Two sides of a right triangle have lengths of 2 centimeters and 6 centimeters. The third side is not the hypotenuse. How long is the third side?

Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.

To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.

For the 2-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $7.00 / 2 lbs

Cost per pound = $3.50 per pound

For the 3-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $10.50 / 3 lbs

Cost per pound = $3.50 per pound

Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.

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Volume First Cylinder: 50.24 in³

Volume Second Cylinder: 127.5625 inch³

Volume Third Cylinder: 904.32 inch³

Volume First Cylinder:

= πr²h

= 3.14(2)² (4)

= 3.14 x 16

= 50.24 in³

Volume Second Cylinder:

= πr²h

= 3.14(2.5)² (6.5)

=3.14 (6.25)(6.5)

= 127.5625 inch³

Volume Third Cylinder:

= πr²h

= 3.14(6)² (8)

=3.14 (36)(8)

= 904.32 inch³

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Answer:

Step-by-step explanation: 462 Divided by 24 = 19.25$

Proof: 19.25 x 24 = 462

Answer: 19.25$

If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot,  the total cost is $1140.

To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.

Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft

Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:

Total cost = Area of the floor x Cost per square foot

Total cost = 240 sq ft x $4.75/sq ft

Total cost = $1140

Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.

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The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.

According to the problem,

The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.

The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].

Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

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Answer:

- 2/1

Step-by-step explanation:

if u look at the graph/line it's going up by 2 then across 1

Using the conversion factor we know that we will spend 180.69€ on memorabilia items.

A conversion factor is a number that is used to multiply or divide one set of units into another.

If a conversion is required, it must be done using the correct conversion factor to get an identical value.

A fraction that is equal to "1" is a conversion factor.  

The numerator and denominator are the same amounts, but they are expressed in different units.  It is used to change a number's unit of measurement.  

By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.

So, in the given situation:

$200 = euros?

We know that:
$1 = 0.90€

Then,

$200 = 180.69€

Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.

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An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

The power-reducing formulas state that:

sin^2(x) = (1 - cos(2x))/2

cos^2(x) = (1 + cos(2x))/2

Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:

18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]

Expanding the right-hand side of the equation, we get:

18[(1 - cos^2(2x))/4]

Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:

18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8

Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

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g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

what is function ?

In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.

In the given question,

To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

Step 1: Apply f to -3

f(x) = 3x + 7

f(-3) = 3(-3) + 7 = -2

Step 2: Apply g to the result of f(-3)

g(x) = 2x - 5

g(-2) = 2(-2) - 5 = -9

Therefore, g°f = -9.

So, the correct answer is (B) -9.

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Answer:

a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.

y = 34.17860108 - 5.682632245ln(x)

b. Setting this equation equal to 10, we have x = 70.44 mph

c. If x = 75 mph, then y = 9.64.

The value of 'x' in the given figure is 14.73.

The given figure is a Right-angled triangle.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

In the given figure,

Hypotenuse is 19.

The adjacent side is 12.

The opposite side is x.

Now, we have to find the value of x.

According to the theorem,

19² = 12²+x²

361 = 144+x²

x² = 361 - 144

x² = 217

x = √217

x = 14.73

Therefore, the value of 'x' in the given figure is 14.73.

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Answer:

100 Minutes

Step-by-step explanation:

Step 1: Break it down-

3¢ can be expressed as 0.3

Step 2: Add monthly charge-

Since there is a 10$ monthly charge: 40-10=30

Step 3: Subtract-

Now divide: 30 ÷ 0.3

Step 4: Final Answer-

Hence the amount of minutes per month= 100

Answer:

88

Step-by-step explanation:

y=2cm h=7cm

CSA=22/7×4×7

the sevens get crossed out and then 22/1 ×4=88.

Answer:

[tex] \frac{w}{3} [/tex]

The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.

Let the width be 'x'.

So, length will be 3x.

From this, we get

⇒ Perimeter = 2 (length + width)

⇒ 42.4 = 2 (3x + x)

⇒ 42.4 = 2 (4x)                             (Using addition operation)

⇒ 42.4 = 8x                                  (Using multiplication operation)                

⇒ x = 5.3                                      (Using division operation)

So,

⇒ Length = 3 * 5.3

⇒ Length = 15.9 inches

Hence, the length of the rectangle is 15.9 inches.

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Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

Answer:

11 dimes and nickels.

Step-by-step explanation:

22 total coins divided by 2 equals 11 for each.

the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.

Answer:15 nickels  and  7 dimes.

Step-by-step explanation:

92 grams of recycled plastic were used to make Chanasia's bucket

Chanasia buys a plastic bucket

The bucket weighs 460 grams

The label on the bucket says it was made with 20% recycled plastic

The number of grams of recycled plastic that was used to make the bucket can be calculated as follows

= 460/100

= 4.6

= 4.6 × 20

= 92

Hence 92 grams of recycled plastic was used to make the bucket

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The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.

To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.

The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.

The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.

Therefore, the probability that all four people regularly use seat belts is:

P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)

P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901

P(all four use seat belts) = 0.656

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The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.

Graph the constraints:

First, we will graph the constraints to visualize the feasible region.

The constraint x + y ≤ 50 represents the region below the line x + y = 50:

The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:

The feasible region is the shaded region that satisfies both constraints:

Identify the corner points of the feasible region:

The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).

Evaluate z at each corner point:

z(0, 0) = 4(0) + 0 = 0

z(0, 50) = 4(0) + 50 = 50

z(30, 20) = 4(30) + 20 = 140

z(45, 0) = 4(45) + 0 = 180

Compare the values of z at the corner points:

The largest value of z is 180, which occurs at the corner point (45, 0).

Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

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Answer:

189.1034.

Step-by-step explanation:

The result of the expression is approximately 189.1035.

To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:

Parentheses: Perform the operation within the parentheses first.

71 + 16 = 87

Division: Perform the division.

84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)

Multiplication: Perform the multiplication.

0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)

Subtraction: Finally, perform the subtraction.

192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)

The result of the expression is approximately 189.1035.

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Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.

Using the tests for symmetry, the following are symmetric with respect to y-axis:

A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.

A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.

A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.

(a) symmetric with respect to the y-axis:

y = 7x - 4 (no)

y = - x + 7 (yes)

y = - 7x² (yes)

y = 6x² - 9 (no)

x = 1/4 × y² (no)

x = - y² + 9 (yes)

y = - 1/6 × x³ (no)

y = x³ - 1 (no)

y = √(x) (no)

y = √(x) - 6 (no)

Therefore, the graphs that are symmetric with respect to the y-axis are:

y = - x + 7

y = - 7x²

x = - y² + 9

None of the graphs are symmetric with respect to the x-axis or the origin.

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B) The domain for #1 and #2 is  ≥ -7 and the domain for #3 is -∞ ≤  ≤ ∞.

1. [tex](f + g)(x) = f(x) + g(x)[/tex]

The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].

2. [tex](f - g)(x) = f(x) - g(x)[/tex]

The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].

3. [tex](fg)(x) - > (f(g(x))[/tex]

The domain of [tex]f(g(x))[/tex] is the set of all values of  [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex]  is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].

Therefore, the correct answer is option:

B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.

========================================================

Work Shown:

[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]

The other diagonal is 4 miles long.

ANSWER:

368

EXPLANATION:

youre given:

l=14

w=5

h=5

just plug those into the given formula,

2×(14×5)+2×(14×6)+2×(5×6)

(you should do it yourself to check my math...)