What is the value of the shaded area of the total diagram?(both squares). Please see attached image.

A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated

The value of KL for the similar triangle ∆JKL is derived to be equal to 10.92

How to evaluate the for the value of x for the triangle ∆JKL

The triangles XYZ and JKL are similar, this implies that the length XY of the smaller triangle is similar to the length JK of the larger triangle

similarly, YZ is similar to KL so;

8.7/12.18 = 7.8/KL

KL = (7.8 × 12.18)/8.7 {cross multiplication}

KL = 95.004/8.7

KL = 10.92

Therefore, the value of KL for the similar triangle ∆JKL is derived to be equal to 10.92.

The product of the values is 20 4/5

A fraction can be defined as the part of a whole number, variable or element.

There are different types of fractions, such as;

Examples of mixed fractions are; 3 1/4, 2 1/4, 31/2

Examples of simple fractions are; 1/2, 4/5

Examples of proper fractions; 2/3, 1/2

Examples of improper fractions; 3/2,4/3

From the information given, we have that;

product of 13/5 and 8

This is written as;

13/5 × 8

Multiply the values

104/5

Divide the values

20 4/5

Learn about fractions at: https://brainly.com/question/11562149

#SPJ1

1. 68% of the students spend between 10.5 hours and 17.5 hours on Statistics each week.

2. 95% of the students spend between 7 hours and 21 hours on Statistics each week.

3. 99.7% of the students spend between 3.5 hours and 24.5 hours on Statistics each week.

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical guideline that applies to data that follows a normal distribution.

According to the Empirical Rule:

Given:

Mean (μ) = 14 hours

Standard Deviation (σ) = 3.5 hours

a) 68% of the students spend between hours and hours on Statistics each week.

Using the Empirical Rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can calculate the lower and upper bounds for this interval:

Lower Bound = Mean - 1 * Standard Deviation

Upper Bound = Mean + 1 * Standard Deviation

Lower Bound = 14 - 1 * 3.5 = 10.5 hours

Upper Bound = 14 + 1 * 3.5 = 17.5 hours

b) 95% of the students spend between hours and hours on Statistics each week.

Using the Empirical Rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, we can calculate the lower and upper bounds for this interval:

Lower Bound = Mean - 2 * Standard Deviation

Upper Bound = Mean + 2 * Standard Deviation

Lower Bound = 14 - 2 * 3.5 = 7 hours

Upper Bound = 14 + 2 * 3.5 = 21 hours

c) 99.7% of the students spend between hours and hours on Statistics each week.

Using the Empirical Rule, we know that approximately 99.7% of the data falls within three standard deviations of the mean. Therefore, we can calculate the lower and upper bounds for this interval:

Lower Bound = Mean - 3 * Standard Deviation

Upper Bound = Mean + 3 * Standard Deviation

Lower Bound = 14 - 3 * 3.5 = 3.5 hours

Upper Bound = 14 + 3 * 3.5 = 24.5 hours.

Read more about Empirical Rule

brainly.com/question/21417449

#SPJ1

Answer:

0.6 kg, 0.603 kg, 0.63 kg, 6.006 kg

Answer:

0,6 kg, 0,603 kg, 0,63 kg, 6,006 kg

Step-by-step explanation:

Given:

0,63 kg, 6,006 kg, 0,6 kg, 0,603 kg

Let's convert the given kilograms to grams (1 kg has 1000 g):

0,63 kg = 630 g

6,006 kg = 6006 g

0,6 kg = 600 g

0,603 kg = 603 g

Now let's arrange them from smallest to largest:

600 g (0,6 kg)

603 g (0,603 kg)

630 g (0,63 kg)

6006 g (6,006 kg)

Answer:

[tex] {h}^{ - 1} (x) = - \frac{7x + 13}{5 - x} [/tex]

Step-by-step explanation:

[tex]y = h(x) \\ y = \frac{5x + 13}{x - 7} \\ x = \frac{5y + 13}{y - 7} \\ (5y + 13) = x(y - 7) \\ (5y + 13) = xy - 7x \\ 5y + 13 - xy + 7x = 0 \\ 5y - xy = - 7x - 13 \\ y(5 - x) = - 7 - 13 \\ y = \frac{ - 7x - 13}{5 - x} \\ y = {h}^{ - 1} [/tex]

The value of x is given as follows:

x = 39.34.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

In the right triangle for this problem, we have that:

Hence the value of x is obtained applying the sine as follows:

sin(24º) = 16/x

x = 16/sine of 24 degrees

x = 39.34.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

Answer:

A or B

Step-by-step explanation:

Bob has A or B type blood. This is because his father is an universal blood donor which means he has blood type O and Bob’s mom is an universal blood receiver which means she has blood type AB.

