Select all the expressions that have a value of 180 when b = 4. o 876 – 179 + 957 - 87 O 336 12 62 + 120 0 516 - 24 ( 115 + 187 – 2,756 - 13​

Considering the descriptions, angle CEB is found to be 93 degrees

Angle CEB is calculated by investigating the sketch attached

From the sketch, angle CEB and angle AEC are supplementary angles

and angle AEC is given to be 87 degrees.

Supplementary angles are angles that have their sum equal to 180 degrees.

hence In the problem, we have that

angle CEB + angle AEC = 180 degrees

where

angle AEC = 87.

substituting the value into the equation will result to

angle CEB + 87 = 180

angle CEB = 180 - 87

angle CEB = 93 degrees

We can therefore say that angle CEB = 93 degrees

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By using Pythagoras theorem we get the height of the roof of dog house is 21 inches.

The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. 

This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. born. 

According to the question:

Given, Hypotenuse(h) = 29 inches

           Base(b) = 40/2 = 20 inches

Using Pythagoras theorem, we get

h² = b² + p²

⇒ 29² = 20² + p²

⇒ p² = 29² - 20²

⇒ p² = 841 - 400

⇒ p² = 441

⇒ p = √441

⇒ p = 21

∴ The height of the roof of dog house is 21 inches.

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Answer:

d

Step-by-step explanation:

Answer:

the local library raised money by having a used book Rebecca volunteered to help. her task was to stick price labels on each of the 198 books on a bookshelf in 5 minutes Rebecca labeled 18 books at this rate what was the total number of minutes rebecca needed to label all 198 books

Given the expression below

Step 1: Using PEMDAS rule

P=> Parenthesis

E=>Exponent

M=>Multiplication

D=>Division

A=>Addition

S=> Subtraction

From the rule above, we will start our simplification with the parenthesis

Step 1: simplify (5-4)

Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))

Step 3: Expand 6(4)=>6 x 4

Step 4: Add 8 and 24

Hence, the final answer is 32

Answer: your answer would be 32

Step-by-step explanation:

using PEMDAS we would first go by parentheses and use the order by each step.

Answer: 0.3

Step-by-step explanation:

\(\frac{3}{10}\) = 0.3

Answer:

the answer is either x=√3+5 or -√ 3+5

Step-by-step explanation:

split it into 2 equations

Answer:

(x-5)(x-5) =3

X^2 -5x -5x +25 = 3

x^2 -10x +22 = 0

x1 = (-b + sqrt(b^2 - 4ac))/2a

a=1

b=-10

c= 22

x1 = (10 +sqrt((-10)^2- 4(1)(22))/2(1)

x1 = (10 + sqrt(100-88))/2

x1= (10 + sqrt(22))/2

x1= (10 + sqrt(4) x sqrt(3))/2

x1=(10 + 2 x sqrt(3))/2

x1 =5 +sqrt(3)

x2 = (-b - sqrt(b^2 - 4ac))/2a

x2 = 5 - sqrt(3)

Answer is C

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

D. (1, 3)

Step-by-step explanation:

The solution is the coordinates of the intersection of the 2 lines

Step-by-step explanation:

the number of pupils are in the lower school

= (1- 1/5 - ¼) × 600

= (20/20 - 4/20 - 5/20)×600

= (11/20) ×600

= 330 pupils

Answer:

Step-by-step explanation:

choose a number for example 20

20-5=15

15x2=30

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

In my opinion I would say No but I could be wrong

Answer:

6.8125

Step-by-step explanation:

Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:

# Load HardyWeinberg package

library(HardyWeinberg)

# Load Mourant dataset

data(Mourant)

# Extract the genotype counts for the 206th row

counts <- Mourant[206, 2:4]

# Calculate the MLE of M allele frequency

mle <- hw_mle(counts)

# Extract the MLE of M allele frequency

mle_M <- mle$p[2]

Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.

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Answer:

Step-by-step explanation:

Radius = OC = OD + DC = 6 + 4 = 10

In ΔODB, OB = radius = 10, OD = 6, so

\(DB=\sqrt{OB^2-OD^2}=\sqrt{10^2-6^2}=8\\\)

Similarly, AD = 8

Then AB = AD + DB = 16

QUESTION 1

the solution is (-1,-5)

To verify the solution algebraically, we need to multiply the first equation with -1 and then sum them up

-y=5

y=3x-2

0=3x+3

3x=-3

x=-3/3

x=-1

Then, we use this value to find the other one

y=3x-2

y=3(-1)-2

y=-3-2

y=-5

Therefore, the solution is (-1,-5), which is the same showed graphically.

QUESTION 2.

Using the same process as we did in the QUESTION 1. The image attached shows both lines and the interception point which is the solution. So, the solution is (6,0).

To verify the solution algebraically, we must multiply the second equation by -6

x+6y=6

-6y=-2x+12

x=-2x+18

x+2x=18

x=18/3

x=6

Then, we use this value to find the other one

x+6y=6

6+6y=6

6y=6-6

y=0/6

y=6

Therefore, the solution is (6,0),

The present value of the nominal rate of the annuity will be $535.

Annuity amount = 20

Number of annuities = 32

APR = 16%

PV of annuities = 357

Number of years to perpetuity = 8

Quarterly perpetuity = 25

PV of perpetuity at 9th year = 625

PV of perpetuity today = 178

Total PV = 357 + 178 = 535

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Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

The exponential form of 6 × 6, is written as: 6².

Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.

Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:

6 × 6 = 6².

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Answer:

The value is  \(E(X) = 4 \ days\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 36^oC\)

    The standard deviation \(\sigma = 3^oC\)

Generally the probability that in June , the midday  temperature is between  

39°C and 42°C is mathematically represented as

      \(P(39 < X < 42) = P(\frac{39 - 36}{3} < \frac{X - \mu }{\sigma} < (\frac{42 - 36}{3} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

      \(P(39 < X < 42) = P(1 < Z <2 )\)

=>   \(P(39 < X < 42) = P(Z < 2) - P( Z <1 )\)

From the z table  the area under the normal curve to the left corresponding to  1 and  2  is

     P(Z   < 2)  = 0.97725

and

    P(Z   < 1)  = 0.84134

    \(P(39 < X < 42) = 0.97725 - 0.84134\)

=>  \(P(39 < X < 42) = 0.13591\)

Generally number of days in June would you expect the midday temperature to be between 39°C and 42°C

      \(E(X) = n * P(39 < X 42 )\)

Here n is the number of days in June which is  n = 30

       \(E(X) = 30 * 0.13591\)

=>    \(E(X) = 4 \ days\)

Answer:

H) 20%

Step-by-step explanation:

40 - 32  = 8

8/40 = .2

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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The intersection points are (6, 6) and (-6, -6).

What is Intersection points?

The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.

The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.

6 sin(Ф) = 6 cos(Ф)

Dividing both sides by 6 and rearranging terms, we get:

tan(Ф) = 1

This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].

Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.

Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).

Therefore, the intersection points are (6, 6) and (-6, -6).

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The systems of equation can be described as linear or non-linear as follows:

1. Linear

2. Linear

3. Linear

4. Linear

5. Non-linear

6. Non-linear

7. Non- linear

8. Linear

9. Linear

Linear equations are those mathematical expressions that have none of their variables raised to a variable that is not 1. They are often in the form of y = mx + b. In the system of equations, we can conclude that a variable is linear if after solving, none of the variables are raised to powers less than or equal to one.

For example, in example 1, we can conclude that the expressions are linear because all of the values of x and y are not raised to any value that is greater than or less than 1.

For the fifth equation, we can conclude that the expression is non-linear because the value, x is raised to two which is greater than 1. Equation F also has y raised to power 3 and this makes it non-linear.

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Answer:

t > 7

Step-by-step explanation:

2 paperclip points = 3 mm apart

After each trial, points are 2mm more apart ;

That is

Trial 1 : 3mm

Trial 2 : 5 mm

Trial 3 : 7 mm

Trial 4 : 9 mm

Trial 5 : 11 mm

Trial 6 : 13 mm

Trial 7 : 15 mm

Trial 8 : 17 mm...

Hannah reports feeling 1 point until the point are 15m apart which is equal to 7th trial

Hence, she starred reporting feeling 2 points after the 7 th trial

t > 7

Hence, the inequality

Standard Form: 2,016

Place Value: From left to right for 2,016

Digit Place Value

2 Thousands

0 Hundreds

1 Tens

6 Ones

Word Form:

2,016 =

two thousand sixteen