Write an equation of a line that passes through (7, 1) and is parallel to y= -x + 3.

The probability that the 5th child is a girl = 1/2

Before the first birth, the probability that the woman would give birth to 5 girls in a row = 0.03125

Step - by - Step expalanation

What to find?

• The probability that the 5th child is a girl.

• Before the first birth, the probability that the woman would give birth to 5 girls in a row.

Probability = required outcome / all possible outcome.

For the first part of the question, the 5th child could either be a boy or girl.

So, all possible outcome = 2 and the required outcome = 1

Hence, the probability that the fifth child is a girl = 1/2

For the second part of the question,

Before, the first birth, the probabilty that the woman would give birth to 5 girls in a row will simply =(probability of given birth to a girl)^no. of times she will give birth.

That is;

Answer:

Yep, it's right! Great job!

Answer:

yes its correct

Step-by-step explanation:

Answer:

$31.05

Step-by-step explanation:

You can get this answer by changing percent (13.5%) to just 13.5, or in other words, a decimal. you also change 230. to a decimal by by moving the decimal point two times to the left to get 2.30. You can then get your answer by multiplying the values together (2.30 x 13.5)

The diagram of the pentagon is missing, so i have attached it.

Answer:

|AE| = 130 m

|DE| = 150 m

Perimeter of pentagon = 720 m

Step-by-step explanation:

From the diagram, we can find AE from pythagoras theorem;

|AE| = √(|AA'|² + 50²)

Where AA' is the length from A to the perpendicular angle.

Now, AB = 150, and A'B is parallel to 30 m. Thus, A'B = 30

AA' = AB - A'B = 150 - 30

AA' = 120

Thus;

|AE| = √(120² + 50²)

|AE| = √(14400 + 2500)

|AE| = √16900

|AE| = 130

Similarly,

|DE| = √(|DD'|² + |ED'|²)

ED' = BC - 50

ED' = 140 - 50

ED' = 90

Also, DD' is parallel to AA' and is = 120

Thus;

|DE| = √(120² + 90²)

|DE| = √22500

|DE| = 150

Perimeter of pentagon = 150 + 130 + 150 + 150 + 140 = 720

Answer: 50/50 :/

Step-by-step explanation:

Answer:

9 and 36 m

Step-by-step explanation:

If the length of the rectangle is 4x the width, then we have that: L = 4W

Use the formula for the perimeter of the rectangle to find width W.

2L + 2W = P

2 * 4W + 2W = 90

8W + 2W = 90

10W = 90

W = 9 m

Find length L.

L = 4 x 9 = 36 m

Answer:

Step-by-step explanation:

if we received 706.25 dollars and a ticket is 6.25

706.25/6.25=113 tickets sold

Answer:

113

Step-by-step explanation:

You have to divided 706.25 by 6.25 and then you get 113. 113 is your anwser.

Hope this helped!

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

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\(in \: pounds \\ 12 \times 288 = 3456 \: pounds\)

\(1 \: kilo = 2.2046 \: pounds\)

\(x \: kilos = 3456 \: pounds\)

\(x = \frac{3456}{2.2046} = 1567.61 \: kilos\)

The gradient of each of the sides of the triangle​ are:

mAB = -2/5

mBC =-14/9

mCA = -3

The gradient of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

Using this formula, we can find the gradients of each side of triangle ABC:

Gradient of side AB:

mAB = (yB - yA) / (xB - xA)

       = (-5 - (-3)) / (7 - 2)

        = -2 / 5

Gradient of side BC:

mBC = (yC - yB) / (xC - xB)

       = (9 - (-5)) / (-2 - 7)

       = 14 / (-9)

       = -14 / 9

Gradient of side CA:

mCA = (yA - yC) / (xA - xC)

       = (-3 - 9) / (2 - (-2))

       = -12 / 4

       = -3

Therefore, the gradients of the sides AB, BC, and CA are -2/5, -14/9, and -3 respectively.

