The area of a rectangle is 2 square feet: The perimeter of the rectangle is 9 ft. Find the length, /, and width, W, of the rectangle. What is /2 + w2 ?

the expression can be simplified to V72√37x323 + V a√z.

V72x323 + Vz = V(72x323 + z)

Since the square roots contain two different terms, we cannot simplify them any further. However, we can remove any perfect squares that are contained inside the square roots. To do this we can factor out the perfect squares from the terms inside the square roots.

For the first square root, 72x323 = 72 x 9 x 37. Since 72 and 9 are both perfect squares, we can factor out these terms to get 72√37x323.

For the second square root, z = a2, where a is a positive real number. We can factor out the perfect square a2 to get a√z.

Therefore, the expression can be simplified to V72√37x323 + V a√z.

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The sum of the two largest 2-digit distinct counting numbers is 45

The term sum in math is defined as the result of arithmetically adding numbers or quantities

Here we have given that we need to find the sum of the two largest 2-digit distinct counting numbers that are not multiples of 1, 2, or 5.

By using the arithmetic progression here we have all two digit odd positive numbers are 11, 13, 15, 17, ...., 99. which are in AP with the value of

=> a=11,

=> d=2,

=> l=99

Then let the number of terms be n, then it can be calculated as,

=> an​=99

=> a+(n−1)d=99

Apply the values on it, then we get,

=> 11+(n−1)×2=99

When we simplify this one then we get the value of n as 45

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The original price of the shirt is $407

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred.

From the question, to find the original price of the shirt

We use the equation:

0.19/100 =77.33/x

0.19x = 7733

dividing both side of the equation by 0.19

x=40700\100

x = 407

Hence, the original price of the shirt before the discount is $407

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$39.99+238.8+1.75x and  $4.99=1.99x+$40 are the algebraic expressions of given data.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that $39.99 /month, unlimited texting , 120MB data (Overages $1.99 /MB talk is $1.75 /minutes

$39.99+120(1.99)+1.75x

$39.99+238.8+1.75x

$4.99 /month, unlimited texting ,$40 for 80MB data talk is $1.99 /minutes

$4.99+1.99x+$40

Hence, $39.99+238.8+1.75x and  $4.99+1.99x+$40 are the algebaic expressions of given data.

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It's difficult to say whether the conditions for constructing a t-confidence interval are met based on the information provided. To construct a t-confidence interval, three conditions must be met:

The sampling method must be random. It's not specified in the problem whether the method of selecting the vehicles was random or not, so it's impossible to say whether this condition is met.

The sample size must be large enough. A sample size of 100 vehicles is considered to be large enough for the normal/large sample condition to be met.

The population must be approximately normally distributed or the sample size must be large. Since the problem does not specify anything about the distribution of the population, it is not clear if this condition is met.

Given that the information provided does not give enough details to state whether the conditions for constructing a t-confidence interval are met or not.

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It depends on the lengths of the sticks. If the lengths form a triangle, then three incongruent triangles can be formed.

1. First, check to see if the lengths of the sticks form a triangle. This can be done by comparing the lengths of the sticks to the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the measure of the third side.

2. If the lengths of the sticks form a triangle, then three incongruent triangles can be formed by using the given sticks. To do this, take any three sides of the triangle and create three different triangles with those sides.

It depends on the lengths of the sticks. If the lengths form a triangle, then three incongruent triangles can be formed.

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Applying proportion, the money her mother donated is: $64.

Proportion is a mathematical concept that describes the relationship between two or more values that are expressed as a ratio. It is used to compare the size of one value to another.

A proportion can be written in the form of an equation, such as a/b = c/d, where a, b, c, and d are values, and a and b are the values being compared to c and d.

We can use the proportion of the pledge to the distance biked to find the amount of money Emily's mother will donate.

The proportion of the pledge to the distance biked is 0.40/$ for every 0.75 mile.

So for 24 miles, the amount of money pledged would be:

0.40/0.75 * 24 = $64

So Emily's mother will donate $64 to charity.

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Answer:

$208.8

Step-by-step explanation:

99% of $210.94

u just need to multiply

Answer:

25,295.91

Step-by-step explanation:

304,770

1%=3047.7

0.1%=304.77

8%=24,381.6

0.3%=914.31

24,381.6+914.31=25,295.91

female viewers =25,295.91

The solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

What is a quadratic equation?

A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a

To solve for x in the equation 2x^2 -19x + 2 = -10x, we need to rearrange it in the standard form of a quadratic equation by isolating the x^2 term and moving the other terms to the other side:

2x^2 -10x -19x +2 = 0

2x^2 -29x +2 = 0

Now we can apply the quadratic formula:

x = (-b ± √(b^2-4ac)) / 2a

x = (-(-29) ± √((-29)^2-422)) / 2*2

x = (29 ± √(841-16)) / 4

x = (29 ± √(825)) / 4

Hence, the solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

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The partial fraction expansion for the rational function is:-25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16))

To determine the partial fraction expansion for the rational function, we first need to factor the denominator into two linear factors. This can be done using the Factoring by Grouping method. We will factor the denominator of the rational function as follows:

(s+3)(s2 + 16)

Now, we can write the partial fraction expansion for the rational function as:

-25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16))

The partial fraction expansion for the rational function is -25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16)).

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Answer:

Candelas - 154cm

Dianas - 162 cm

Step-by-step explanation:

Median is the mean of the two middle numbers when the numbers are arranged in an ascending order.

We will first have to workout the order when they are placed in ascending order.

Note: Everything here is in ascending order.

Albertos cannot be the shortest as if that happened, the median will not be 160 (Dianas will have to be 179cm as the given range is 21 cm and the mean of Candelas and Bill can never be 160 cm.)

Albertos will have to be second as it cannot be third.( The median will not be 160 when the third number is greater than the second number.)

Now, Dianas will have to be third. ( It can't be first, nor it can be fourth as the median of the height will not be possible to be 160 again without changing the order.)

So, next, obviously, Candelas is first.

So, the order is,

Candelas, Albertos, Dianas, Bill

or,

Candelas , 158, Dianas, 175cm.

Dianas is 162 cm if the mean of 158 cm and Dianas's height is 160 cm.

Candelas's height is 175 - 21 = 154 cm

So the height of Candelas is 154 and height of Dianas is 162.

Answer:

80 grow into plants

Step-by-step explanation:

Fraction word problems:

   Out of 13 seeds, 8 grew into plants.

[tex]\sf \text{Number of seeds grown out of 130 okra seeds} = \dfrac{8}{13}*130[/tex]

                                                                       = 8 * 10

                                                                       = 80

Out of 130 seeds, 80 grow into plants.

(a) 21/144 probability of selecting 1 red and 2 black. (b) 35/144 probability of selecting 2 black. (c) 61/144 probability of selecting 2 same color.

What is probability ?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will occur with certainty. The probability of an event can also be expressed as a percentage or a fraction. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

(a) The probability of selecting one red and two black balls is (3/12) * (7/12) * (7/12) = 21/144.

(b) The probability of selecting exactly two black balls is (7/12) * (7/12) * (5/12) = 35/144.

(c) The probability of selecting exactly two balls of the same color is (3/12) * (3/12) + (2/12) * (2/12) + (7/12) * (7/12) = 61/144.

(a) 21/144 probability of selecting 1 red and 2 black. (b) 35/144 probability of selecting 2 black. (c) 61/144 probability of selecting 2 same color.

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Answer:

x = 4

Step-by-step explanation:

For this question we can use the theorem which states that "if the chords of a circle is equal, it is equidistant from the center."

Therefore, FC = CE

or 3x + 8 = 8x - 12

5x = 20

x = 4

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The number of non-empty subsets of the given set that consist entirely of prime numbers is [tex]$31-16=7$[/tex]

The total number of non-empty subsets of [tex]$\{1,2,3,4,5,6,7,8,9,10,11\}$[/tex] that consist entirely of prime numbers is 7. The prime numbers in the given set are {2,3,5,7,11}. The formula to calculate the number of non-empty subsets of a set with n elements is [tex]$2^n-1$[/tex]. Thus, the number of non-empty subsets of the given set is [tex]$2^{5}-1=31$[/tex]. To calculate the number of subsets that consist of prime numbers only, we need to subtract the number of subsets that contain at least one non-prime number from 31. There are 16 such subsets, as the non-prime numbers in the given set are[tex]$\{4,6,8,9,10\}$[/tex]. Thus, the number of non-empty subsets of the given set that consist entirely of prime numbers is[tex]$31-16=7$.[/tex]

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With a speed of 0.419 m/s, the rider fast is a rider rising when his seat is 16m above ground level

The formula for tangential velocity is 2*pi*r/T --> 2*pi*10/120 --> pi/6.

It is 6 meters above the center of the wheel while the rider is 16 meters above the ground.

The horizontal portion of this distance must be 8 meters as its separation from the wheel's center is 10 meters (depending on the radius).

This indicates that the velocity and seat both make angles of 36.87 degrees off vertical and arctan(6/8) over the origin, respectively.

We will take into account the vertical component of the tangential velocity since the rate at which the seat is rising is what we're interested in.

Pi/6 * cos(arctan(6/8)) yields a value of 0.419 m/s.

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[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-20}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-20}-\underset{x_1}{(-15)}}} \implies \cfrac{-12 +10}{-20 +15} \implies \cfrac{ -2 }{ -5 } \implies {\Large \begin{array}{llll} \cfrac{2 }{ 5 } \end{array}}[/tex]

Answer: The slope is -2/5

Step-by-step explanation:

In this subsection, we examine the ways in which the graphs of functions alter or transform as a result of certain, specialized adjustments to their formulations.

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Answer:

f(x) = - x + 2

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

f(0) = 2 means y = 0 when x = 2 and f(5) = - 3 means y = - 3 when x = 5

thus there are 2 points (2, 0 ) and (5, - 3 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (5, - 3 )

m = [tex]\frac{-3-2}{5-0}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

then

f(x) = - x + 2

The radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

To calculate the radius of the circle, we need to first calculate the perimeter of the equilateral triangle. The perimeter of an equilateral triangle is equal to 3 times the side length of the triangle. Thus, we can say that the perimeter of the equilateral triangle is 3s.

Now, we need to calculate the area of the circumscribed circle. The area of a circle is equal to π times the square of the radius. Thus, the area of the circumscribed circle is equal to πr2.

Therefore, we can say that 3s = πr2. Solving this equation for r, we get r = s√3π. Thus, the radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

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In a trapezium, the sum of the outer angles is always equal to 360 degrees because, in any convex quadrilateral, the sum of the four angles is consistently 360 degrees. As a trapezium is a type of convex quadrilateral, the sum of its four angles is 360 degrees, regardless of its shape or size.

We can simplify this equation by combining like terms on one side and isolating the variable on the other.

First, combine like terms: x + 5 + 3x - 8 + 5x + 10 + x + 10 = 360

(x + x) + (5 + 10 + 10) + (3x + 5x) = 360

10x + 17 = 360

Then, subtract 17 from both sides to isolate the variable on one side:

10x = 343

Finally, divide both sides by 10 to solve for x:

x = 34.3

So the solution to the equation is x = 34.3

The function below shows the number of hours f(x) Greg took to make pudding after he had made it x times is f(x) = 2(0.8)ˣ and the graph of the function is attached below.

The term function in math is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we have given that Greg made pudding every weekend.

And here we also know that the more times he made pudding, then the more practice he gained.

According to the time he took to make the same amount of pudding every week decreased with practice.

Here we need to write the function below shows the number of hours f(x) Greg took to make pudding after he had made it x times.

Then the function is written as,

=>  f(x) = 2(0.8)ˣ

While we plot the function on the graph then we get the graph like the following.

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The two step equation for the scenario that your cousin is in where they pay for their textbooks is:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks would be $30.

The total amount paid by your cousin in order to be able to cover a book for their 7 classes and the fee for art class is $ 230.

Assuming that the cost of each book from his 7 classes is denoted as x, then the expression would be:

= 7 x number of classes

= 7x

This amount is then added to the cost of the art class which is $ 20 so it becomes:

= 7x + 20

The two step equation is therefore:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks is:

x = (230 - 20) / 7

x = $ 30

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The probability of getting at least 6 oranges in a bag of 10 fruits is the sum of probability of getting 6 oranges, probability of getting 7 oranges, probability of getting 8 oranges, probability of getting 9 oranges and probability of getting 10 oranges.

We can use the binomial probability formula to calculate the probability of getting at least 6 oranges in a bag of 10 fruits, which is:

P(X >= 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Where X is the number of oranges in the bag, and the probability of getting an orange is p and the probability of getting an apple is (1-p)

Now, since we don't know the proportion of oranges to apples in the bin, we can't find p. However, we can use the cumulative binomial distribution function to find the probability of getting 6 or more oranges in a bag of 10 fruits.

The cumulative binomial distribution function is the probability of getting r or less successes in n trials, where a success is getting an orange and a failure is getting an apple.

So

P(X >= 6) = 1 - P(X <= 5)

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Answer:

I don't know if it is true

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

Explanation:

Let z be adjacent to angle y, and angle z is inside the triangle on the right.

Adding up the inside angles of any triangle always gets us to 180 degrees.

We'll use this fact to find z.

z+30+50 = 180

z+80 = 180

z = 180-80

z = 100

Angle y and angle z are supplementary angles. They form a straight line of 180 degrees.

So,

y+z = 180

y+100 = 180

y = 180-100

y = 80

--------------

We can follow the same steps as in the previous section to determine that angle x is 110 degrees.

A shortcut is to use the Remote Interior Angle Theorem.

This theorem says that adding two interior angles will get us the exterior angle that isn't adjacent to either interior angle mentioned.

Notice for instance that angle x is not adjacent to the bottom-left 30 degree angle nor is it adjacent to angle y.

Furthermore, you could use the Remote Interior Angle Theorem to determine the measure of angle y. Note how y = 30+50 = 80. This time the "30" we focus on here is inside the triangle on the right.

For Palanzios' Pizzeria and Guido’s Pizza to cost the same, the number of toppings needed is 2.

Let's begin by assigning a letter to represent our unknown:

   x = Number of toppings to be added to each pizza

Now,

Based on the Given information :

Expressions for the cost of each pizza with its toppings:

   Palanxio's Pizza:  6.80 + 0.90x

   Guido's Pizza:      7.30 + 0.65x

Now,

Equating the costs of both pizzas and solve for our unknown (x):

   ⇒ 6.80 + 0.90x = 7.30 + 0.65x

  ⇒ 0.90x - 0.65x = 7.30 - 6.80

   ⇒ 0.25x = 0.50

   ⇒ x = 0.50/0.25

   ⇒ x = 2

Therefore, There are 02 toppings to be added to each pizza.

Finally, we can verify our answer by putting the values back into our equation :

   6.80 + 0.90x = 7.30 + 0.65x    

   6.80 + 0.90(2) = 7.30 + 0.65(2)

   6.80 + 1.80 = 7.30 + 1.30

                       = $8.60        [both costs are the same]

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The probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards is 0.050

Since, a deck of cards contain 52 cards,

So, we have the value of sample space = n(S)=52

Consider the following values

A=in first draw there is a face card but

B= in the second draw there is a face card

[tex]$$\begin{aligned}& E=\{\boldsymbol{\bullet} J, \bullet J, \boldsymbol{\bullet} J, \boldsymbol{\wedge} J, \bullet Q, \bullet Q, \bullet Q, \wedge Q, \bullet \mathrm{K}, \bullet \mathrm{K}, \boldsymbol{\bullet} \mathrm{K}, \boldsymbol{\wedge} \mathrm{K}\} \\& n(E)=12\end{aligned}$$[/tex]

The probability in the first draw is a face card will be

P(A)=(12/52)

The Probability in the second draw there is also a face card will be

(B/A)=(11/52)

Now, from the formula for P(A and B),

We will get it as:

[tex]$$P(A \cap B)=P(A) \times P\left(\frac{B}{A}\right)$$[/tex]

Therefore,

[tex]P(A \cap B) & =\frac{12}{52} \times \frac{11}{51}[/tex]

=(132/2652) = 0.052

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