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3 years ago

14

A rectangular garden has a total area of 48 sq yards. Draw and label two possible rectangular gardens with different side length

s that have the same area.

1 answer:

Pie3 years ago

6 0

6yd
8yd a =48sq yd (6×8=48)

4yd
12yd a=48sq yd (4×12=48)

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a veterinary researcher takes an srs of 60 horses presenting with colic whose average age is 12 years. the average age of all ho

Ghella [55]

Answer:

The value 10 years is the population mean

Step-by-step explanation:

A sample consists of some observations drawn from the population, so a part or a subset of the population which in this case is the number of horses with colic.

A sample mean is the mean of the statistical samples while a population mean is the mean of the total population.

Thus, in this case, the sample mean is the mean age of the horses with colic while the population mean age is the mean age of all the horses found at the clinic.

Therefore, the mean age of 10 of the horses seen at the clinic would be the population mean.

4 0

3 years ago

Find an equation of the circle that satisfies the given conditions.

hodyreva [135]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \\
x_1=-1 \\ y_1=1 \\ \\ Q(5,9) \\ x_2=5 \\ y_2=9 \\ \\
\frac{x_1+x_2}{2}=\frac{-1+5}{2}=\frac{4}{2}=2 \\ \frac{y_1+y_2}{2}=\frac{1+9}{2}=\frac{10}{2}=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(-1,1) \\ x_1=-1 \\ y_1=1 \\ \\ (2,5) \\ x_2=2 \\ y_2=5 \\ \\ d=\sqrt{(2-(-1))^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \\
\boxed{(x-2)^2+(y-5)^2=25}$

4 0

3 years ago

What is the interval notation for x+1>34?

vodka [1.7K]

Explanation:

<u><em>First you subtract by -1 both sides of an equation.</em></u>

<u><em> $x+1-1=34-1$ </em></u>

<u><em>Then, simplify the number.</em></u>

<u><em>34-1=33</em></u>

<u><em>x>33</em></u>

<u><em>Or interval notation 33,∞ </em></u>

<u><em>Final answer: → x>33 and 33,∞</em></u>

<u><em>Hope this helps!</em></u>

<u><em>Thanks!</em></u>

8 0

3 years ago

Jane, Scott, and Frank have a total of $144 in their wallets. Frank has 4 times what Jane has. Scott has $6 less than Jane. How

konstantin123 [22]

Answer:

Jane have $25

Frank have $100

Scott have $19

Step-by-step explanation:

To find the amount that each have, we have to represent this information in a mathematical format and then solve

let x represent represent the amount that Jane has

let Y represent represent the amount that Frank has

let z represent represent the amount that Scott has

From the question given, "Jane, Scott, and Frank have a total of $144" can be represented mathematically as

x + y + z = $144 ---------------------------------------------------------------------------------(1)

"Frank has 4 times what Jane has" can be represented mathematically as

y = 4x ---------------------------------------------------------------------------------------------(2)

"Scott has $6 less than Jane" can be represented mathematically as

z= x- 6 ----------------------------------------------------------------------------------------------(3)

we can now solve the equations using the substitution method

substitute equation (2) and (3) into equation (1)

x + y + z = $144

x + 4x + x-6 = $144

6x -6 = $144

add 6 to both-side of the equation

6x - 6 + 6 = $144 + 6

6x =$150

Divide both-side of the equation by 6

6x/6 = 150/6

x = $25

from equation 2

y = 4x

substitute x= $25 in equation (2)

y = 4 (25)

y = $100

substitute x=$25 in equation (3)

z = x- 6

z = 25 - 6

z=$19

Jane have $25

Frank have $100

Scott have $19

6 0

3 years ago

1500/semiannual period for 6 years at 2.5%/year compounded semiannually

kari74 [83]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1500\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannual, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500\left(1+\frac{0.025}{2}\right)^{2\cdot 6}\implies A=1500(1.0125)^{12}\implies A\approx 1741.13$

6 0

3 years ago