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Answer:

2.5 in.

Step-by-step explanation:

The triangle formed by the beams is a right triangle so we can apply the Pythagoras theorem:

6.5^2 = x^2 + 6^2

x^2 = 42.25 - 36

x^2 = 6.25

x = 2.5,

answer:

117/1000

step-by-step explanation:

put 0.117 as 117/1000

i don't think you can simplify.

Answer:

117/1000

Step-by-step explanation:

The seven is in the thousands place so you move the decimal to the right and put 117 over 1000.

The estimated cost of a 2.25-carat round diamond would be around $16,875. Based on the linear relationship between the weight and price of diamonds, we can estimate the cost of a 2.25-carat round diamond.

Given that the average price of a 0.5-carat diamond is $3,900 and the average price of a 0.75-carat diamond is $5,400, we can calculate the cost using proportional reasoning. A 2.25-carat diamond is 4.5 times the weight of a 0.5-carat diamond and 3 times the weight of a 0.75-carat diamond. By applying this proportionality, we can estimate the cost of the 2.25-carat diamond to be around $14,040.

To estimate the cost of the 2.25-carat diamond, we need to consider the proportional relationship between the weight and price of the diamonds. We know that a 0.5-carat diamond has an average price of $3,900, while a 0.75-carat diamond has an average price of $5,400.

First, let's compare the weight of the 2.25-carat diamond to the 0.5-carat diamond. The 2.25-carat diamond is 4.5 times the weight of the 0.5-carat diamond because 2.25 divided by 0.5 equals 4.5.

Next, let's compare the weight of the 2.25-carat diamond to the 0.75-carat diamond. The 2.25-carat diamond is 3 times the weight of the 0.75-carat diamond because 2.25 divided by 0.75 equals 3.

Since the price of the diamond is linearly related to its weight, we can use this proportionality to estimate the cost of the 2.25-carat diamond. Multiplying the average price of the 0.5-carat diamond ($3,900) by the weight ratio (4.5), we get $17,550. Similarly, multiplying the average price of the 0.75-carat diamond ($5,400) by the weight ratio (3), we get $16,200.

To obtain a more accurate estimate, we can take the average of these two values. Adding $17,550 and $16,200 gives us $33,750, and dividing by 2 gives us $16,875. Therefore, the estimated cost of a 2.25-carat round diamond would be around $16,875.

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The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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Answer:

2x + 4y = 84

Step-by-step explanation:

Did the test

The statement ''the condition ∑ fi = 0 is sufficient to assure that a rigid body is in equilibrium.'' is false because the condition ∑ fi = 0, where ∑ fi represents the vector sum of all external forces acting on a rigid body, is necessary but not sufficient to ensure that the body is in equilibrium.

In addition to the balance of forces, the body must also satisfy the condition of zero net torque or moment about any point.

This condition is expressed as ∑ τi = 0, where ∑ τi represents the vector sum of all external torques acting on the body.

Equilibrium of a rigid body requires both force equilibrium and torque equilibrium.

Force equilibrium ensures that the body remains stationary or moves with constant velocity in a straight line, while torque equilibrium ensures that the body does not rotate.

Therefore, in order for a rigid body to be in equilibrium, both conditions ∑ fi = 0 and ∑ τi = 0 must be satisfied. Only when these conditions are met can we conclude that the body is in a state of static equilibrium.

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(g ◦ f)(x) = 49x^2 - 70x + 26.

To find (f ◦ g)(x), we need to substitute g(x) into f(x).

First, let's find g(x):

g(x) = x^2 - 4x + 5

Now, substitute g(x) into f(x):

f(g(x)) = 7(g(x)) - 3
        = 7(x^2 - 4x + 5) - 3
        = 7x^2 - 28x + 35 - 3
        = 7x^2 - 28x + 32

So, (f ◦ g)(x) = 7x^2 - 28x + 32.

To find (g ◦ f)(x), we need to substitute f(x) into g(x).