Two possibilities of the blood type that Bob can have are A or B.

Blood group is the group designated to the blood of each individual depending upon the specific antigens present.

The 4 groups are A, B, O and AB.

Here, given that,

Bob's father is an universal blood donor and his mother an universal blood receiver.

We know that, group O is the universal donor and group AB is the universal blood receiver.

Possibilities for the group of children are either A or B.

Hence the possibilities of the group that Bob can have are either A or B.

Learn more about Blood Groups here :

https://brainly.com/question/17052766

#SPJ

Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

To calculate Miranda's discretionary income, we need to first add up her expenses:

$60 + $85 + $195 + $55 + $575 = $970

Next, we need to calculate her monthly income.

Since Miranda gets paid semi-monthly, we'll need to multiply her paycheck amount by 24 (the number of pay periods in a year) and divide by 12 (the number of months in a year):

$550 x 24 / 12 = $1,100

Now we can calculate her discretionary income by subtracting her expenses from her income:

$1,100 - $970 = $130

Therefore, Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

(0, -6)

Step-by-step explanation:

you could’ve substituted zero in for y, and solver for x, or you could’ve simply graphed the parabola.

Answer:

(0,-6)

Step-by-step explanation:

The counterexample to the conjecture is z = 11.5 cm.

Option D is the correct answer.

We have,

To determine whether the given conjecture is true or false, we need to check whether a quadrilateral can always be formed with side lengths of 3 cm, 4 cm, 3 cm, and z, where z can be any value between 1 cm and 12 cm.

The only way for a quadrilateral to be formed with these side lengths is if the sum of the lengths of any three sides is greater than the length of the fourth side.

In other words:

3 + 4 + 3 > z

or

z < 10

Therefore, any value of z that is greater than or equal to 10 cm would be a counterexample to the conjecture.

Out of the given values of z:

z = 2 cm satisfies the condition z < 10, so it does not provide a counterexample.

z = 7 cm satisfies the condition z < 10, so it does not provide a counterexample.

z = 8.5 cm satisfies the condition z < 10, so it does not provide a counterexample.

z = 11.5 cm does not satisfy the condition z < 10, so it provides a counterexample.

Therefore,

z = 11.5 cm does not satisfy the condition z < 10, so it provides a counterexample.

Learn more about quadrilaterals here:

https://brainly.com/question/29934440

#SPJ1

It should be noted that 6 2/3÷1/5 as a mixed number in simplest form will be 33 1/3.

First, you want to make 6 into a fraction with a bottom/denominator of 3 to make adding 6 and 2/3 easier. Now, add the 18/3 and the 2/3 to get 20/3 divided by 1/5.

After this, you want to divide.  To divide fractions, you use Keep, Change, Flip.

4. Simplify this by multiplying 20 by 5 and 3 by 1 to get 100/3.

5. Now we have to create 100/3 into a mixed number.  This will be:

= 20/3 × 5

= 100 / 3

= 33 1/3

Learn more about fractions on

https://brainly.com/question/11562149

#SPJ1

6 2/3÷1/5 Express your answer as a mixed number in simplest form. Enter your answer in the box.

Answer:

(1,-1) and (2,4)

Step-by-step explanation:

By graphing the two inequalities, we can see that all possible solutions will be located in the DOUBLE-SHADED region - meaning that the inequality is true for both equations in that region.

See attached graph.

The only two points in the double-shaded region are (1,-1) and (2,-4).

Answer:

23

Step-by-step explanation:

How old is Christopher?

