Which equation is the correct translation of the following statement?

Four less than a number is nine.

4 - x = 9
9 - 4 = x
9 - x = 4
x - 4 = 9

Answer: The hook would be 2.2 inches (approximately) above the top of the frame

Step-by-step explanation: Please refer to the picture attached for further details.

The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (longest side) and AB and BC are the other two sides

5^2 = 4.5^2 + BC^2

25 = 20.25 + BC^2

Subtract 20.25 from both sides of the equation

4.75 = BC^2

Add the square root sign to both sides of the equation

2.1794 = BC

Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches

To find the distance above the frame for hanging, use the Pythagorean theorem by considering the diagonal created by the ribbon. The hook needs to be approximately 5.39 inches above the top of the frame.

To find how far above the top of the frame the hook needs to be, we need to consider the diagonal of the frame created by the ribbon. Using the Pythagorean theorem, we can calculate this distance.

Therefore, the hook needs to be approximately 5.39 inches above the top of the frame.

Answer:

Step-by-step explanation:

1 1/5

Answer:

5/18

Step-by-step explanation:

There is a 1/3 chance of going to k. From K, there is a 1/2 chance of going to b, so that way has a prob of 1/6. By the same concept, there is a 1/9 chance of going to B via J. The prob you are asking for is 5/18

Answer:

4 cm

Step-by-step explanation:

It's just what cubed is 64. The answer is 4 by the way since

4*4*4=16*4=64

The height (or length of one side) of the cube is 4 cm.

To find the cube's height, we need to use the formula for the volume of a cube.

The volume of a cube is given by the formula:

V = s³, where V is the volume and s is the length of one side of the cube.

In this case, we are given that the volume of the cube is 64 cubic cm. So, we can set up the equation:

64 = s³

To find the height (or length of one side), we need to take the cube root of both sides of the equation:

∛64 = ∛(s³)

Taking the cube root of 64, we get:

∛64 = 4

Therefore, the height (or length of one side) of the cube is 4 cm.

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Answer:

12

Step-by-step explanation:

X^2 = (7+9)(9) -->

X^2 = 16(9) -->

X = 12

Answer:

  p = (-1/5000)x +11

Step-by-step explanation:

We are given two points (x, p) as (5000, 10) and (15000, 8). Using the two-point form of the equation of a line, we can find the equation to be ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . 2-point form

  p = (8 -10)/(15000 -5000)(x -5000) +10

  p = -2/10000(x -5000) +10

  p = -x/5000 +11 . . . . . linear demand function

Final answer:

A student asked how to find the demand function for a baseball team's ticket prices based on attendance. By finding the slope between two given points and using the point-slope form, the demand function is determined to be p = $11 - 0.0002x.

Explanation:

To find the demand function that relates the price p of baseball tickets to the average attendance x, we can use the two given points (x, p) = (5,000, $10) and (15,000, $8) and assume the relationship is linear. We can express the demand function as p = mx + b, where m is the slope and b is the y-intercept.

First, find the slope m:

m = (p2 - p1) / (x2 - x1)

m = ($8 - $10) / (15,000 - 5,000)

m = -$2 / 10,000 = -0.0002

Next, we'll use the slope and one of the points to find b, the y-intercept. Plugging into the point-slope form:

p - p1 = m(x - x1)

$10 - p = -0.0002(5,000 - x)

$10 - p = -1 + 0.0002x

p = $11 - 0.0002x

The demand function is p = $11 - 0.0002x.

Answer:

200\cdot25-84\cdot\frac{91}{12-65}\cdot\frac{8412}{1.000}-2000000\cdot46512

Step-by-step explanation:=−9.30227818×1010

Answer:

8 square units

Step-by-step explanation:

Draw vertical and horizontal lines, dividing the triangle into 9 equally sized smaller triangles.  4 of the smaller triangles are shaded, so the area of the square is 4/9 the area of the triangle.

A = 4/9 (½ (6)(6))

A = 8

Step-by-step explanation:

Putting value of x

Y = 1/2 ( - 4) - 6

Y = - 2 - 6

Y = - 8

( - 4, - 8)

Answer:

  x^2 +y^2 -8x +4y +11 = 0

Step-by-step explanation:

The center of the given circle is located at (x, y) = (4, -2). Its radius is 3.

You know this because the center is halfway between the vertical and horizontal extremes, and the radius is half the difference of those extremes. You can determine this by counting squares, or "by eye," or by working with the coordinates of the extreme points.

For example, the horizontal extremes are (1, -2) and (7, -2). The diameter is the difference of the x-values: 7 -1 = 6, so the radius is 6/2 = 3. The x-coordinate of the center is (1+7)/2 = 4.

__

The standard form of the equation of a circle is ...

  (x -h)^2 + (y -k)^2 = r^2

where (h, k) is the center, and r is the radius.

