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In accordance with the provided assertion, (A) the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches (B) the longer leg is 4√3 cm and the hypotenuse is 8 cm.

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object.

For a 30°−60°−90° triangle, the ratios of the side lengths are:

Using these ratios, we can solve the problems:

Longer leg = x√3 = 9

x = 9/√3 = 3√3

Shorter leg = x = 3√3

Hypotenuse = 2x = 2(3√3) = 6√3

Therefore, the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches.

    2. If the shorter leg is 4 cm, we have:

Shorter leg = x = 4

Longer leg = x√3 = 4√3

Hypotenuse = 2x = 2(4) = 8

Therefore, the longer leg is 4√3 cm and the hypotenuse is 8 cm.

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If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.

Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.

To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:

3 + 2 = 5

So there are 5 small triangles in the third row.

To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:

5 + 2 = 7

So there are 7 small triangles in the fourth row.

To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:

n = (last term - first term) / common difference + 1

n = (7 - 1) / 2 + 1

n = 4

So there are 4 rows in the triangle.

Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:

sum = (n / 2) * (first term + last term)

sum = (4 / 2) * (1 + 7)

sum = 4 * 4

sum = 16

So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:

area = 16 * (1/2)

area = 8

Therefore, the original triangle has an area of 8 square units.

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The length of segment in the given circle x is 5 cm.

A circle is formed by all points in a plane that are at a particular distance from the centre. The radius of a circle is the separation between any point on the circle and its center.

The product of the measures of the secant segment and its external secant segment equals the square of the measure of the tangent segment if a tangent segment from a location outside the circle, secant segments are drawn.

In the circle shown, if

AB=6cm

AC=4cm and

CD=x?

AC×AD=[tex]AB^{2}[/tex]

4(4+x)=[tex]6^{2}[/tex]

4+x=36/4

x=5

Hence, The length of segment in the given circle x is 5cm.

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The probability that a son will inherit the​ disease would be

P{E} = 1/4.

Given is that men have XY​ (or YX) chromosomes and women have XX chromosomes.​ X-linked recessive genetic diseases​ (such as juvenile​ retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase​ x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

The probability that a son will inherit the​ disease if a father has the

defective {x} chromosome and the mother has good {XX}​ chromosomes

as -

P{E} = 4/16

P{E} = 1/4

Therefore, the probability that a son will inherit the​ disease would be

P{E} = 1/4.

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Answer:

159

Step-by-step explanation:

So first you work on the (3 + 5) which is 8 but don't forget the ^2 so 8^2 is 64. Then you work on your next term which is 10^2 which is 100. So now our equation is 100 + 64 -5 and you can solve this by going left to right. So 100 + 64 is 164 then - 5 is 159.

Of the first 100 vehicles, there are nine convertible green cars.

The sequence of green cars:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

The sequence of convertible cars:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.

Convertible and Green cars (in the very first 100 cars):

12, 24, 36, 48, 60, 72, 84, and 96.

Thus, of the first 100 vehicles of auto assembly line, there are nine convertible green cars.

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The complete question is-

On an automobile assembly line, every third car is green. Every fourth car is a convertible. How many cars out of the first 100 will be green convertibles?

Answer: b

Step-by-step explanation:

The height of the parallelogram is 5.4 units.

What is area ?

In mathematics, the area is the measure of the size of a two-dimensional surface or region, usually expressed in square units, such as square inches or square meters. The area of a flat shape or planar figure is the amount of space inside its boundary, or the surface of the object, that is covered by a two-dimensional geometric shape.

One way to find the height is to draw a perpendicular line from point B to line segment AD, forming a right triangle. Let's call the length of this perpendicular line h.

Now we can see that the base of the parallelogram is 10 units (from A to D), and the height is h units (from B to the perpendicular line we drew). The area of the parallelogram is given as 54 units², so we can set up the following equation:

Area = base x height

54 = 10h

Solving for h, we get:

h = 54/10 = 5.4

Therefore,  the height of the parallelogram is 5.4 units.

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The ratio for the area and the ratio for the circumferences of the circles are 9 : 1 and 6 : 1 respectively.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

If the radius of one circle is three times the radius of another circle, then we can use this information to determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing their actual measurements.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "3r".

Ratio of areas -

The area of a circle is proportional to the square of its radius, so the ratio of the areas of the two circles is -

= (area of larger circle) / (area of smaller circle)

= (π(3r)²) / (πr²)

= 9r²/r²

= 9/1

Therefore, the ratio of the areas of the two circles is 9:1.

Ratio of circumferences -

The circumference of a circle is proportional to its radius, so the ratio of the circumferences of the two circles is -

= (circumference of larger circle) / (circumference of smaller circle)

= 2π(3r) / 2πr

= 6r/r

= 6/1

Therefore, the ratio of the circumferences of the two circles is 6:1.

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The solution for the given system of equations is (1,0) using the addition method.

