between 16 & 21 days

P(16 < x < 21) = p( (16-15)/5 <  (X - μ)/б - (21-15)/5]

                     = p (0.2 < Z < 1.2 )

                     = p[Z < 1.2] - P[Z < 0.2]

                     = 0.8849 - 0.5792

                     = 0.30567

(d)

standard normal table z is 0.65

p (Z < 0.65) = 0.74215

using Z score formula

X = Z x  б + μ

X = 0.65 x 5 + 15

X = 13

This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

Velocity in still air: 760 mi/ hr

Velocity against the wind: 210 mi/ hr

Step-by-step explanation:

Given

See attachment for complete question

Required

The rate in still air

The rate of the wind

From the question, the velocity (v) against the wind is:

\(v =\frac{distance}{time}\)

\(v =\frac{3040}{4}\)

\(v_1 =760mi/hr\)

The velocity with the wind is:

\(v_2 = \frac{8260}{7}\)

\(v_2 = 1180mi/hr\)

Let:

\(x \to\) velocity in still air

\(y \to\) velocity of the wind

So, we have:

\(x - y = 760\)

\(x + y = 1180\)

Add both equations

\(x + x -y + y = 760 + 1180\)

\(2x = 1940\)

Divide by 2

\(x = 970\)

Substitute \(x = 970\) in \(x - y = 760\)

\(970 - y= 760\)

Make y the subject

\(y = 970 - 760\)

\(y = 210\)

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Answer:

reciprocal

Step-by-step explanation:

mark me brainliest pls

Answer:

6/8

Step-by-step explanation:

if there are 8 selections and 2 are yellow it would be 6/8 of not getting yellow

Answer:2/3

Explanation:

There are

3

equally likely possibilities; red, white and blue.

Therefore the chances of it not being blue are the same as the chances of it being red + the chance that it will be white.

Each option has a

1

3

chance of happening, so the chances that it will be red or white is

2

×

1

3

=

2

3

Step-by-step explanation:

The entries of the table, denoted as T(i, j), represent the length of the longest nicely spaced subsequence ending at index i, with the difference between the last element and the element at index j.

The recurrence relation for the entries of the table can be defined as follows:

  T(i, j) = max(T(j, k) + 1), where 0 <= k < j and |S(i) - S(j)| <= 5.

  This means that we consider all previous elements (j) that have a difference of at most 5 with the current element (i), and we update the maximum length of the nicely spaced subsequence by adding 1 to the length of the subsequence ending at index j (T(j, k)).

  The base case is T(i, j) = 1, where there are no previous elements that satisfy the nicely spaced condition.

Pseudocode for the algorithm:

  Initialize an array T with length n, where n is the length of the input sequence S.

  Set all values in T to 1.

  Initialize a variable max_length to 1.

  for i = 1 to n:

      for j = 1 to i-1:

          if |S[i] - S[j]| <= 5:

              T[i] = max(T[i], T[j] + 1)

              max_length = max(max_length, T[i])

  Return max_length as the length of the longest nicely spaced subsequence of S.

The running time of this algorithm can be analyzed as follows:

  - The outer loop iterates through each element of the sequence, so it takes O(n) time.

  - The inner loop iterates through all previous elements for each element, so it takes a total of O(n^2) time in the worst case.

  - Therefore, the overall time complexity of the algorithm is O(n^2).

  Since we only use an array of size n (T) to store the lengths of subproblems, the space complexity is O(n).

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Answer:

15 multiple choice 5 true false

Plzzzzz give me Brainliest!!!!!  

To find one machine that does not work, you expected to buy 200 machines on average.

One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.

A company named Batco sells batteries.

And Batco claims that  99.5% of their batteries are in working order.

That means, 100 - 99.5 = 0.5% of their machines have defect.

0.5 as a fraction of 100% is 0.005.

To find the one machine that does not work;

Divide 1 by fraction of machines not working,

1 / 0.005

= 200

Therefore, you need to buy 200 machines.

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Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

Step-by-step explanation:

Let the other 4 friends arrange themselves first. There are 4! ways to do so.

