If X = 6 cm and Z = 10 cm, what is the length of Y?

Answer:Yes

Step-by-step explanation:A=16 B=30 C=34

16*16= 256 30*30=900 34*34=1156

256+900=1156

Answer:

let's check first is it Right Triangle because we can do it using Pythagorean theorem:

let's sides 16 and 30 be legs, and 34 hypotenuse

1156=1156...so, this is true and your triangle IS Right Triangle

but, it is also a scalene triangle with a right angle

Step-by-step explanation:

Jill owns approximately 60,000 acres of land.

Let's first find out how many trees Jill has per acre based on the information given.

Jill has 150 peach trees on 1/2 of her land, which means she has 300 peach trees on her entire land. If there are 5 trees for every 1,000 square feet of land, we can calculate the total square feet of land that Jill owns:

[tex]\[ \text{Total trees} = \text{Trees per acre} \times \text{Total acres} \]\[ 300 = \frac{5}{1000} \times \text{Total acres} \][/tex]

Solving for the total acres:

[tex]\[ \text{Total acres} = \frac{300}{\frac{5}{1000}} \]\[ \text{Total acres} = \frac{300 \times 1000}{5} \]\[ \text{Total acres} = \frac{300000}{5} \]\[ \text{Total acres} = 60000 \][/tex]

Now, we can convert the total acres from square feet to acres using the conversion factor given:

[tex]\[ \text{Total acres in square feet} = 60000 \times 43560 \]\[ \text{Total acres} = \frac{60000 \times 43560}{43560} \]\[ \text{Total acres} = 60000 \][/tex]

So, Jill owns approximately 60,000 acres of land.

Jill owns approximately 1.38 acres of land.

To find out how many acres of land Jill owns, we first need to determine the total number of peach trees on all her land.

Since she counts 150 peach trees on half of her land, we can assume there are 300 peach trees in total (since half of her land has 150 trees and the other half will also have 150 trees).

Now, if there are 5 trees for every 1,000 square feet of land, we can set up a proportion to find out how many square feet of land these 300 trees occupy:

[tex]\( \frac{5 \text{ trees}}{1000 \text{ square feet}} = \frac{300 \text{ trees}}{x \text{ square feet}} \)[/tex]

Cross-multiplying, we get:

[tex]\( 5x = 300,000 \)[/tex]

Dividing both sides by 5:

[tex]\( x = 60,000 \)[/tex]

So, Jill's 300 peach trees occupy 60,000 square feet of land.

To convert this to acres, we use the conversion factor provided: [tex]1 acre = 43,560 square feet.[/tex]

[tex]\( \text{Number of acres} = \frac{60000}{43560} \)[/tex]

[tex]\( \text{Number of acres} = 1.38 \)[/tex]

Complete correct question:

Jill counts 150 peach trees on 1/2 of the land she owns. She determines that there are 5 trees for every 1,000 square feet of land. About how many acres of land does Jill own? [tex]1 acre= 43,560 square feet.[/tex]

FOLLOW ME FOR CLEARING YOUR NEXT DOUBT

The length of the hypotenuse QS of the triangle ΔRPQ will be 16 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of the right-angle triangle will be 8√3 units and 8 units.

Then the length of the hypotenuse QS will be given as,

H² = (8√3)² + (8)²

H² = 192 + 64

H² = 256

H² = 16²

H = 16 units

The length of the hypotenuse QS of the triangle ΔRPQ will be 16 units.

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Answer:Stan used 19/40 of a gallon of gasoline.

Step-by-step explanation:

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank. It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

After he mowed, 1/4 of a gallon was left in the tank. Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Final answer:

Stan used a total of 0.475 gallons of gasoline for mowing, calculated by adding the initial and added amounts of gasoline and then subtracting what was left after mowing.

Explanation:

To calculate the total amount of gasoline Stan used, we will first need to know the total gasoline added to the mower and then subtract the amount left after mowing.

Firstly, Stan started with ⅛ of a gallon (which is the same as 0.125 gallons) and added ⅔ of a gallon (0.6 gallons) to the tank. To find out how much gas was in the tank after refilling, we add these two amounts together:

0.125 + 0.6 = 0.725 gallons (total gas in the tank after refilling).

Once Stan finished mowing, he had ¼ of a gallon left in the tank. We need to subtract this amount from the total gas in the tank after refilling to find out the amount of gas used:

0.725 - 0.25 = 0.475 gallons (total gas used by Stan while mowing).

Therefore, Stan used a total of 0.475 gallons of gasoline for mowing.

Answer:

-5

Step-by-step explanation:

To solve for z, divide both sides of this equation by -0.25:

        1.25

z = ----------- = -5

       -0.25

Answer:

The correct answer is -5.

Step-by-step explanation:

To find my answer, I divided both sides by -0.25.

-0.25z = 1.25

-0.25z ÷ -0.25 = 1.25 ÷ (-0.25)

z = -5

Hope this helps,

❤Nicki❤

Answer:

1.666666

Step-by-step explanation:

Answer:

One and two thirds or 1 2/3

Step-by-step explanation:

2/6*5=10/6=1 4/6= 1 2/3

Answer: 28 (exponent 2) = 56

Step-by-step explanation:

28 and exponent two (sry my keyboard doesnt have the special characters) = 56, since 28 x 2 = 56.

Answer:

1:12

Step-by-step explanation:

Answer:

d. sin 80.

Step-by-step explanation:

Use the identity cos x = sin (90-x).

So cos 10 = sin(90 - 10)

= sin 80.

Cos 10 when written in terms of sine would be d. sin 80.

The relationship between cosine and sine for complementary angles can be expressed as:

cos ( θ ) = sin ( 90 ° - θ )

This relation arises from the definition of cosine and sine in a right triangle. They are complementary functions. The cosine of an angle in a right triangle is the sine of its complement, and vice versa.

Given this relationship, we can express cos(10°) as:

cos ( 10 ° ) = sin ( 90 ° - 10 ° ) = sin ( 80 ° )

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9514 1404 393

Answer:

  Sally's work: StartFraction b Over 12 EndFraction = 16. B = 192

Step-by-step explanation:

Of the offered choices, the only one that is solved correctly is Sally's work.

Here are the solutions for the equations the students wrote:

  [tex]\dfrac{12}{b}=16\ \rightarrow\ 12=16b\ \rightarrow\ \dfrac{12}{16}=b=0.75\\\\\dfrac{b}{12}=16\ \rightarrow\ b=12\cdot16=192[/tex]

_____

Comment on the wrong answers

The "solution" value of 1.3 appears to be a rounded version of 16/12, a value that will not show up as a solution to any of the equations written.

Comment on dimensional analysis

The dimensions of "16" are "cases." The dimensions of "12" are "bottles per case", or bottles/case. Multiplying this by the number of cases, gives the number of bottles. This is where I'd start:

  (bottles/case)×(cases) = bottles    ⇒    12×16 = b

The ratios the students wrote had units of ...

  b/12 = (bottles)/(bottles/case) = cases = 16

and (incorrectly) ...

  12/b = (bottles/case)/(bottles) = 1/cases = 16 . . . . wrong

It can be useful to consider what the numbers represent. That can help avoid math mistakes.

a bought 16 cases of water bottles. There were 12 water bottles in each case. Four students wrote and solved equations to find b, the number of bottles that Clara bought. Which student wrote and solved the equation correctly?

Maya’s work:

StartFraction b Over 12 EndFraction = 16. b = 1.3

Larissa’s work:

12 b = 16. b = 1.3

Sally’s work:

StartFraction b Over 12 EndFraction = 16. b = 192.

Anika’s work:

StartFraction 12 Over b EndFraction = 16. b = 192.

Step-by-step explanation:

Answer:

equal to: =

Step-by-step explanation:

1 gallon has 4 quarts and half a gallon has two quarts, all together there is 6 quarts in 1 1/2 gallons

1 1/2 gallons is equal to 6 quarts.

1 1/2 gallons is equivalent to 6 quarts. Since the two quantities are equal, 1 1/2 gallons is not greater than 6 quarts. This can be shown by converting the gallons to quarts.

