A 12m by 12m square garden has a 1m wide path through the centre, parallel to one side of the square. calculate the area of the garden left for planting.​

Answer:

11.2 cm

Step-by-step explanation:

The missing side = the hypotenuse

Apply pythagorean theorem to find he hypotenuse which is given as:

c² = a² + b³

a = 10 cm

b = 5 cm

c = Hypotenuse (missing side)

(Hypotenuse)² = 10² + 5² = 125

Hypotenuse = √125

Hypotenuse = 11.1803399 ≈ 11.2 cm (nearest tenth)

Answer:

horizontal asymptote at y = 0

Step-by-step explanation:

According to the definition of asymptotes, it is a line that the function gets closer and closer to as x goes to plus or minus infinity. The definition clearly does not mention anything about the finite value of x.

However, crossing of asymptotes does not happen in the case of vertical asymptotes because for a given x, the function has only one value but the same y can be obtained for different values of x.

It is a common misconception that graphs of functions can’t cross the asymptotes. This is true only for vertical asymptotes. In fact, there are several examples of functions whose graphs cross the horizontal asymptote. For example:

f(x) = (xe)^((-x)^2)

The horizontal asymptote of the above function is y=0 but it still crosses the x axis at x=0.

hope that helps, I really don't know thought. Quite tricky

Answer:

980 students are freshmen.

Step-by-step explanation:

2800*.35=980

Answer:

area = 138 m²

Step-by-step explanation:

radius of large circle = 12 m

radius of small circle = 10 m

large circle area = πr² = (3.14)(12²) = 452.16 m²

small circle area = πr² = (3.14)(10²) =314 m²

452.16 - 314 = 138.16 m²

Answer:

B) (1/2, -8)

Step-by-step explanation:

(1, -6) and (0, -10)

Midpoint formula:

((x1+x2)/2, (y1+y2)/2)

Solving for x:

(x1+x2)/2

(1 + 0)/2

1/2

Solving for y:

(y1+y2)/2

(-6-10)/2

(-16)/2

-8

Step-by-step explanation:

subtract the whole equation by 85 on both sides to get v by itself on the left side

85-85-v=213-85

-v=128

Now we divide the whole equation by negative 1

-1v/-1=128/-1

v=-128

Hope that helps :)

Answer:

sdfsefsesfsfsefsefsefsefsfsefesef

Step-by-step explanation:

Answer:

$6.50/gallon

Step-by-step explanation:

22.75 / 3.5 = $6.50/gallon

I will try i had this unit last year, basically the diameter is 5 in this problem, which you multiply by pi (in this case I will use 3.14 as the shortened version since its on-going) which gives you 15.7, then you multiply that by 3 in this problem to get 47.1!

Answer:

Step-by-step explanation:

Volume of a cylinder formula = πr^2h

r (radius) = 5/2 = 2.5

h (height) = 3

Answer: 3π(2.5)^2 = 3π(6.25) = 18.75π cubic units

Answer:

Step-by-step explanation:

[tex]\text{To maximize -4x + 5y + 70 subject to } \\ \\ 2x + y \le 8 --- (1) \\ \\ x + 3y \ge 5 --- (2) \\ \\ x + y \le 6----(3) \\ \\ x \ge 0, y \ge 0[/tex]

[tex]\text{From above equationn (1)} : 2x + y = 8 \\ \\ \text{Divide boths sides by 8} \\ \\ \dfrac{2x}{8} + \dfrac{y}{8} = \dfrac{8}{8}[/tex]

[tex]\dfrac{x}{4} + \dfrac{y}{8} = 1 \\ \\ x = 4; y = 8[/tex]

[tex]\text{From above equationn (2)} : x + 3y = 5 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{5} + \dfrac{3y}{5} = \dfrac{5}{5} \\ \\ x = 5; \ y = 1.66[/tex]

[tex]\text{From above equation (3)} : x + y = 6 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{6} + \dfrac{y}{6} = \dfrac{6}{6} \\ \\ x = 6; \ y = 6[/tex]

[tex]\text{From the image attached below, we can see the representation in the graph}[/tex]

-   [tex]\text{Now from equation (1) ad (III)} \\ \\ 2x + y = 8 \\ \\ x+y = 6[/tex]

    [tex]x[/tex]      [tex]= 2[/tex]

[tex]From : x + y = 6 \\ \\ 2 + y = 6 \\ \\ y = 6-2 \\ \\ y =4[/tex]

[tex]\text{From equation (1) and (II) } \\ \\ \ \ 2x + y = 8 \\ - \\ \ \ x + 3y = 5 \\ \\[/tex]

[tex]-5y = -2 \\ \\ y = \dfrac{2}{5} \ o r\ 0.4 \\ \\ From : 2x+ y = 8 \\ \\ 2x = 8 - \dfrac{2}{5} \\ \\ x = \dfrac{ 8 - \dfrac{2}{5} }{2} \\ \\ x = 3.8[/tex]

Answer:

is your answer

0.00483091

Step-by-step explanation:

Answer:

Step-by-step explanation:

let X be free stickers

let y be number of T-shirts bought

TABLE

X       Y (PUT THIS IN THE BLUE PLACE)

2        1

4         2

6        3

8        4

10       5 (don't have to put this in)

Answer:

i think x= 13.5

Step-by-step explanation:

Answer:

a) y=4

b) x=8

Step-by-step explanation:

we know the a line is on point 4 on the y axis. So it would be y=4

The second one is the same. line b is on the point 8 on the x axis, so x=8

Answer:

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Put the equation into vertex form.

y = 2x² + 10x + 8

= 2(x² + 5x) + 8

= 2(x² + 5x + 2.5²) - 2·2.5² + 8

= 2(x+2.5)² - 4.5

vertex (-2.5, -4.5)

Answer: where is the trapezoid

Step-by-step explanation:

Answer:

The temperature went up by 29 degrees.

Step-by-step explanation:

Since -24 is negative,

Add 5 to 24 = 29.

Answer:

We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.

Step-by-step explanation:

Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.

This means that the null hypothesis is: [tex]H_0: \mu = 12[/tex]

The production group believes that the mean weight has changed.

This means that the alternate hypothesis is:

[tex]H_a: \mu \neq 12[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:

This means that [tex]\mu = 12[/tex]

They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.

This means, respectibely, that [tex]n = 15, X = 12.05, \sigma = 0.08[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{12.05 - 12}{\frac{0.08}{\sqrt{15}}}[/tex]

[tex]z = 2.42[/tex]

Pvalue of the test:

We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.

Looking at the z-table, z = 2.42 has a pvalue of 0.9922

1 - 0.9922 = 0.0078

2*0.0078 = 0.0156

What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?

0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.

The answer is (2x+6)(3x-1)

Answer:4

Step-by-step explanation: Since she did it by completing the square, then you must do the same thing to get the same form so you can see what that number is.

So first subtract the constant which is -12 so we need to add twelve to get the constant on the other side. So we now have 2x^2+16x=12

The constant of the x^2 must be 1 so we need to divide by 2 on every term to get x^2+8x=12

So to make it so to get a perfect factor we need to divide the x factor by 2 so we get 4.

So the answer is 4 cause it is a perfect factor so were going to get 4 on both factors.

Answer:

4

Step-by-step explanation:

x²+2(x)(?)+?²=22

multiply by 2 because the coefficient of the higher degree in the first equation is 2

2x²+2(2(x)(?))+2(?²)-2(22)=0

2x²+4x(?)+2?²-44=0

Comparison

4x(?)=16x

?=4

2?²-44=-12

So, 2?²=-12+44

2?²=32

?²=16

?=4

Answer:

$6.20

Step-by-step explanation:

5.75 * 2.40= 13.80

20-13.80= 6.20

$6.20

Answer: 4 and 1/4

Step-by-step explanation:

1st question is 4-- count the points that fall above the line

2nd question is 2 out of 8, or 1 out of 4

there are only 2 players who played at least 17 matches AND scored about 5000. There are 8 players who played at LEAST 17 matches

Answers:

1. 4

2. ¼

Explanations:

1. the question is asking how many players were awarded more points than the prediction of the line of best fit (trend line), which can be translated to how many dots are above the line on the graph. 4 dots can be counted above the line

2. 8 players played at least 17 tournaments. of these 8 players, only 2 scored more than 5000 ranking points.

thus, to find the probability, we take 2 ÷ 8 = ¼

i hope this helps! :D

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

2.5 mg

Step-by-step explanation:

Given the data:

23 24 23 29 28 26 27 28 26

The sample standard deviation, s

s = sqrt[Σ(x - mean)²] ÷ (n - 1)

Mean, m = ΣX / n

n = 9

Mean = 234 /9 = 26

Using a calculator :

s = 2.236

The margin of error, MOE

MOE = Tcritical * s/sqrt(n)

Tcritical at df = (n-1) = 9-1 = 8 , α = 0.01 = 3.35536

MOE = 3.35536 * 2.236/sqrt(9)

MOE = 3.35536 * 2.236/3

MOE = 3.35536 * 0.7453333

MOE = 2.50086

MOE = 2.5

Answer:

c=$60/3.  $20 dollars per class.

Step-by-step explanation:

Answer:

17 degrees

Step-by-step explanation:

-23 + 6 = 17

Answer:

x = 35 degrees

Step-by-step explanation:

supplementary angles = 180 degrees

m<A + m<B = 180

(2x - 5) + 3x = 180

5x - 5 = 180

5x = 175

x = 35