Now there are 3 spaces between the 4 friends, and 1 at each end (total 5 spaces)

Example: _F_F_F_F_

Alice can choose to stand in any of the 5 spaces. David can choose to stand in any of the 4 remaining spaces (now Alice and David are not next to each other)

Total number of ways = 4! * 5 * 4 = 480.

Answer and Explanation: The conditions when the net force and the net torque are zero are called static equilibrium.

Answer:

mPS = 80°

Step-by-step explanation:

angles on a circle subtended by the same arc are congruent

∠ PQS and ∠ PRS are both subtended by arc PS , then

10 + 3x = 110 - 7x ( add 7x to both sides )

10 + 10x = 110 ( subtract 10 from both sides )

10x = 100 ( divide both sides by 10 )

x = 10

then

∠ PQS = 110 - 7x = 110 - 7(10) = 110 - 70 = 40°

the inscribed angle PQS is half the measure of its intercepted arc PS , then

PS = 2 × 40° = 80°

The value of line integral is: 73038

A line integral is any integral that is evaluated over a path. There are several ways to go about evaluating a line integral. Since our path is a simple line segment.

The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)

x(t) = (1-t)0 + t × 2 = 2t  

y(t) = (1-t)0 + t × 3 = 3t

z(t) = (1-t)0 + t × 4 = 4t

We have to differentiation w.r.t "t"

x'(t) = 2

y'(t) = 3

z'(t) = 4

The given line integral is:

\(\int\limits_C {xe^y^z} \, ds=\int\limits^1_0 2te^1^2^t^2\sqrt{2^2+3^3+4^2} \, dt\\\\ds = \sqrt{2^2+3^3+4^2} dt\)

Now, We have to solve the integration and we get :

\(\int\limits_C {xe^y^z} \, ds=\frac{\sqrt{29} }{12} (e^1^2-1)\)

=> 73037.99 ≈ 73038

Hence,  the value of line integral is, 73038.

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Debbie is using the method of "exhaustive search" or "brute-force" problem solving to ensure 100% accuracy in finding the last three words in her word search.

In an exhaustive search, all possible solutions or combinations are systematically checked or examined to find the correct answer.

Debbie is looking at every possible word combination in order to locate the three words she is having difficulty finding.

By examining each combination, she eliminates the possibility of missing any potential solutions and ensures a comprehensive search of all options.

While this approach guarantees accuracy, it can be time-consuming and resource-intensive, especially when dealing with a large number of possibilities.

However, in Debbie's case, she is committed to achieving a 100% accurate solution by considering every single word combination.

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As Debbie completes her daily word search there are three words she is having difficult finding. In order to be sure to solve the problem with 100% accuracy, she looks at every possible word combination to find these last three words. What method of problem solving is Debbie using ??

Answer:

The answer would be 2/3.

Step-by-step explanation:

There are 6 faces on a dice 3 of which are odd which would be 1/2. Then there is one face on a dice that has 3 dots on it which would 1/6. So 1/2+1/6= 4/6 which simplifies to 2/3.

Unfortunately, we don't have explicit information about the function x = x(t) or y = y(t) or their derivatives. Without further information or additional equations relating x and y, it is not possible to find the exact value of dy/dt or dx/dt.

To find dy/dt given the information that dy/dx = -4 when x = -1.8 and y = 0.81, we can use the chain rule of differentiation.

The chain rule states that if y is a function of x, and x is a function of t, then the derivative of y with respect to t (dy/dt) can be calculated by multiplying the derivative of y with respect to x (dy/dx) and the derivative of x with respect to t (dx/dt). Mathematically, it can be expressed as:

dy/dt = (dy/dx) * (dx/dt) In this case, we are given that dy/dx = -4 when x = -1.8 and y = 0.81. To find dy/dt, we need to find dx/dt.

If you have any additional information or equations relating x and y, please provide them, and I will be able to assist you further in finding the value of dy/dt.

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Answer:

x= 45°

Step-by-step explanation:

When you add the all of the angles together, it should equal 180°. You have 90° already so 180-90= 90. Now divide- 90÷2 (because there are two congruent angles)=45°