PLEASE HELP!!!!

Sixteen more than twice a number is the same as 24 less than 4 times the same number. What is the number?

Answer:

\(\huge\boxed{\sf 3599}\)

Step-by-step explanation:

= 61 × 59

You can write 61 = 60 + 1 and 59 = 60 - 1

Hence,

= ( 60 + 1 ) ( 60 - 1 )

According to the formula:

\((a+b)(a-b) = a^2-b^2\)

= (60)² - (1)²

= 3600 - 1

= 3599

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

it was dilated by 1/2 so:

choice 3) (x,y) -> (0.5x, 0.5y)

Step-by-step explanation:

Answer:

It's C (x,y) --> (0.5x, 0.5y)

Step-by-step explanation:

ABCD are the original and A'B'C'D" is the dilation

Point A is (4,10) and Point A' is (2,5) so the dilation is .5

The smaller percent change of push-ups is on Monday with 50%

On Monday, the change in pushups is:

(30 - 20)/20 = 10/20 = 1/2

This represents (1/2) * 100 = 50 percent

On Friday, the change in pushups is:

(40 - 25)/25 = 15/25 = 3/5

This represents (3/5) * 100 = 60 percent

Monday is 50%

Friday is 60%

Therefore, the smaller percent change occured on Monday, with 50 percent

Answer: To find the number of flowers needed to surround a circular garden with a 100-ft radius, we need to first find the circumference of the garden, which is the distance around the circle. We can use the formula:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

So, for a garden with a 100-ft radius, we have:

C = 2πr

C = 2 × 3.14 × 100

C = 628 feet (rounded to the nearest foot)

Step-by-step explanation: Number of flowers = Circumference / Spacing

Number of flowers = 628 feet / (1/3) feet

Number of flowers = 1884 (rounded to the nearest whole number)

Therefore, we need approximately 1884 flowers spaced every 4 inches to surround a circular garden with a 100-ft radius.

Answer:

7/15

Step-by-step explanation:

2/3 of those means 2/3 of the 7/10 books sold by the used book store

2/3 of 7/10 means 2/3 * 7/10 = 14/30 = 7/15

Hope this helps :)

Have a nice day!

The probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

To calculate the probability that he gets exactly one rose given that at least one of the flowers he gets is pink, we need to use conditional probability. Let R be the event that he gets a rose and P be the event that he gets a pink flower. Then, we want to find P(R=1 | P≥1).

Using Bayes' theorem, we have:

P(R=1 | P≥1) = P(R=1 and P≥1) / P(P≥1)

We can calculate the probability of getting at least one pink flower as:

P(P≥1) = 1 - P(P=0)

Assuming the probabilities of getting a rose and a pink flower are independent, we can calculate the probabilities of getting exactly one rose and at least one pink flower as:

P(R=1 and P≥1) = P(R=1) * P(P≥1) = (2/5) * (1 - 3/5) = 2/5 * 2/5 = 4/25

P(P=0) = 3/5, since there are 3 flowers that are not pink out of a total of 5.

Therefore, we have:

P(R=1 | P≥1) = (4/25) / (1 - 3/5) = 4/7

So the probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

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Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)

Answer:

A=130

Step-by-step explanation:

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

I think its neither because

Step-by-step explanation:

Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel. Perpendicular lines are a bit more complicated.

Answer:

perpendicular

Step-by-step explanation:

They form a 90 degree angle because one is vertical and the other is horizontal.

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Answer:

After 3 hours.

Step-by-step explanation:

60 + 30x = y

40x = y

Beach Shack:

60, 90, 120, 150, 180, 210

Surf Shop:

40, 80, 120, 160, 200

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Based on the information given, it should be noted that the mean and standard deviation of Y will be 0.72 and 0.8485 respectively.

Calculating the mean:

Based on the information given, it should be noted that the probability distribution for y will be:

Y                   0        1.         2          3             4

Probability 0.58.   0.23.   0.11      0.05      0.03

The mean of Y will be:

Y= (0 × 0.58) + (1 × 0.23) + (2 × 0.11)+(3×0.05)+(4×0.03)

Y= 0 + 0.23 + 0.22+0.15+0.12

Y= 0.72

The variance will be 0.72 Therefore, the standard deviation will be:

sd= ✓0.72

sd= 0.8485

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Answer:

12

Hope this helps! -xox

We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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Step-by-step explanation:

Amount they will earn=Principal+Interest

Interest=$1200×0.12×7=$1008

Amount=$(1200+1008)=$2208

To find the differential of f(x,y) at the point (1,3), we need to compute its partial derivatives with respect to x and y at that point, and then combine them with the differentials of x and y using the formula:

df = (∂f/∂x) dx + (∂f/∂y) dy

where df is the differential of f, dx and dy are small changes in x and y, and (∂f/∂x) and (∂f/∂y) are the partial derivatives of f with respect to x and y, respectively.

∂f/∂x = \((1/2) (x^2 + y^3)^(-1/2) * 2x = x / \sqrt{ (x^2 + y^3)}\)

∂f/∂y = \((1/2) (x^2 + y^3)^{-1/2} * 3y^2 = (3y^2) / (2 \sqrt{(x^2 + y^3))\)

Now, we can plug in the values x = 1, y = 3 to get the partial derivatives at the point (1,3):

∂f/∂x (1,3) = 1/10

∂f/∂y (1,3) = \((27/10)\sqrt{10}\)

we have df = (∂f/∂x) dx + (∂f/∂y) dy = \((1/10) dx + (27/10)\sqrt{10}dy\)

Note that we didn't specify the values of dx and dy, as they represent small changes in x and y around the point (1,3). The differential df represents the corresponding small change in f around that point.

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Using the relationship between the degree and radian. Then the equivalent of \(\rm sin^{-1} (-0.4)\) is 5.87 radians.

The equivalent is the functions that are in different forms but are equal to the same value.

Given

The expression is \(\rm sin ^{-1}(-0.4)\).

Then the angle will be

\(\rm sin^{-1} (-0.4) = -23.58\\\\sin^{-1} (-0.4) = -23.58 + 360\\\\sin^{-1} (-0.4) = 336.42\)

The angle 336.42 is in degrees.

Conversion of degree into radian.

\(\begin{aligned}\rm 1 degree &= \dfrac{2\pi}{360}\\\\336.42\rm \ degrees &= \dfrac{\pi}{180}*336.42 \\\\336.42 \rm \ degrees &= 5.87\end{aligned}\)

Thus, The equivalent of \(\rm sin^{-1} (-0.4)\) is 5.87 radians.

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Answer:

use the line segment instead

Step-by-step explanation:

2x+3>4x-8

or, 3+8>4x-2x

or, 11>2x

or, 11/2 > x

or, x < 11/2

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

oh no that's tough bro

hope you get through

Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

Answer:

20sqrt2, or aprox 28.3

Step-by-step explanation:

It is a 45-45-90 triangle, meaning that the ratio of the sides is x-x-xsqrt2.

In this case, x=20. So, HK = 20sqrt2.

Answer:

4(152-x)

Step-by-step explanation: