The sum of a number and 3 more than twice the number is less than 36. Find the number

Answer:

1/4/4/3 is the same as 1/4 x 3/4

Step-by-step explanation:

first fraction-keep

Division sign-flip to multiplacation

Second sign-flip

Answer:

a) x⩽ -4

Step-by-step explanation:

This is because the required region is anything to the left of -4 that is x < -4. Now since x = -4 is inclusive, we have the inequality x ≤ -4.

We thus draw a dashed boundary line to represent the equality at the boundary for x ≤ -4.

Since that is done, we then shade to the left of the boundary line which is the required region of x ≤ -4.

the probability that a woman has cancer given that she has a negative test result is 0.964.

A certain form of cancer is known to be found in women over 60 with probability 0.7. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative and 5% of the time the test gives a false positive.

For a woman over the age of 60, the probability of having cancer is 0.7.

Let A be the occurrence of a woman having cancer, and let B be the occurrence of a woman receiving a favorable test result. We need to calculate the probability that a woman has cancer given that she has a negative test result.

Using Bayes’ theorem, we can calculate

P(A | B) = P(B | A) * P(A) / P(B).P(B | A) = probability of receiving a favorable test result if a woman has cancer = 0.9 (10% false negative rate).

P(A) = probability of a woman having cancer = 0.7.P(B) = probability of receiving a favorable test result = P(B | A) * P(A) + P(B | ~A) * P(~A).

The probability of receiving a favorable test result if a woman does not have cancer is P(B | ~A) = 0.05.

The probability of a woman not having cancer is P(~A) = 0.3.P(B) = (0.9 * 0.7) + (0.05 * 0.3) = 0.655.P(A | B) = (0.9 * 0.7) / 0.655 = 0.964.

Hence, the probability that a woman has cancer given that she has a negative test result is 0.964.

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Answer:

less than or equal to the test statistic.

Step-by-step explanation:

Jonathan and Oscar will have the same amount of money saved after  2 weeks.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

If they have same amount of money then,

f(x) = g(x)

18x+5 = 8x+25

10x = 20

x = 2 weeks

Therefore, Jonathan and Oscar will have the same amount of money saved after  2 weeks.

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To find the Laplace transform of a function, we use the formula:

L{f(t)} = ∫[0,∞) e^(-st) f(t) dt
where s is a complex number.

a. f(t) = t

Using the Laplace transform formula, we get:
L{t} = ∫[0,∞) e^(-st) t dt

Integrating by parts, we get:
L{t} = [-t e^(-st) / s]∞₀ + ∫[0,∞) e^(-st) / s dt

Evaluating the limits, we get:
L{t} = 0 + [1 / s^2] ∫[0,∞) s e^(-st) dt

Using the fact that ∫[0,∞) s e^(-st) dt = 1 / s^2, we get:
L{t} = 1 / s^2

Therefore, the Laplace transform of f(t) = t is 1 / s^2.

b. f(t) = t^2

Using the Laplace transform formula, we get:
L{t^2} = ∫[0,∞) e^(-st) t^2 dt

Integrating by parts twice, we get:
L{t^2} = [-t^2 e^(-st) / s]∞₀ + [2t e^(-st) / s^2]∞₀ + ∫[0,∞) 2e^(-st) / s^3 dt

Evaluating the limits, we get:
L{t^2} = 0 + 0 + [2 / s^3] ∫[0,∞) e^(-st) dt

Using the fact that ∫[0,∞) e^(-st) dt = 1 / s, we get:
L{t^2} = 2 / s^3

Therefore, the Laplace transform of f(t) = t^2 is 2 / s^3.

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The equation for adding "n" numbers in a row is [a + (a + 1) + (a + 2) +.... a + (n-1)]. As a result, (n/2) (first number + last number) is the sum of "n" consecutive numbers or "n" terms of AP (Arithmetic Progression). The formula for even consecutive numbers is 2n, 2n+2, 2n+4, 2n+6, and so on.

The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11. Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.

Any collection of consecutive odd numbers starting with 1 has a sum that is always equal to the square of the total number of digits. If the numbers 1, 3, 5, 7, 9, 11,..., and (2n-1) are odd, then the sum of the first odd number is 1. First two odd numbers added together equal 1 + 3 = 4 (4 = 2 x 2). Two successive odd numbers added together are always divisible by 4.