First, let's find f(x):

f(x) = 7x - 3

Now, substitute f(x) into g(x):

g(f(x)) = (f(x))^2 - 4(f(x)) + 5
        = (7x - 3)^2 - 4(7x - 3) + 5
        = (49x^2 - 42x + 9) - (28x - 12) + 5
        = 49x^2 - 42x + 9 - 28x + 12 + 5
        = 49x^2 - 70x + 26

So, (g ◦ f)(x) = 49x^2 - 70x + 26.

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The option (a) 12 ounces of beer (360ml) contain more alcohol

Alcohol content is something that is important to understand, especially if you are of legal drinking age. It can affect your health and your ability to make sound decisions.

First, let's start with 12 ounces of beer. A typical beer has an alcohol content of around 5%, which means that 12 ounces of beer contains 0.6 ounces (18 ml) of alcohol. This is the same as the fourth option.

Next, let's consider 4 ounces of wine. The alcohol content of wine varies depending on the type and brand, but a typical wine has an alcohol content of around 12%. This means that 4 ounces of wine contains 0.48 ounces (14.2 ml) of alcohol.

Finally, we have 1.5 ounces of spirits. The alcohol content of spirits is generally higher than beer and wine, with a typical range of 40-50%. For the sake of this comparison, let's assume the spirits have an alcohol content of 40%. This means that 1.5 ounces of spirits contains 0.6 ounces (18 ml) of alcohol, the same amount as 12 ounces of beer.

So, in summary, 12 ounces of beer and 1.5 ounces of spirits contain the same amount of alcohol, which is 0.6 ounces (18 ml). 4 ounces of wine contains less alcohol, with 0.48 ounces (14.2 ml).

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a. In an independent-measures design, each treatment condition has its own separate group of subjects.

Therefore, the number of subjects participating in the experiment would be equal to the sum of subjects in both treatment conditions.

In this case, there are 10 scores for each treatment condition, so there would be a total of 10 + 10 = 20 subjects in the experiment.

b. In a repeated-measures design, the same subjects are exposed to both treatment conditions. Therefore, the number of subjects participating in the experiment would be the same as the number of subjects in each treatment condition. In this case, there are 10 scores for each treatment condition, so there would be a total of 10 subjects in the experiment.

c. In a matched-subjects design, each subject is matched or paired with another subject based on specific criteria. The number of subjects participating in the experiment would depend on the matching criteria and the number of matched pairs.

Since the information about the matching criteria is not provided, it is not possible to determine the exact number of subjects in this design. The number of subjects in a matched-subjects design can vary depending on the specific study design and requirements.

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Answer:

c

Step-by-step explanation:

c will be the answer g g g t g

Answer: D

Step-by-step explanation: +2 would be an upwards translation

Answer: Where is the figure??

Answer:

I think it this one but picture would help...

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.  

Answer:

Step-by-step explanation:

1) = (0,6)

2) = 0

3) = (0,3.75)

4) = (0,6)

I rushed so I may be incorrect, I think I'm correct though

Step-by-step explanation:

According to graph, the answers are:

(1) H(0) = 6

(2) H(x) = 0, there are 5 points:

(3) The domain is:

(4) The range is:

Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Answer:

Step-by-step explanation:

step-1: find the sum of the polygon interior angles

=(7-2)×180°

=5×180°

=900°

step-2: find x

according to the question

113+112+123+168+99+148+x=900

=>773+x=900

=>x=900-773

therefore

x=127

according to the question

127+y=180

=>y=180-127

therefore

y=53

Answer:

4 (5a + 7b)

Don't worry I helped my brother with this.

The slope of function y = 2x-3 is positive whereas for the 2nd function y = -x/2 +7 is negative.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

In the 1st function y =2x-3

The slope is m = 2 and constant c = -3

In the 2nd function

m=-1/2 and constant c = 7

So the equation of the function, y = -x/2 +7

Hence The slope of function 1 is positive whereas for the 2nd functions is negative.

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