The addition method, also known as the elimination method, is a technique used to solve a system of linear equations by adding the two equations together in such a way that one of the variables is eliminated.

Multiply the first equation by -2:

-10x - 12y = -10

Add the second equation to the first:

-10x - 12y = -10

10x + 12y = 10

0 + 0 = 0

We can solve one of the original equations for x in terms of y and then replace into the equation to represent the solutions in terms of y. For instance, when we solve the first equation for x, we obtain:

5x + 6y = 5

5x = 5 - 6y

x = (5 - 6y)/5

By substituting this into the second equation, we get:

10x + 12y = 10

10((5 - 6y)/5) + 12y = 10

2(5 - 6y) + 12y = 10

10 - 4y = 10

-4y = 0

y = 0

So the solution to the system is (x, y) = ((5 - 6y)/5, y) = (1, 0)

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The clerk did not give Mary any change, so that is the correct response.

A price decrease from the normal or list amount or a proportional deduction from such a debt account, typically applied in exchange for on-time or cash payments.

The total cost of the shirt and three skirts before the coupon is:

$22.65 + 3($33.31) = $122.58

With the 10% discount, the total cost becomes:

$122.58 - 0.1($122.58) = $110.32

To find out how much change the cashier gave back to Mary, we need to subtract the total cost from the amount of money Mary's mom gave her:

$100.00 - $110.32 = -$10.32

Since the result is negative, it means Mary did not have enough money to pay for her purchases and would have to give the cashier an additional $10.32 to cover the full cost of her shopping.

Therefore, the answer is that Mary did not receive any change from the cashier.

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The rate of speed of the jet is given by S = 98 miles per hour

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the rate of speed of the jet be represented as S

Now , the value of S is

The distance traveled by the jet D = 490 miles

The time taken by the jet to travel 490 miles T = 5 hours

So , the speed of the jet is given by

Speed = Distance / Time

On simplifying , we get

The speed of the jet S = 490 / 5

The speed of the jet S = 98 miles per hour

Now , the distance traveled by the jet in 11 hours be D₁

The time taken to travel D₁ distance is 11 hours

where D₁ = Speed x Time

On simplifying , we get

D₁ = 98 x 11

D₁ = 1,078 miles

Hence , the distance traveled at a speed of 98 mph for 11 hours is 1,078 miles

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The organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given:

Two events take place.

Let event A be flipping a coin

Let event B be rolling a 6-sided die.

Now, a coin has two faces; one is the head and the other is the tail.

So, the possible outcomes of event A are: {H, T}

H → Head, T → Tail.

Now, a six-sided die has six faces each marked with a number. The numbers marked ranges from 1 to 6.

So, the possible outcomes of event B are {1, 2, 3, 4, 5, 6}

Now, each element of set A should match all the elements of set B.

Now, the tabular form should have a row of outcomes of B and a column of outcomes of event A. Thus,

Outcomes          1          2       3        4         5          6  

   H                 H1         H2     H3     H4       H5      H6

   T                 T1         T2     T3        T4      T5         T6

Therefore, the organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

Finally, the correct tree diagram is attached below.

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Complete question:

The IQ score given the mean and the standard deviation, can be found to be 105. 25.

To find the indicated IQ score corresponding to a right tail area of 0.3694, we can use a standard normal distribution table or calculator. Using a calculator, we can find that the z-score corresponding to a right tail area of 0.3694 is approximately 0.35.

Once we have the z-score, we can use the formula z = (x - μ) / σ to solve for the IQ score :

0.35 = (x - 100) / 15

Solving for x, we get:

x = 0.35 x 15 + 100

= 105.25

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The number of students who scored more than 70 but less than 80 is zero.

A stem-and-leaf diagram is a quantitative analysis of a collection of data points that are separated into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

To find the number of students who scored more than 70 but less than 80, we need to look at the stem-and-leaf plot and count the number of leaves that fall within this range.

Stem 7 has a leaf of 6, which represents a score of 76. Therefore, at least one student scored between 70 and 76.

The stem 8 has leaves of 2, 5, and 8, which represent scores of 82, 85, and 88, respectively. Therefore, no students scored between 76 and 80.

Therefore, the number of students who scored more than 70 but less than 80 is zero.

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The sοlutiοn tο the given prοblem οf expressiοn cοmes οut tο be  1.2516883 x 10⁴ is the abbreviated fοrmula in scientific nοtatiοn.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

The priοr respοnse was cοndensed,

[tex]\frac{[(0.0070)(50)(55)]} {[(1.4)(0.0011)(.25)]} = 12516.883[/tex]

We can describe the following respοnse in scientific notatiοn as the sum of a decimal number between 1 and 10 and a pοwer of 10:

12516.883 = 1.2516883 x 10⁴

Therefοre, 1.2516883 x 10⁴ is the abbreviated fοrmula in scientific notation.

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The correct solution for the given absolute function |x/5| = 1 is: x = 5 and x = -5.

The variable inside this absolute value bars makes up an essential algebraic function known as the absolute value function.