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Answer:

( x + 4 ) ( x + 1 )

Step-by-step explanation:

x² + 5x + 4

= x² + 1x + 4x + 4

= x ( x + 1 ) + 4 ( x + 1 )

= ( x + 4 ) ( x + 1 )

Hence, factorised.

Answer:

x = 3

Step-by-step explanation:

Step 1: Write out equation

x + 9 = 18 - 2x

Step 2: Add 2x on both sides

x + 2x + 9 = 18 - 2x + 2x

3x + 9 = 18

Step 3: Subtract 9 on both sides

3x + 9 - 9 = 18 - 9

3x = 9

Step 4: Divide both sides by 3

3x/3 = 9/3

x = 3

Answer:

0000000000000

Step-by-step explanation:

0000000000000

Answer:

The answer for a) is 2/5 and the answer for b) is 2/5.

Step-by-step explanation:

a) 8/20

then divide both numbers with 2 = 4/10.

again divide both numbers by 2 = 2/5.

So, the answer for (a) is 2/5.

b) 12/30

Again it can divide by 2 = 6/15.

now, you can divide both numbers with 3 = 2/5.

So, the answer for (b) is also 2/5.

It stops the program with the HLT (halt) instruction.

The mnemonic code in Figure Q5(c) can be constructed into a flowchart as shown below:

The loop flowchart is shown in the image above. As seen in the flowchart, this mnemonic code represents the flowchart in a sequence of steps that eventually forms a loop.

The LOOP is the starting point and then continues to perform a set of operations in sequence. In the end, it comes back to the starting point. This will continue until the condition is satisfied.

Further, the loop begins with loading 3000OH into accumulator A.

Here, A is then transferred to E and A is increased by one. It then moves on to load 01 into register B, and loads the value at 3001 into register C.

C is then decremented and the value at register B is added to register C.

Next, the register C is checked to determine if it is equal to zero (JNZ). If it is not, the program will return to the LOOP section.

If it is equal to zero, the result is stored in memory location 2010H.

Finally, it stops the program with the HLT (halt) instruction.

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By using the concept of function, it can be seen that the given figure does not represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the x axis represents the domain and the values on the y axis represents the Range.

From the figure it can be seen that

For x = 2, there are three points on the y axis.

So the point x = 2 maps to different points on the y axis

So this is not a function

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The depth of the water if the speed of the tsunami is 10 m/s is approximately 0.34 meters, or 34 centimeters, given by the equation d = s / (3v).

Speed is the rate at which an object moves through a distance per unit of time. It is often expressed in meters per second (m/s) or kilometers per hour (km/h).

An equation is a mathematical statement that shows that two expressions are equal. It usually contains variables, constants, and mathematical operations, and can be solved to find the value of the variables.

According to the given information:

The equation relating the speed of a tsunami and the depth of the water is s = 3vd, where s is the speed of the wave (in m/s), v is the velocity of gravity (which is approximately 9.8 m/s²), and d is the depth of the water (in meters).

We can rearrange the equation to solve for d, which gives us:

d = s / (3v)

Plugging in the given values, we get:

d = 10 m/s / (3 × 9.8 m/s²)

Simplifying, we get:

d = 10 / 29.4

Therefore, the depth of the water is approximately 0.34 meters, or 34 centimeters.

So, if the speed of the tsunami is 10 m/s, the depth of the water is approximately 0.34 meters.

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The value of h that causes the system to be inconsistent is h = 15. the value of h that causes the system to be inconsistent, we can use the determinant method.

The determinant of a system of equations is given by : \(| a b c || d e f || g h i |\)
Where a, b, c, d, e, f, g, h, and i are the coefficients of the variables in the system of equations. If the determinant is equal to zero, then the system is inconsistent.

For the given system of equations:\(x + y - 2z = -12x + hy - z = 3x + 3y + 2z = 1\)
The determinant is:
\(| 1 1 -2 || 2 h -1 || 1 3 2 |\)
Determinant by using the formula:
\(D = aei + bfg + cdh - ceg - bdi - afh\)


Plugging in the values from the determinant:
\(D = (1)(-1)(2) + (1)(-1)(3) + (-2)(2)(3) - (-2)(-1)(3) - (1)(2)(2) - (1)(h)(-1)\)
Simplifying:
D = -2 - 3 - 12 + 6 - 4 + h
D = -15 + h

For the system to be inconsistent, the determinant must be equal to zero: -15 + h = 0, Solving for h: h = 15. Therefore, the value of h that causes the system to be inconsistent is h = 15.