For this circle with center (4, -2) and radius 3, the standard form equation is ...

  (x -4)^2 + (y +2)^2 = 9

General form has the parentheses removed and the polynomial written in descending powers of the variables:

  x^2 -8x +16 +y^2 +4y +4 = 9

  x^2 +y^2 -8x +4y +11 = 0

Answer:

x(12-3)

Step-by-step explanation:

The expression given is equal to 9x. The only given answer equivalent to 9x is the last one, x(12-3).

Answer:

$651.46‬

Step-by-step explanation:

$596.95 * 9.25% = 55.21

$596.25 + 55.21 =651.46‬

Answer: A

Step-by-step explanation: Because you have a dot in the middle and it is very equal

Answer: the distribution is symmetrical.

Step-by-step explanation:

Answer:

The original number was 54.5.

Step-by-step explanation:

If a number is increased by 2.8%, then it is 102.8% of it's original number.

In mathematics, "of" in virtually all cases means "multiplied by".

Therefore, we do the opposite:

1. Convert to a decimal.

102.8% = 1.028

2. Divide by the decimal.

[tex]56 \div 1.028 = 54.47[/tex]

3. Round it to the nearest tenth.

54.47 rounds to 54.5.

To find the original number when increased by 2.8%, we set up and solve an equation. The original number to the nearest tenth is approximately 54.4.

To find the original number, we can set up the equation:

x + 0.028x = 56

Simplifying gives:

1.028x = 56

Dividing both sides by 1.028 gives:

x = 56 / 1.028 ≈ 54.41

So, the original number to the nearest tenth is approximately 54.4.

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Answer:

50

Step-by-step explanation:

Hope this helped

:)

Answer:

(-2y+5x) / (3x - 2y)

Step-by-step explanation:

If we write this sentence, we have:

((-2/x) + (5/y)) / ((3/y) - (2/x))

If we do LCM in the denominators of each fraction, we have:

((-2y+5x)/xy) / ((3x - 2y)/xy)

We can cut the 'xy' in the numerator and denominator of the whole fraction:

(-2y+5x) / (3x - 2y)

The final expression we have is (-2y+5x) / (3x - 2y)

Answer:

a

Step-by-step explanation:

(-2y+5x) / (3x-2y)

Answer:

6 yards.

Step-by-step explanation:

You can find this answer by using the Pythagorean theorem. Because c in the equation will always stand for the hypotenuse, the longest side, it's easier to fill in the blanks with the stuff given to you.

In this case, 1.1^2 + a^2 = 6.1^2

If you simplify, the answer should be 6 yards.

Answer:

12 minutes !

Step-by-step explanation:

Hope this helps!!

Answer:

12 minutes

Step-by-step explanation:

3 x 4 = 12

Answer:

where are the answer choices?

Step-by-step explanation:

Answer:

It is 3^-4

Step-by-step explanation:

-6+2=-4

Answer:

the answer is 4

Step-by-step explanation:

if my calculations are right

Answer:

=>9.4966×10^2

Step-by-step explanation:

9.22×103

=>949.66

in standard form

=>9.4966×10^2

Answer:

Jenna earned 1330 in first two weeks working at the coffee stand.

Step-by-step explanation:

Given:

Amount earned in 1 week = 557

Amount earned in next week =773

We need to find the amount earned in 2 weeks.

Solution:

Now we know that;

Amount earned in 2 weeks is equal to sum of Amount earned in 1st week and Amount earned in next week.

framing in equation form we get;

Amount earned in 2 weeks = [tex]557+773 = 1330[/tex]

Hence Jenna earned 1330 in first two weeks working at the coffee stand.

Answer:

I'm just answering for no reason.

Step-by-step explanation:

No reason.

Answer:

Step-by-step explanation:

hello :

the system is : 6x+2y=46

                       3x+y=23

if you multiply the second equation by : 2 you have 6x+2y =46(same  first equation )

conclusion : the system have infinity solutions ( graphically same line)

conclusion :

Answer:

[tex]\frac{169\pi }{180}[/tex]

Step-by-step explanation:

To convert from degree measure to radian measure

radian = degree × [tex]\frac{\pi }{180}[/tex], thus

radian measure = 169 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{169\pi }{180}[/tex]

Answer:

Expression:

[tex]\frac{9}{8}+(-\frac{1}{2})=\frac{5}{8}[/tex]

Step-by-step explanation:

We are given that

Bryce traveled distance from his home=[tex]\frac{9}{8}miles[/tex]

Bryce traveled distance back=[tex]\frac{1}{2}miles[/tex]

We have to find the expression and then simplify.

According to question

Total distance traveled by Bryce

=[tex]\frac{9}{8}+(-\frac{1}{2})[/tex]

This is required expression.