1 gallon is equal to 4 quarts, so 1 1/2 gallons is equal to 6 quarts (1.5 x 4 = 6). Therefore, 1 1/2 gallons is not greater than 6 quarts.

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Answer

Step-by-step explanation:The fine schedule for overdue books at the county library is modeled by the values in the table.

Library Fines for Overdue Books

Days overdue

Amount of fine

0

0 ¢

2

5 ¢

4

10 ¢

6

15 ¢

8

20 ¢

10

25 ¢

Which equation best models the fine schedule for overdue books?

y = five-halves x, where x is the cost in cents for a book that is y days overdue

y = five-halves x, where y is the cost in cents for a book that is x days overdue

y = 5 x, where x is the cost in cents for a book that is y days overdue

y = 5 x, where y is the cost in cents for a book that is x days overdue

Answer:

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

A maximum area for the rectangular garden is achieved when the rectangle is a square, having side lengths of 15 and 30 feet. This yields an area of 450 square feet.

The question is a classic problem of optimization in Mathematics, where we want to maximize the area of the garden given a constraint, which in this case, is the total length of fence available. We consider the garden to have sides of lengths x and y, where y is the side against the building, and we don't need fencing there. Because we're working with a total of 60 feet of fencing, the length of the other three sides of the rectangle (two sides of length x, one side of length y) give us the equation 2x + y = 60.

We want to maximize the area of the rectangle, which is given by A = x*y. We can substitute y from the above equation into this to give A = x*(60-2x) = 60x - 2x^2. This is a quadratic function and it attains its maximum when x = -b/2a. Here, a = -2, b = -60, so x is 15 feet. The maximum area occurs when x and y are equal, which is when the rectangle is a square.

So, the corresponding value of y = 60 - 2*15 = 30 feet. Therefore, we have a maximum area  of 15*30 = 450 square feet.

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The requried volume of the cylinder is approximately 1017.9 cubic meters.

The volume of a cylinder can be calculated using the formula:

Volume = π * (diameter/2)² * height

where π (pi) is a mathematical constant approximately equal to 3.14159, diameter is the base diameter of the cylinder, and height is the height of the cylinder.

In this case, the height is 9m and the base diameter is 12m. We need to first calculate the radius, which is half of the diameter:

Radius = diameter/2 = 12m/2 = 6m

Now we can substitute the values into the formula and calculate the volume:

Volume = π * (6m)² * 9m

Volume ≈ 1017.88 cubic meters

Rounding to the nearest tenth place, the volume of the cylinder is approximately 1017.9 cubic meters.

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Final answer:

The volume of a cylinder with a height of 9m and a base diameter of 12m is approximately 9160.9 cubic meters when rounded to the nearest tenth.

Explanation:

The student is asking for the volume of a cylinder with a given height and base diameter, which is a common problem in mathematics related to geometry and measurements. To find the volume, we use the formula for the volume of a cylinder V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. Given that the diameter is 12 meters, the radius (r) is half of that, which is 6 meters. We then substitute these values into the formula:

V = π(6m)²(9m)

V = 3.1416 × 36m² × 9m

V = 3.1416 × 324m² × 9m

V = π × 2916m³

V = 9160.88m³

After calculating, we round the volume to the nearest tenths place, obtaining V ≈ 9160.9m³.

Answer:

that is the solution to the question

Final Answer:

31 degree.

Explanation:

The sum of the interior angles of any triangle in a Euclidean plane is always 180°.
Given one angle of the isosceles triangle measures 118°, we can find the possible measures of the other two angles using the following steps:
Step 1: Calculate the sum of the two remaining angles.
Since the total sum of the angles in a triangle is 180° and we already have one angle measuring 118°, we can subtract the known angle from 180° to find the sum of the remaining two angles:
180° - 118° = 62°
Step 2: Divide the sum between the two equal angles.
Because the triangle is isosceles, the remaining two angles are equal in measure. We found their sum (62°), so to determine each individual angle's measurement, we divide that sum by 2:
62° ÷ 2 = 31°
Thus, both of the remaining angles in the isosceles triangle must measure 31° each.
In conclusion, an isosceles triangle with one angle measuring 118° will have the other two angles both measuring 31°.

Answer:

[tex]X \sim Binom(n=10, p=0.96)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

For this case the expected value is given by:

[tex] E(X) = np = 10 *0.96 = 9.6[/tex]

Part b

For this case the standard deviation is given by:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of workers in the sample who are union members", on this case we now that:

[tex]X \sim Binom(n=10, p=0.96)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

For this case the expected value is given by:

[tex] E(X) = np = 10 *0.96 = 9.6[/tex]

Part b

For this case the standard deviation is given by:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]

A. The mean number of union members in a sample of 10 workers is 9.6. B. The standard deviation is approximately 0.620.

A) Mean (Expectation) Calculation

The number of union members in the sample can be modeled using a binomial distribution since each worker either is or isn't a union member.

For a binomial distribution, the expectation (mean) is given by:

Mean (μ) = n * p

where n is the number of trials (in this case, the number of workers in the sample), and p is the probability of success in a single trial (the probability that a worker is a union member).

Here, n = 10 and p = 0.96, so:

Mean (μ) = 10 * 0.96 = 9.6

B) Standard Deviation Calculation

For the same binomial distribution, the standard deviation (σ) is given by:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(10 * 0.96 * (1 - 0.96))

= √(10 * 0.96 * 0.04)

= √0.384

= 0.620

Thus, the standard deviation of the distribution is approximately 0.620

Answer: False.

Step-by-step explanation:

There does not exist a "quarter circle" as a circle with a radius of 4 units, the only notable circle that does exist is the unit circle, that is the circle where the radius is equal to 1, represented by the equatin x^2 + y^2 = 1

The term "quarter circle" actually does refer to a fourth part of a circle, not to a circle of radius 4.

So the statement is false

Answer: 1 ounce = 0.0295735 liters rounded it is 0.03  liters

Formula: Divide the volume value by 33.814

1÷33.814 =0.0295735

0.02957354941 rounded to the nearest hundredths is 0.03  

Answer:

[tex]1 litre =33.814 \: \: us \: \: fluid \: \: \: ounces[/tex]

Step-by-step explanation:

So to find the amount of liters you have to multiply amount by 33.814 ounces

And to find the amount of ounces you have to divide the amount by 33.814.

hope this helps.

thanks..

Answer:

$9

Step-by-step explanation:

set up a proportion where 20% is represented as 20/100 and set it equal to 1.80/x

cross multiply and you should get 180=20x

divide by 20 to solve for x

you then get 9, which is the amount you were looking for

Answer:

25(x)

Step-by-step explanation:

if you cave 4 quarters, this will be 25(40) which is 100 cents.

Answer:

24

Step-by-step explanation:

1250/ 54 = 23.14814814

Answer:

c

Step-by-step explanation:

Answer:

Question

Select the correct answer. Which expression is equivalent to x + y + x + y + 3(y + 5)? A. 2x + 5y + 5 B. 2x + y + 30 C. 2x + 5y + 15 D. 2x + 3y + 10 Reset          Answer C.

Step-by-step explanation:

Answer:

C) Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.

Step-by-step explanation:

When naming congruent shapes, the orders of the congruent vertex letters need to be the same.

Since these are isosceles triangles, the base angles are the same:

m∠R = m∠T = m∠A = m∠C

Therefore the congruency statement can be written two different ways.

ΔABC ≅ ΔRST

ΔABC ≅ ΔTSR

Both statements could be correct.

Choosing between B) and C):

To move ΔABC to where ΔRST or ΔTSR is, you could either:

i) Translate 6 units to the left, and translate 3 units down

ii) Reflect across the y-axis, and translate 3 units down

It can be the result of two translations or a reflection and a translation.

In the result, the base side RT is on the bottom of the shape, like side AC. If you rotated the shape, the base side would not be on the bottom. Therefore B) is incorrect.

Answer:

c

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

both sides are going up by 2 .

so the number after 6 in the x column would have to be 8 because in the y column it went up by two.

then for the missing number in the y column we see that the x value went up from 8 to 10. that means that the y column value went up by 2. so you get 23

After 4 hours: 60 ng/mL, After 8 hours: 30 ng/mL, After 12 hours: 15 ng/mL, After 16 hours: 7.5 ng/mL.