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The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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Answer:

9

Step-by-step explanation:

All you have to do is subtract the temperatures once you get the final answer for them.

4 days, -7°C, = 43°C

5 days, -6°C, = 34°C

43 - 34 = 9

9°C = 9

~ LadyBrain

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Answer:

Kenji is wrong

Step-by-step explanation:

3⁵ · 4⁵ = (3 · 4)⁵ = 12⁵

but 12¹⁰ ≠ 12⁵

so , kenji is wrong

Answer: 100% increase

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

u start at (0,9.5) and with every increasing x value the y value is decreasing by .5 units

Therefore, the length of the missing leg is 6 feet.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In this case, we have one leg that measures 8 feet and the hypotenuse measures 10 feet. Let's call the length of the missing leg "x". So, using the Pythagorean theorem, we can write:
8^2 + x^2 = 10^2
Simplifying this equation, we get:
64 + x^2 = 100
Subtracting 64 from both sides, we get:
x^2 = 36
Taking the square root of both sides, we get:
x = 6

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Answer:2d+4=

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

Evaluate 7 r − 15 /s

Given that r = 3 and s = 5

7r - 15/s

Substitute 3 for r and 5 for s in the above expression

7(3) - 15/5

= 21 - 3

= 18

Answer:

18

Step-by-step explanation:

(i) The number of different divisions possible when 15 children divide themselves into teams of 5 each (Team A, B, and C) is 756.

(ii) If the teams are not distinguishable, the number of different divisions possible is 756 divided by 3!, which equals 126.

(i) To determine the number of different divisions when 15 children divide themselves into three teams of 5 each, we can calculate the number of combinations.

Since the order of the teams does not matter, we use the combination formula.

The formula is nCr = n! / (r! * (n - r)!), where n is the total number of children and r is the number of children per team.

Plugging in the values, we have 15C5 * 10C5 = (15! / (5! * 10!)) * (10! / (5! * 5!)) = 756.

(ii) If the teams are not distinguishable, we need to account for the fact that the order of the teams doesn't matter.

Each division would be counted multiple times if we considered the teams distinguishable. Since there are 3! (3 factorial) ways to arrange the teams, we divide the previous result by 3!, which gives us 756 / 3! = 126.

This accounts for the different arrangements of the same teams and gives us the number of distinct divisions.

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We conclude that there is zero (0) fraction of coal left in the bag with Tom.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

The number is represented mathematically as a quotient, where the numerator and denominator are split.

Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, a fraction of coal left in the bag:

After 1 week the was 2/3 full. So, we have:

1 - 2/3 = 1/3

Next week, he used the remaining 1/3 coal. Now, we have:

1/3 - 1/3 = 0/0

Therefore, we conclude that there is zero (0) fraction of coal left in the bag with Tom.

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Correct question:
Tom bought a bag full of coal. After one week the bag was 2/3 full. During the next week, he used 1/3 of the remaining coal. What fraction was left in the bag?

G for bag A could also be written as 1g

The equation could then be written as 1g - 0.40g, which if you subtract can be solved as 0.60g

The answer is 0.60g

Answer:

C. 3

Step-by-step explanation:

One of the (many) properties of definite integrals is
\(\mbox{\large \int\limits _{a}^{b}f(x)\,dx + \int\limits _{b}^{c}f(x)\,dx = \int\limits }_{a}^{c}f(x)\,dx\)

Therefore
\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx + \int\limits _{5}^{2}f(x)\,dx = \int\limits }_{-2}^{2}f(x)\,dx\)

Given

\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx = 11}}}\para\)

and

\(\mbox{\large \int\limits _{-2}^{2}f(x)\,dx = 14}}\)

We get

\(\mbox{\large 11+ \int\limits _{5}^{2}f(x)\,dx} = 14\)

Subtracting 11 from both sides we get

\(\mbox{\large \int\limits _{5}^{2}f(x)\,dx} = 14 - 11 = 3\\\)

Answer: Choice C which is 3