Total distance traveled by Bryce=[tex]\frac{9-4}{8}=\frac{5}{8}miles[/tex]

Hence, the total distance traveled by Bryce from his home=[tex]\frac{5}{8}miles[/tex]

Final answer:

To find the total distance Bryce walked, we add 9/8 miles to 1/2 mile, which equals 13/8 miles or simplified to 1 5/8 miles.

Explanation:

Bryce initially walks 9/8 miles from home. On his way back, he walks 1/2 mile before meeting up with his friend Mya. To describe this situation with an expression and simplify it, we add these distances together:

Total distance walked = 9/8 miles + 1/2 mile

To simplify, find a common denominator (which in this case is 8), and then add the numerators:

Total distance walked = (9/8) + (4/8)

Total distance walked = (9 + 4) / 8

Total distance walked = 13/8

Total distance walked = 1 5/8 miles

This is the sum describing the distance Bryce walked before meeting Mya, which simplifies to 1 and 5/8 miles.

Answer:

The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]

Step-by-step explanation:

The standard form of the equation of an ellipse with center (0 , 0) is

[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex] , where

∵ The ellipse is centered at the origin

∴ The center of it is (0 , 0)

∵ It has foci at (± 8 , 0)

- The coordinates of the foci are (± c , 0)

∴ c = ±8

∵ It has Vertices at (± 17 , 0)

- The coordinates of the vertices are (± a , 0)

∴ a = ±17

∵ c² = a² - b²

- Substitute the values of c and a to find b

∴ (8)² = (17)² - b²

∴ 64 = 289 - b²

- Add b² to both sides

∴ b² + 64 = 289

- Subtract 64 from both sides

∴ b² = 225

- Take √  for both sides

∴ b = ± 15

∵ The equation of the ellipse is [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]

- Substitute the values of a and b in it

∴ [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex] ⇒ [tex]\frac{x^{2}}{289}+\frac{y^{2}}{225}=1[/tex]  

∴ The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]

The standard form equation for this ellipse is (x²/17²) + (y²/15²) = 1.

To find the equation of an ellipse centered at the origin with foci at (±8,0) and vertices at (±17,0), we need to follow these steps:

Determine the values of 'a' and 'c': The vertices give us the value of 'a', which is the distance from the center to a vertex. Here, a = 17.

The foci give us the value of 'c', which is the distance from the center to a focus. Here, c = 8.

Using the relationship c² = a² - b², we can calculate 'b'.

c² = a² - b²

8² = 17² - b²

64 = 289 - b²

b² = 225

b = 15

So, the standard form of the equation of the ellipse is: (x²/17²) + (y²/15²) = 1

Answer:

You played 4 games

Step-by-step explanation:

You start with $18 and subtract 6 from the entry fee. Then, you divide the 12 you got from that and divide it by 3

Final answer:

To determine the number of games played, subtract the access fee from the total cost and then divide by the per-game price. In this case, the student paid for an access fee of $6, and played 4 games at $3 each to reach a total cost of $18.

Explanation:

The question posed is a basic algebra problem involving a fixed entry fee and a variable cost per game. The given information states that the access fee is $6 and the per-unit price, which in this case is the cost per game, is $3. If the total amount paid was $18, the number of games played can be calculated.

To solve, let's denote the number of games played as x. The total cost is made up of a fixed access fee plus the cost of the games played. The expression for the total cost is thus $6 (access fee) + $3x (cost of games).

The equation based on the total amount paid would be:

6 + 3x = 18

To find the value of x, we subtract the access fee from the total amount paid:

18 - 6 = 3x

That simplifies to:

12 = 3x

Which can then be solved by dividing both sides by 3:

x = 12 / 3

x = 4

The student thus played 4 games.

Answer:

26 %

Step-by-step explanation:

you just go from 80 and count backwards all the way to 56 and count how many spaces or tally's that was and then you got your answer.

Answer:

95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].

Step-by-step explanation:

We are given that the weights, in pounds, of a sample of 13 adult female golden retriever dogs :

59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                         P.Q. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean weight =  [tex]\frac{\sum X }{n}[/tex]  = 54.9 pounds

            s = sample standard deviation =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]  = 3.12 pounds

           n = sample of female = 13

           [tex]\mu[/tex] = population mean weight

Here for constructing 95% confidence interval we have used One-sample t test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.179 < [tex]t_1_2[/tex] < 2.179) = 0.95  {As the critical value of t at 12 degree

                                          of freedom are -2.179 & 2.179 with P = 2.5%}  

P(-2.179 < [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.179) = 0.95

P( [tex]-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X -\mu}[/tex] < [tex]2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] =  [tex]\bar X \pm 2.179 \times {\frac{s}{\sqrt{n} } }[/tex]

                                             = [ [tex]54.9 - 2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] , [tex]54.9 +2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] ]

                                             = [53.01 pounds , 56.78 pounds]

Therefore, 95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].