The length of the longer leg of a right triangle is 3 cm more than three times the length of the shorter
leg. The length of the hypotenuse is 4 cm more than three times the length of the shorter leg. Find the
side lengths of the triangle.
Length of the shorter leg:________ cm
Length of the longer leg:
cm
Length of the hypotenuse:
_cm

The cutoff for a failing score is 51 and about 2.28% of the students failed the psychology exams.

An equation is an expression that shows the relationship between two or more numbers and variables.

Z score is given by the equation:

z = (raw score - mean) / standard deviation

Given mean of 61 and a standard deviation of 5.

The z score that corresponds to 2 or more standard deviations below the mean is -2. Hence:

-2 = (x - 61) / 5

x = 51

P(z < -2) = 0.0228

The cutoff for a failing score is 51 and about 2.28% of the students failed the psychology exams.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

he difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be –3x² + 7x – 18. Then the correct option is D.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The expressions are given below.

(2x² + 6x – 11) and (5x² – x + 5)

Then the difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be

⇒ (2x² + 6x – 11) - (5x² – x + 5)

⇒2x² + 6x – 11 – 5x² + x – 5

⇒ –3x² + 7x – 18

Then the correct option is D.

The complete expression is given below.

(2x² + 6x – 11) and (5x² – x + 5)

More about the subtraction link is given below.

https://brainly.com/question/4319655

#SPJ1

The simplified form of the expression is 3b+2a/(ab)²

Fractions are written as a ratio of two integers. Given the expression below;

3/a^2b + 2/ab^2

Find the LCM

3/a^2b + 2/ab^2 = 3b+2a/a²b²

3/a^2b + 2/ab^2 = 3b+2a/(ab)²

Hence the simplified form of the expression is 3b+2a/(ab)²

Learn more on sum of fraction here: https://brainly.com/question/11562149

#SPJ1

To solve this problem, just use multiplication.

[tex]7\text{ pairs of pants}*3\text{ shirts}*5\text{ ties}*6\text{ jackets}=\large\boxed{630\text{ outfits}}[/tex]

You can somewhat think of this situation as a sort of tree. You start with 7 large branches representing the pants, then for every one of those you have 3 medium-sized branches to represent the pairs of pants. Each one of those has 5 sticks for the ties, which in turn each have 6 leaves to represent the jackets and therefore a complete outfit. The solution is found by getting the total number of leaves on the tree.

Answer:

T [1;11].

Step-by-step explanation:

x-coordinate of the point T is:

x(T)=2*x(W)-x(S); ⇒ x(T)=2*(-3)+7=1;

y-coordinate of the point T is:

y(T)=2*y(W)-y(S); ⇒ y(T)=2*1+9=11.

Finally, T(1;11).

Answer:

34.2°

Step-by-step explanation:

sinB/b = sinA/a

sinB/7 = sin(40°)/8

sinB = 7sin(40°)/8

B=arcsin(7sin(40°))/8

So, to the nearest tenth, B is 34.2°.

The translation of the question is:

The solar park is a concentrated zone of development of solar power generation projects and provides developers an area that is well characterized, with proper infrastructure and access to amenities and where the risk of the projects can be minimized.

How many solar parks are there in China?

Learn more about solar energy here:

https://brainly.com/question/9704099

#SPJ1

Answer:

1/2 = c*8 or c*8=1/2

Step-by-step explanation:

It says 1/2 is equal to which means 1/2 is on the side for one of the equations. It doesn't really matter. It says is equal to a number, c and eight. Its implying that you multiply c and 8 together because if it meant for another number to be multiplied then a third symbol would be in the operation.

Answer: 112.5 square cm

Step-by-step explanation:

The area of the rectangle is [tex](20)(9)=180[/tex] square cm.

The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.

So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.

The probability that number of credit cards is 0 is 0.61

Probability is the likeliness of an event to happen ,

It has a range from 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty

The data for the college students is given and it has been asked to determine P(0)

The total students are 200

and the students that have no credit card from the data is 122

Therefore

P(0) = 122/200 = 0.61

Therefore the probability that number of credit cards is 0 is 0.61

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

The surface area of the given triangular prism is 960 yd²

From the question, we are to calculate the surface area of the given figure

The given figure is a triangular prism

Surface area of the triangular prism =

[tex](26 \times 12 )+ 2(\frac{1}{2} \times 10\times 24) + (24 \times 12) + (12 \times 10)[/tex]

= 312 + 240 + 288 + 120

= 960 yd²

Hence, the surface area of the given triangular prism is 960 yd²

Learn more on Calculating surface area here: https://brainly.com/question/23213707

#SPJ1

Answer:

???????