The half-life of a drug is the time it takes for the concentration of the drug in the body to reduce by half. In this case, the half-life of the drug is 4 hours. When a patient discontinues taking the medication, the concentration of the drug decreases exponentially over time.

The initial concentration is given as 120 ng/mL. After the first 4 hours, which is one half-life, the concentration reduces to 60 ng/mL. Subsequent half-lives continue to halve the concentration. After 8 hours, it becomes 30 ng/mL, after 12 hours it's 15 ng/mL, after 16 hours it's 7.5 ng/mL.

This exponential decrease reflects the nature of drug elimination from the body, with each half-life reducing the concentration by half. The rounded values in the table represent the decreasing drug concentrations at different time intervals after the patient stops taking the medication.

Answer:

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is [tex]\sqrt{length^2+width^2}[/tex]

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

                                                            [tex]=\sqrt{4x^2+24x+36+x^2}[/tex]

                                                             [tex]=\sqrt{5x^2+24x+36}[/tex] cm

According to the problem,

[tex]\sqrt{5x^2+24x+36}=15[/tex]

Squaring both sides

[tex]\Rightarrow{5x^2+24x+36}=15^2[/tex]

[tex]\Rightarrow{5x^2+24x+36}=225[/tex]

[tex]\Rightarrow{5x^2+24x+36-225=0[/tex]

[tex]\Rightarrow{5x^2+24x-189=0[/tex]

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0  or,   5x-21=0

[tex]\Rightarrow x=-9, \frac{21}5[/tex]

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

                                                  =14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

To find the dimensions of a rectangle with a given diagonal length and a relationship between its length and width, we can set up a system of equations and use the Pythagorean theorem.

To solve this problem, we can set up a system of equations using the given information. Let's assume the width of the rectangle is x. The length of the rectangle is then 2x + 6. We can use the Pythagorean theorem to set up an equation using the diagonal and the sides of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

x^2 + (2x + 6)^2 = 15^2

Simplifying and solving this equation will give us the value of x, which is the width of the rectangle. We can then calculate the length of the rectangle by substituting the value of x into the expression 2x + 6.

Let's solve the equation:

x^2 + (2x + 6)^2 = 15^2

Expanding the equation and simplifying:

x^2 + 4x^2 + 24x + 36 = 225

Combining like terms:

5x^2 + 24x + 36 = 225

Moving 225 to the other side of the equation:

5x^2 + 24x + 36 - 225 = 0

Simplifying further:

5x^2 + 24x - 189 = 0

Now we can solve this quadratic equation for x. We can factor it or use the quadratic formula.

By factoring, we find that x = -9 or x = 7.8. Since we are dealing with dimensions, we can ignore the negative value and take x = 7.8 centimeters as the width of the rectangle.

The length would then be 2(7.8) + 6 = 22.6 centimeters. So, the dimensions of the rectangle should be a width of 7.8 centimeters and a length of 22.6 centimeters.

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Answer:

(-2,-3)

Step-by-step explanation:

The first step is to find the equations of the two lines. For the first line, the slope is 3/2, while the y intercept is 0. This gives it an equation of y=3/2x. For the second line, it has a slope of -3/2, and a y intercept of -6. This gives it an equation of y=-3/2x-6. Setting these two equations equal to each other, you get

3/2x=-3/2x-6

3x=-6

x=-2

y=-3

(-2,-3) Hope this helps!

Answer:

-85/8

Step-by-step explanation:

- 10 5/8  is a mixed fraction

- 10 and  5/8 =  -85/8

The mixed number -10 5/8 is equivalent to the improper fraction -85/8, which is found by converting the mixed number to an improper fraction and then applying the negative sign.

When converting a mixed number with a negative sign, you first convert the fractional part and then apply the negative sign. The mixed number -10 5/8 can be converted to an improper fraction by multiplying the whole number 10 by the denominator 8, adding the numerator 5, and then placing the result over the same denominator. Finally, place a negative sign in front.

The calculation would be as follows:

Therefore, the expression equivalent to -10 5/8 is -85/8.