The given function is-

|x/5| = 1

Solving the bars will give:

x/5 = 1 and x/5 = -1

So,

x = 5 and x = -5 are the solution of the absolute function.

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Answer:

f=-15

Step-by-step explanation:

f/3 +22=17

take away 22 from both sides

f/3=-5

then times by 3

f=-15

so f=-15

Answer:

To find the average speed in miles per hour, we need to divide the total distance by the time taken:

Average speed = Total distance / Time taken

Average speed = 234 miles / 6 hours

Average speed = 39 miles per hour

Therefore, Nathan's average speed was 39 miles per hour.

Step-by-step explanation:

Answer:

Nathan drove an average of 39mph

Step-by-step explanation:

r=d/t

rate=234/6

234+6=240

240/6=40

Because we added a six, we need to subtract one:

40-1=39

Nathan drove an average of 39mph

Using expressions, we get that$836 will be paid in total throughout the first 12 months.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression.

Given is that the starting balance is 62. As a result, the sum rises by 4%.

The time period is 12, but he will pay for 11 extra months, not including the first month's 62 dollars.

The formula is: y=62(1+0.11

y=62(1.04) ^11

The amount to be paid in the previous month is: y=95.45$

This geometric sequence has r equal to 1.04 in this case. The total will be determined as follows:

Sum = 62(1.04¹¹-1)/1.04-1

Sum = $836

Hence, $836 will be paid in total throughout the first 12 months.

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The two functions have equivalent zeros if k = 60.

Here we have two functions which are:

f(x) = 4x - 20

g(x) = -12x + k

We want these two functions to have equivalent zeros, so first let's find the zero of f(x), we will get:

f(x) = 4x - 20 =0

4x  = 20

x = 20/4

x = 5

And that must also be a zero of g(x), then:

-12*5 + k = 0

Solving this for k.

-60 + k = 0

k = 60

That must be the value of k.

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The table that shows proportional relationship is x = 1,3,4,5 and y = 50, 150, 200,250 ( table 1).

The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

To determine the proportionality the ratio of x toby must be thesame Ina table

in table 1

x/y = 1/50 = 3/150 = 4/200 = 5/250 = 1/50

table 1 show proportional relationship

in table 2

3/1.5 is not equal to 7/3 , therefore table 2 does not show proportional relationship

in table 3

1/1.5 is not equal to 3/6 , therefore table 3 does not show proportional relationship

therefore the table that show proportional relationship is table 1

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The total cost of the deal for the router for Tina is given by A = $ 1059.81

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the total cost of the deal be represented as A

Let the initial price of the router be = $ 39.99

Now , the percentage of discount for the router = 15 %

So , the final cost of the router = ( 85/100 ) x 39.99

On simplifying , we get

The final cost of the router = $ 33.9915

Now , the number of months = 18 months

The contract rate = $ 56.99 per month

So , the total contract rate for 18 months = 18 x 56.99

The total contract rate for 18 months = $ 1,025.82

Now , total cost of the deal A = final cost of the router + total contract rate for 18 months

On simplifying the equation , we get

The total cost of the deal A = $ 1,025.82 + $ 33.9915

The total cost of the deal A = $ 1059.8115

The total cost of the deal A = $ 1059.81

Hence , the total cost of the deal is $ 1059.81

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It is the last one ...................

From the given situation of equation Diamond worked 24 overtime hours that week.

The hourly rate that is paid for the typical hours worked within a pay period is known as regular pay. For full-time employees in the US, this is typically referred to as 40 hours a week. On the other hand, overtime pay is the hourly rate paid for any additional hours worked. Most businesses give time-and-a-half (1.5 times the usual pay rate) or double-time (two times the regular pay rate) for extra hours, which is often more than regular compensation.

Let us suppose the number of hours = x.

Let us suppose the overtime hours = y.

From the given situation we have:

7.5x + 11.25y = 352.5 (equation 1)

x + y = 35 (equation 2)

Substituting equation 2 into equation 1 and simplifying:

7.5x + 11.25(35 - x) = 352.5

7.5x + 393.75 - 11.25x = 352.5

-3.75x = -41.25

x = 11

Substitute the value of x = 11.

11 + y = 35

y = 24

Hence, Diamond worked 24 overtime hours that week.

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Answer:

look in the comments have a good day

Using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.

When a shape is magnified and each side is multiplied by the same number, this is known as a scale factor.

The scaling factor is this figure. Scale factors are used on maps to accurately depict distances between locations.

With a scale factor of 2, the new shape that results from scaling the old shape is twice as large.

So, get the volume of the larger cylinder as follows:

x/5 = 28/2

2x = 28*5

2x = 140

x = 70m³

Therefore, using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.

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Complete question:

The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?

Question 8 options:

A. 700 m3

B. 350 m3

C. 70 m3

D, 437.5 m3

E. 175 m3

Answer:

equilateral triangle

Step-by-step explanation: