find the value of a and b in the given figure​

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

for such more question on perpendicular

https://brainly.com/question/18991632

#SPJ8

The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

To learn more about standard deviation from the given link

https://brainly.com/question/475676

#SPJ1

Answer: First one is 12

Second is 6:8

Third is 3:5

Fourth is 240

Last one is 3:5

Step-by-step explanation:

If you get 2 loaves of bread for 3 cups of raisins and you need 8 loaves then you do 3x4 to get 12

Do 3x2=6 then 4x2=8 so 6:8

Do 3x4=12 and 5x4=20 so 3:5

12/4 is 3 so we know that we divide by 3 720/3 is 240

Same question as #3

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

Know more about   normal distribution  here:

https://brainly.com/question/4079902

#SPJ8

Answer:

(38,121

Step-by-step explanation:

============================================

Work Shown:

P(A and B) = P(A)*P(B|A)

P(A and B) = 0.8*0.31

P(A and B) = 0.248

The notation P(B|A) means "Probability of B given A". It's the same as "P(B) given event A has happened". It is conditional probability notation. The symbol between the A and B is a vertical line and not a letter.

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

For more such questions on Amy:

https://brainly.com/question/25319846

#SPJ8

Answer:

the correct answer is 100

Answer:

The answer is B

Step-by-step explanation:

Btw if its wrong im sorry

Answer: B

Step-by-step explanation:

The percentage is the indicating hundredth is  12.5%.

A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.

Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A student was marked tardy five different times in a 40-day period.

Percentage of 5 among 40

= (5/40) x 100

= 12.5%

Hence, The percentage of times the students marked will be 12.5%".

Learn more about percentage here:

brainly.com/question/13450942

#SPJ1

Answer:

It all starts with something that creates "Tension" between you and another person. "Tension" leads to "Role Dilemma" or blaming the other person for the tension and the problem. ... Then both of you start "Gathering Injustices" to use as ammunition for the inescapable showdown.

Answer:

1.05 sorry it took so long.

Step-by-step explanation:

  15  3 ones x 5 hundredths = 15 hundredths

+ 90  3 ones x 3 tenths = 9 tenths = 90 hundredths

  105 hundredths = 1.05

this is what i got from the example on the top. Compare the example with number 2.

Answer:

Step-by-step explanation:

Answer:

4 cups=2 pint

3 cups=1.5 pint

5 cups=2.5 pints

Step-by-step explanation:

Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.

4/2=2

3/2=1.5

5/2=2.5

Let me know if you have any questions!

Answer:

B -1-tan(2x)/1+(-1)(tan(2x))

Step-by-step explanation:

Edge 2020

the original expression listed in the question can be simplified to -1+tan(2x)/1-tan(2x). expression B can also be simplified to -1+tan(2x)/1-tan(2x)

The expression equivalent to tan(3π/4 -2x) is  -1-tan(2x)/1+(-1)(tan(2x))

It is the trigonometric identity.

Using the trigonometric formula , tan (A-B) = tanA - tanB/ (1+tanA tanB )

tan(3π/4 -2x) = tan(3π/4) - tan2x / 1+ tan(3π/4)tan2x

tan(3π/4 -2x) = -1-tan(2x)/1+(-1)(tan(2x))

Thus, the expression equivalent to tan(3π/4 -2x) is  -1-tan(2x)/1+(-1)(tan(2x))

Learn more about  tangent.

https://brainly.com/question/10053881

#SPJ5

Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

Answer:

4 seconds

Step-by-step explanation:

Step-by-step explanation:

g = 28000 - 700t

because your started with 28000 gallons and every hour you have 700 less.

Answer:

A' = (-2, -3)

B' = (0, -3)

C' = (-1, 1)

I did this on edg

Step-by-step explanation:

Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.

After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)

Answer:.

Step-by-step explanation:

Answer:

Approximatly 12.65

Step-by-step explanation:

You would use the pythagorean Theoram for this.

\(a^{2}+6^{2}=14^{2}\)

\(a^{2}+36=196\)

Subtract 36 from both sides:

\(a^{2}=160\)

Square 160 to remove the exponent on "a":

\(a=\sqrt{160}\)

\(a≈ 12.65\)

If the ladder reaches the flat​ roof, then the height of the building will be 12.65 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The base of 14​ feet ladder is 6 feet from a building. Then the length of the hypotenuse is 14 feet and the base is 6 feet. Then the height of the building will be given by the Pythagoras theorem.

If the ladder reaches the flat​ roof, then the height of the building will be

H² = P² + B²

14² = P² + 6²

196 = P² + 36

P² = 196 - 36

P² = 160

P = 12.65 feet

If the ladder reaches the flat​ roof, then the height of the building will be 12.65 feet.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ2

Answer: C

Step-by-step explanation:

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

for such more question on expression

https://brainly.com/question/4344214

#SPJ8

Answer:

-11 and -12

Step-by-step explanation:

first integer:  x

second integer:  x + 1

x + x + 1 = -23

2x + 1 = -23

2x = -24

x = -12

first integer:  -12

second integer:  -12 + 1 = -11

Answer:

3.17

Step-by-step explanation:

got dat big brain