Step-by-step explanation:

?????

The set when z = -5 is {-27, -9, -5}

The set is given as:

{(4z-7,z-4,z) |z is any real number}

When z=-5, we have:

4z - 7 = 4(-5) - 7 = -27

z - 4 = -5 - 4 = -9

z = -5

So, we have:

{(4z-7,z-4,z) |z is any real number} ⇒ {-27, -9, -5}

Hence, the set when z = -5 is {-27, -9, -5}

Read more about sets at:

https://brainly.com/question/8053622

#SPJ1

Step-by-step explanation:

there is a right angle formed in this question

this leads us to Pythagoras theorem

Hyp²=opp²+Adj²

Hyp²=11²+6²

Hyp²=121+36

Hyp²=157

Hyp=√157

Hyp=12.529964086

Hyp=12.5

if I am right mark as brainliest but if you consider I am wrong then you can correct me, Everyone learns everyday I am glad I help

The 5 number summary are

Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19

The complete question is in the attached image

The 5 number summary of box plot are:

Each of these summaries are represented by the vertical lines of the box plot

From the attached box plot, we have:

Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19

Read more about 5 number summary at:

https://brainly.com/question/12490978

#SPJ1

The required distance AB is given by .[tex]\sqrt{17}[/tex]

Transformation, is process which is used to change the position of the bor shapes.

Since, coordinate of A(0,0) B(1,4)

After transformation T: (x, y) (x + 2, y + 1) of A, B it become A'(2, 1), B '(3,5)
Now,
Distance = √(x2-x1)^2+(y2-y1)^2

AB =  [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ; A'B' =  [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ;
   A(0,0) B(1,4)                                     A'(2, 1), B '(3,5)
 AB= [tex]\sqrt{(1-0)^2+(4-0)^2}[/tex]                  A'B'= [tex]\sqrt{(3-2)^2+(5-1)^2}[/tex]
 AB= √17                                            A'B' = √17

Thus, the required distance AB and A'B'  = √17.

Learn more about Transformation here:
https://brainly.com/question/11709244

#SPJ1

Step-by-step explanation:

So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get

Opportunity Loans:

 [tex]A = 1600(1+\frac{0.0345}{12})^{(12)(1)}[/tex]

 [tex]A = 1600(1.002875)^{12}[/tex]

 [tex]A \approx 1600(1.035)[/tex]

 [tex]A = \$1,656.08[/tex]

  Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount

 [tex]Interest=1656.08-1600\\Interest=56.08[/tex]

General Loans:

 [tex]A = 1600(1+\frac{0.042}{4})^{(4)(1)}[/tex]

 [tex]A = 1600(1.0105)^4[/tex]

 [tex]A \approx 1600(1.042)[/tex]

 [tex]A = 1,668.27[/tex]

 To find the interest we do the same thing we did in the previous problem

 [tex]interest = 1668.27-1600\\interest=68.27[/tex]

Opportunity loans has the least amount of interest after a year

Answer:

3

Step-by-step explanation:

AD/AB = AE/AC

8/10 = 12/AC

AC = 12(10/8) = 15

EC = 15 - 12 = 3

The statement which best explains whether the student is correct is: D. the student is completely incorrect because there is "no solution" to this inequality.

An inequality refers to a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Since |x-9| is greater than or equal (≥) to zero (0), we can logically infer that this student is completely incorrect because there is "no solution" to this inequality.

Read more on inequalities here: https://brainly.com/question/24372553

#SPJ1

Complete Question:

A student found the solution below for the given inequality.

|x-9|<-4

x-9>4 and x-9<-4

x>13 and x<5

Which of the following explains whether the student is correct?

