135 physical therapists were asked if they use their complimentary gym membership and if they bring their own lunch to work. the following table shows the results. brings lunch to work does not bring lunch to work total uses gym membership 24 72 96 does not use gym membership 18 21 39 total 42 93 135 according to the table, what is the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work? give your answer as a fraction in simplest form.

Answer: 20

Step-by-step explanation:

8x5= 40

40/2=20

Triangle formula base times height divide by two.

Answer: 20cm2

Step-by-step explanation: I researched it :)

Answer:

(4, 0) and (3, 0)

Step-by-step explanation:

x - 4 = 0;  x = 4

x - 3 = 0;  x = 3

Step-by-step explanation:

i think its A

Answer:

Step-by-step explanation:

Let the equation be:

Multiply both sides by 4 and complete the square:

Since -3 = 1(-3) = (-1)*3, we have following options:

1)

Eliminate k by adding up equations:

2)

Eliminate k by adding up equations:

Answer: the value is 0

Step-by-step explanation:

we simply substitute the letter for the number 3.

10 - 3 - 7

7 - 7

0

Answer:

104%

Step-by-step explanation:

(275 × p) / 100 = 286

((275 × p) / 100) × 100 = 286 × 100

275p = 28600

275p / 275 = 28600 / 275

p = 104

Percent Increase = 104

Answer:

==> 104%

Step-by-step explanation:

Working Out

The problem we are solving is:

Work out the percentage increase between 275 and 561.

Difference is 561 - 275 = 286.

Divide the difference between the original number:

286 / 275 = 1.04.

Multiply by 100 to change to a percentage:

1.04 x 100 = 104%.

This number is positive so we have a percentage increase of 104%.

x + 54 + 5x = 90°

6x = 90 - 54

6x = 36

x = 36/6 = 6

value for x is 6

Manjit is donating a total of $14,000 to Charities A, B, and C in the ratio of 6 : 1 : 3. The task is to determine the amount of money he is donating to each charity.

To calculate the amount of money donated to each charity, we need to divide the total donation amount based on the given ratio.

Calculate the total ratio value:

The total ratio value is obtained by adding the individual ratio values: 6 + 1 + 3 = 10.

Calculate the donation for each charity:

Charity A: (6/10) * $14,000 = $8,400

Charity B: (1/10) * $14,000 = $1,400

Charity C: (3/10) * $14,000 = $4,200

Therefore, Manjit is donating $8,400 to Charity A, $1,400 to Charity B, and $4,200 to Charity C.

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The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

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Answer:

Tienes 30 años, ya que cuando tendras el doble de la edad de 10 años, o sea 20 años y dentro de 10 años da igual a 30 años.

Espero que ayude

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Before applying the zero product rule, we must first ensure that the quadratic equation is in standard form.

\(ax^2 + bx + c = 0\)

where "a," "b," and "c" are coefficients of the quadratic condition, and "x" is the variable.

In case the quadratic condition isn't as of now in standard shape, you ought to improve it by moving all the terms to one side of the condition to induce:

\(ax^2 + bx + c =0\)

Once the quadratic condition is in a standard frame, you'll at that point apply the zero item run the show, which states that in case the item of two components is rise to to zero, at that point at the slightest one of the factors must be zero.

Within the case of a quadratic condition, you'll use the zero item run the show to illuminate for "x" by figuring the quadratic condition into two straight variables.

setting each figure rise to zero, and after that understanding for "x".

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Answer:

\((\frac{6}{1})(\frac{11}{4} )\)

\((-\frac{10}{3})(-\frac{17}{5})\)

\((-\frac{9}{2} )(\frac{26}{3} )\)

\((\frac{11}{6})(-\frac{9}{1} )\)

Step-by-step explanation:

I hope this help you

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

let's solve ~

Perimeter of the composite figure :

Perimeter of rectangle + circumference of semi circle - common side.

Perimeter of rectangle :

\(\qquad \tt \dashrightarrow \:2(4 + 12)\)

\(\qquad \tt \dashrightarrow \:2(16)\)

\(\qquad \tt \dashrightarrow \:32 \: \: ft {}^{} \)

Circumference of Semicircle :

\(\qquad \tt \dashrightarrow \:\pi r\)

\(\qquad \tt \dashrightarrow \:3.14 \times 2\)

\(\qquad \tt \dashrightarrow \:6.28 \: ft\)

Length of common side = 4 feet

So, perimeter of composite figure :

\(\qquad \tt \dashrightarrow \:32 + 6.28 - 4\)

\(\qquad \tt \dashrightarrow \:34.28 \: ft\)

Answer:

-25 ,B

Step-by-step explanation:

The * must be replaced by a digit of 1, hence the solution to the equation is given as follows:

x = 143.

A number is divisible by 10 if and only if its last digit is 0. This is because 10 is a multiple of 5 and 2, which are the prime factors of 10. Therefore, a number is divisible by 10 if it can be divided evenly by both 5 and 2.

For this problem, the equation is given as follows:

10x + 11 = 144*

Hence, when * = 1, we have that:

10x + 11 = 1441

10x = 1430.

Then the solution for the equation is obtained as follows:

x = 1430/10

x = 143.

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The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

\(\dfrac{27}8\)

Step-by-step explanation:

\(= \left(\dfrac{32}{243} \right)^{-\tfrac 35}\\\\\\= \left(\dfrac{2^5}{3^5} \right)^{-\tfrac 35}\\\\\\=\left(\dfrac 23 \right)^{-\tfrac{3\times 5}5 \right)\\\\\\=\left(\dfrac 23 \right)^{-3}\\\\\\=\dfrac{3^3}{2^3}\\\\\\=\dfrac{27}8\)

The graph that represents the function f(x) = 4[x] is option C.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4 [x]

[x] is the greatest integer function.

We see that,

f(0) = 4 [0] = 0

f(0.5) = 4 [0.5] = 4 x 0 = 0

f(x) = 0 for 0 ≤ x < 1

f(1) = 4 [1] = 4

f(1.5) = 4 [1.5] = 4 x 1 = 4

f(x) = 4 for 1 ≤ x < 2

f(2) = 4 [2] = 4 x 2 = 8

f(2.5) = 4 [2.5] = 4 x 2 = 8

f(x) = 8 for 2 ≤ x < 2

Thus,

The graph on option C has the required coordinates.

f(x) = 0 for 0 ≤ x < 1

f(x) = 4 for 1 ≤ x < 2

f(x) = 0 for 2 ≤ x < 2

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Answer:

y=3x^2,y=5^2,y=7x^2

Step-by-step explanation:

y=3x^2 is the widest, y=7x^2 is the narrowest, which leaves y=5x^2 in the middle

Answer : 2..A perfect square is an integer which is the square of another integer n , that is, n2 . (Since a negative times a negative is positive, a perfect square is always positive.

...

The radius of curvature of the lens is = 8cm

The radius of curvature is defined as the radius of the circle that is made by a spherical mirror or lens.

The focal length is defined as the distance between the point of convergence of your lens and the sensor

The refractive index is the measure of bending of a light ray when passing from one medium to another.

The relationship between focal length and radius of curvature is that R=2f

Where R = radius of curvature

f= Focal length

Therefore, radius of curvature = 2×4 =8cm

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Answer:

5: d

6: c

7: parallel ‌ ‌ ‌ ‌ ‌ ‌ ‌

Answer:

"A" option is correct

Step-by-step explanation:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion,

so if you take proportion of corresponding sides you will get n=1

Answer:

38 x^13/35

Step-by-step explanation:

when it's dividing, you substract 6 from 19

so it'll be x^13