Let x represent the youngest sibling's age

Second sibling's age: x + 2

Christopher's age : x + 4

x + x + 2 + x + 4 = 63

3x + 6

= 63

subtract by 6

3x = 63 - 6

3x = 57

divide by 3

x = 57 ÷ 3

x = 19

Christopher age is : x + 4 : 19 + 4 = 23

We have used the calculation below to show that the definition to show that lim (x,y)→(3,4) f(x, y) = 3 / 26

In order to show that lim (x,y)→(3,4) f(x, y) = 3 / 26, we need to show that for any ε > 0, there exists a δ > 0 such that if 0 < √((x-3)² + (y-4)²) < δ, then |f(x,y) - 3/26| < ε.

Using the given function, we have:

|f(x,y) - 3/26| = |x/(x²+y²+1) - 3/26|

= |(26x - 3(x²+y²+1)) / 26(x²+y²+1)|.

To simplify this expression, we can use the fact that x² + y² ≥ 0 for any x and y. Therefore,

26(x²+y²+1) ≥ 26(0+0+1) = 26.

Using this inequality, we can write:

|f(x,y) - 3/26| = |(26x - 3(x²+y²+1)) / 26(x²+y²+1)|

≤ |(26x - 3(x²+y²+1)) / 26|

≤ |26x / 26| + |3(x²+y²+1) / 26x²+26y²+26|

= |x| + 3(x²+y²+1) / (26(x²+y²+1))

= |x| + 3 / 26 (1 + 1 / (x²+y²+1)).

Now, we choose δ = ε / (1 + 3/26). Then, if 0 < √((x-3)² + (y-4)²) < δ, we have:

|x| ≤ √((x-3)² + (y-4)²) < δ,

and also

1 < 1 + 1 / (x²+y²+1) ≤ 1 + 1 / δ².

Therefore, |f(x,y) - 3/26| ≤ δ + 3 / 26 (1 + 1 / δ²)

< ε / (1 + 3/26) + 3 / 26 (1 + δ²)

≤ ε / (1 + 3/26) + 3 / 26 (1 + ε² / (1 + 3/26)²).

Since the last term does not depend on x and y, we can choose ε sufficiently small such that ε / (1 + 3/26) + 3 / 26 (1 + ε² / (1 + 3/26)²) < ε. Therefore, we have shown that lim (x,y)→(3,4) f(x, y) = 3 / 26.

Learn more about functions on

https://brainly.com/question/11624077

SPJ1

A model which is best for making predictions about the data set include the following: A. y = 2.0259x + 0.167763.

In order to determine an equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values (variable 1) and y-values (variable 2), an equation for the line of best fit is given by

y = 2.0259x + 0.167763

Read more on scatter plot here: brainly.com/question/28220792

#SPJ1

Note that the area of the compound (or composite ) shape is 14 inches.

A complex shape, which is also referred to as a composite shape, is defined as a shape composed of two or more geometric shapes. A perfect illustration would be a shape consisting of both a square and a triangle.

The above complex shape is divided into three quadrilaterals (rectangles): A, B, and C.


Recall that the formula for finding the area of rectangles is:

Length (L) x Breadth (B). Hence the area of:

A) 1 x 2 = 2in

B) 2 x 1 = 2 in

C) 2 x 5 = 10in

Total Area  =

2 + 2 + 10 = 14inches.

Hence the area of the complex shape is 14 inches.

Learn more about compound shapes at:

https://brainly.com/question/30546858

#SPJ1

The surface area of the cube is calculated as:

13.5 square inches.

The surface area of a cube (S) = 6a², where a represents the side length of the cube.

All the side lengths of a cube are the same, that is, the are equal. Therefore, we are given the following:

Side length of a cube = 1.5 inches

Use the formula above to find the surface area of the cube:

Surface area of the cube (S) = 6a² = 6 * 1.5²

Surface area of the cube (S) = 6 * 2.25

= 13.5 square inches.

Learn more about the surface area of a cube on:

https://brainly.com/question/28776132

#SPJ1

The total budget for their student film $800

11% of total budget = (11/100) * total budget

= 0.11 * total budget

Let P be the amount the group spent on props.

Now we can write the equation:

P = 0.11 * total budget

We also know that this group spent $712 on equipment. Let E be the amount they spent on equipment.

So it looks like this:

E=$712

Your total budget is the total cost of your equipment and props. This can be written as:

Total Budget = E + P

Plugging in the E and P values, we get:

Total Budget = $712 + 0.11 * Total Budget

Simplifying this equation, we get:

0.89 * total budget = $712

Dividing both sides by 0.89 gives:

Total budget = $800

So her student film had a total budget of $800. 

To know more about dividing visit:-

https://brainly.com/question/15381501

#SPJ1

The best estimate of the area in square inches of the stove top that does not include the area of the burners is 421 square inches.

The area of the stove top without the burners can be found by subtracting the total area of the four burners from the total area of the rectangular stove top.

The total area of the stove top is [tex]length \times width[/tex] , [tex]= 22 \times 24 = 528\ square\ inches[/tex].

The total area of the four burners = sum of the area of each burner

= [tex]\pi(3)^2 \times 4 = 36\pi[/tex] square inches.

Therefore, the area of the stove top without the burners is approximately 528 - 36π square inches.

Using a calculator, this is approximately [tex]420.99 \approx 421\ sq. \ inches[/tex]

To know more about rectangle, visit:

https://brainly.com/question/29123947

#SPJ1

As a result, all ordered pairs (A, B) that meet this equation can be said to be the solutions that satisfy this requirement.

what is solutions ?

An response or collection of answers that fulfils the requirements of a topic or equation is referred to as a solution in the context of arithmetic and problem-solving. Any x number that causes the equation to be true is a solution, for instance, if the equation is 2x + 3 = 7. The answer in this situation is x = 2, as 2(2) + 3 = 7, an answer that, as a valid result, is obtained when x=2 is substituted into the equation. Many solutions or sets or remedies that meet the stated conditions may exist for more complicated situations. It is critical in these situations to ensure that the answers are correct and meet any additional requirements or criteria of the problem.

given

a. We must first acknowledge that this is a linear equation in two variables in order to locate the solutions that satisfy the restriction 4A + 2B = 16. B = 8 - 2A can be used to rewrite this equation.

As a result, all ordered pairs (A, B) that meet this equation can be said to be the solutions that satisfy this requirement.

A = 0, B = 8

A = 2, B = 4

A = 4, B = 0

A equals 6, B equals -4, etc.

b. By rewriting this inequality as B -2A + 8, we may identify the solutions that satisfy the restriction 4A + 2B 16. All ordered pairs (A, B) that also meet this inequality are the solutions to this restriction. For instance:

A = 0, B = 8

A = 1, B = 6

As a result, all ordered pairs (A, B) that meet this equation can be said to be the solutions that satisfy this requirement.

To know more about solution visit :-

brainly.com/question/16989201

#SPJ1

Answer:5.41

0.87 is correct

Step-by-step explanation:

We can solve this quadratic equation in terms of cos(θ) by using the quadratic formula:

cos(θ) = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = 7, and c = -7. Substituting these values, we get:

cos(θ) = (-7 ± sqrt(7^2 - 4(6)(-7))) / 2(6)

cos(θ) = (-7 ± sqrt(169)) / 12

cos(θ) = (-7 ± 13) / 12

Therefore, we have two possible solutions:

Answer:

Hi, option A). 3 to 1 is the correct option.

Step-by-step explanation:

See there are 6 yellow and 2 red.

It will be 6:2

And if we simplify it further both of the numbers are multiples of 2.

Therefore:

The answer is option A). 3:1

Answer: B. 4 to 1

Step-by-step explanation:

green = (3/4) purple

Substituting the expression for green from the first conversion, we get:

yellow = (5/6) (3/4) purple

yellow = (5/8) purple

Finally, we can use the third ratio to convert purple to red:

5 purple = 2 red

purple = (2/5) red

Therefore, the ratio between yellow to red is 4 to 1.

Therefore, about 68.4% of women are between 58.1 inches and 61.9 inches. Therefore, about 93.3% of women are between 56.2 and 63.8 inches.