A. The student is completely correct because the student correctly wrote and solved the compound inequality.

B. The student is partially correct because only one part of the compound inequality is written correctly.

C. The student is partially correct because the student should have written the statements using “or” instead of “and.”

D. The student is completely incorrect because there is “ no solution “ to this inequality.

Quick process:

⇒ Square has  4 sides

⇒ We have been given that the perimeter is 24 centimeters

⇒ Each side is equal in value and each side added up together must equal 24.

⇒ So to finish this out we need to divide the given perimeter which is 2 4 by the amount of side a square has which is 4.

⇒ So 24/4 = 6

Check the answer:

6 + 6  = 12

12 + 12 = 24 √

Perimeter of a square =24cm

Formula=4s

So 4s=24

s=24/4

s=6

Therefore side of the square is 6cm.

Mark me brainliest

Answer:

[tex]dy \ = \ 0.1[/tex]

Step-by-step explanation:

Considering the Leibniz notation to represent the derivative of [tex]y[/tex] with respect to [tex]x[/tex], suppose [tex]y \ = \ f\left(x\right)[/tex] is a differentiable function, let [tex]dx[/tex] be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable [tex]dy[/tex] as

                                                  [tex]dy \ = \ f'\left(x\right) \ dx[/tex],

where [tex]dy[/tex] is the function of both [tex]x[/tex] and [tex]dx[/tex]. Hence, the terms [tex]dy[/tex] and [tex]dx[/tex] are known as differentials

Dividing both sides of the equation by [tex]dy[/tex], yield the familiar expression

                                                         [tex]\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)[/tex].

Given that [tex]f\left(x\right) \ = \ x[/tex] and [tex]dx \ = \ 64.1 \ - \ 64 \ = \ 0.1[/tex], hence

                                                 [tex]f'\left(x\right) \ = \ 1[/tex].

Subsequently,

                                               [tex]dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1[/tex].

Answer:

Length = 120 ft

Total cost = 1500$

Step-by-step explanation:

First, to find the length of the backyard we reverse the formula (A = l * w) and divide 10,800 by 90.

10,800 ft^2 / 90 ft = 120 ft.

we can check this by plugging the length of 120 ft into the formula:

120 ft * 90 ft = 10,800 ft^2.

Next, to find the cost of the single length of fence we multiply our length (120 ft) by the cost ($12.50):

120 * 12.50 = $1500

Answer:

-1

Step-by-step explanation:

-3 + 9 = 6, 6 - 7 = -1

Answer:

16, 100

Step-by-step explanation:

A perfect square is a number that can be achieved by multiplying a number by itself.

Example: 100 = 10 x 10, so it is a perfect square

2 is not a perfect square because it has no factors that can be multiplied with each other to equal 2. An easy way to check is to use the square root function on your calculator.

If the result is a whole number then it's a perfect square.

The length of the rectangle that makes the area to be 273 square feet is 21 feet.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the length of the rectangle, hence:

Length * width = area

13 * x = 273

x = 21 feet

The length of the rectangle that makes the area to be 273 square feet is 21 feet.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

the mean and the median of the set of scores are the same.

Step-by-step explanation:

median = 89

mean = 96+77+86+97+89 = 445 / 5

= 89

mode = none

The mean and the median of the set of scores are the same.

Introduction to Mean, Median, and Mode: In statistics, we frequently choose a representative value to roughly characterise the entire collection of data. The name "measure of central tendency" denotes that this representative value is one around which the data is centred. The mean, median, and mode are these central tendencies. The most typical way to measure central tendency is with the mean. In actuality, it represents the mean of the specified set of data. Both continuous and discrete data can be used with it. In most cases, the median shows the midpoint of the given set of data when it is arranged in a specific order.

Mean: - Average value

Median: - Middle term (after arranging in either accending or descending order)

Mean = 445/5 = 89

Median = Middle term = 3rd term = 89

Mean and median are equal.

Hence, option D is correct

Learn more about mean and median from the link.

https://brainly.com/question/14532771

#SPJ2

Work is attached. Hope it helps!

The length, width, and area will be 25m, 15m, and 375m².

From the information given, the scale in the drawing is 2cm : 5m and the length and width are given as 10cm and 6cm respectively.

Length = 10cm = 10 × 2.5 = 25m

Width = 6cm = 6 × 2.5m = 15m

Area = Length × Width

Area = 25 × 15

Area = 375m²

Therefore, the area is 375m².

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer: ( C ) the average would approach a set value.