The mean, also known as the average, is a measure of central tendency in statistics. It is found by adding up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to extreme values, or outliers, in the data set, and can be influenced by them. It is one of the most commonly used measures of central tendency, along with the median and mode.

Here,

a) Since the mean is 60 inches, the percentage of women taller than 60 inches is the area to the right of the mean on the normal distribution curve. This is 50% because the normal distribution curve is symmetric.

b) Similarly, the percentage of women shorter than 60 inches is the area to the left of the mean on the normal distribution curve, which is also 50%.

c) To find the percentage of women between 58.1 inches and 61.9 inches, we need to find the area under the curve between those two values. First, we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the given value, μ is the mean, and σ is the standard deviation.

For 58.1 inches:

z = (58.1 - 60) / 1.9

z = -0.89

For 61.9 inches:

z = (61.9 - 60) / 1.9

z = 0.47

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -0.89 and z = 0.47, which is approximately 0.684 or 68.4%.

d) Similarly, to find the percentage of women between 56.2 and 63.8 inches, we standardize the values:

For 56.2 inches:

z = (56.2 - 60) / 1.9

z = -1.89

For 63.8 inches:

z = (63.8 - 60) / 1.9

z = 1.68

Using the standard normal distribution table or calculator, we can find the area under the curve between z = -1.89 and z = 1.68, which is approximately 0.933 or 93.3%.

e) The percentage of women shorter than 63.8 inches is the area to the left of that value on the normal distribution curve. To find this area, we standardize the value:

z = (63.8 - 60) / 1.9

z = 1.68

Using the standard normal distribution table or calculator, we can find the area under the curve to the left of z = 1.68, which is approximately 0.9535 or 95.35%.

Therefore, about 95.35% of women are shorter than 63.8 inches.

To know more about mean,

https://brainly.com/question/14724376

#SPJ1

Answer:

z = 1

Step-by-step explanation:

the angle bisector divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

[tex]\frac{z}{1.5}[/tex] = [tex]\frac{3}{4.5}[/tex] ( cross- multiply )

4.5z = 1.5 × 3 = 4.5 ( divide both sides by 4.5 )

z = 1

The probability that a person who files for their first divorce is at most 32 years old is 0.7881 (or approximately 78.81%).

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½

according to the question the average age of first divorce in the United States is 28, and that the standard deviation is 5. We are asked to find the probability that a person who files for their first divorce is at most 32 years old.

So Let X be the random variable representing the age at first divorce. Now X ~ N(28, 5²), where N represents the normal distribution.

Then ,to find P(X ≤ 32), which is the probability that a person's age at first divorce is at most 32 years old.

By using the standard normal distribution, we get standardize X as follows:

Z = (X - μ) / σ = (32 - 28) / 5 = 0.8

where μ is the mean of X and σ is the standard deviation of X.

Now, we can use a standard normal distribution table or calculator to find the probability that Z is less than or equal to 0.8:

P(Z ≤ 0.8) = 0.7881 (rounded to four decimal places)

Hence, the probability that a person who files for their first divorce is at most 32 years old is 0.7881 (or approximately 78.81%).

Learn more about Probability here

https://brainly.com/question/30034780

#SPJ1

Answer:0.7881

Step-by-step explanation:

The mean is μ=28, and the standard deviation is σ=5.

1. Open Excel and click on any empty cell. Click Insert function, fx.

2. Search for NORMDIST in the search for a function dialog box and click GO.

3. Make sure NORMDIST is on top in select a function. Then click OK.

4. In the function arguments of the NORMDIST function, enter 32 for X, 28 for Mean, 5 for Standard_dev, and TRUE for Cumulative.

Thus, the answer, rounded to four decimal places, is P(X<32)≈0.7881.

The area of Bob's triangular ice skating rink would be approximately 180 square feet.

We have,

To find the area of a triangle, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter (half the perimeter), and a, b, and c are the lengths of the sides.

Substituting the values.

Now,

s = (19 + 20 + 25)/2 = 32

Area = √(32(32-19)(32-20)(32-25))

= 180 square feet

Therefore,

The area of Bob's triangular ice skating rink would be approximately 180 square feet.

Learn more about the heron's formula here:

https://brainly.com/question/29184159

#SPJ1