Paul purchased a new fish tank, represented by the diagram below.
The height, h, of the tank is 3 feet, and the width, w, is 6 feet longer than the length, l. The volume of the tank (V=lwh) is 60 ft^3.
Write an equation that could be used to calculate the length of the tank.
Determine the exact length of the tank in simplest radical form.

Answer:

15 square units

Step-by-step explanation:

If you were to cut off the bottom triangle (separated by the dotted line), and put it on top of the other triangle, you would get a rectangle.

All you have to do is length x height

5 x 3 = 15

Answer:

Option B, 105 would be correct

Step-by-step explanation:

The Vertical Angles Theorem states that angles that are opposite diagonally are congruent, therefore; ? = 105°

Hope this helps!

Answer:

Sin(a)= [tex]\frac{z}{x}[/tex]

Hope this helps!

Answer:

1/4

Step-by-step explanation:

For this, think of dividing 3/4 into 3 parts, each of them being 1/3 of the original amount.

With this, it would be 1/4, as 1/4 + 1/4 + 1/4 = 3/4.

Answer:

you language is i don't know

Step-by-step explanation:

for now I did

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

Work Shown:

L = theta*r

L = (5pi/4)*1

L = 5pi/4

L = 3.92699081698724 approximately

L = 3.927 units

The formula above only works if theta is in radians.

If the angle is in degrees, then you need to convert using the rule

y = (pi/180)*x

where x is the angle in degrees and y is the equivalent angle measure in radians.

In the fourth step, I used my calculator to get that value. You could use pi = 3.14, but in this case, your teacher wants you to use the stored value of pi found in the calculator.

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

Extra info (optional section):

If you're curious why that formula works, then consider a circle with circumference C = 2*pi*r. This is the distance around the circle, aka the perimeter.

The arc length in red is only a fractional portion of the full perimeter. Specifically, that fractional amount is theta/2pi. We multiply this fraction by the full perimeter and simplify

L = arc length

L = (full circle circumference)*(fractional amount)

L = (2*pi*r)*(theta/2pi)

L = theta*r

The "2pi" terms cancel in the last step. Again, this formula only works if theta is in radians. This is due to the fractional portion theta/2pi.

There is an equivalent formula for theta being in degrees, which is

L = (theta/360)*2*pi*r

but this version is a bit messier in my opinion.

Answer:3.927

Step-by-step explanation:

Answer:

The standard error of the sample proportion is 0.0993.

The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

73% of voters support it.

This means that [tex]p = 0.73[/tex]

Sample of 20 voters

This means that [tex]n = 20[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.73[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.73*0.27}{20}} = 0.0993[/tex]

The standard error of the sample proportion is 0.0993.

The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is

12/20 = 0.6, so this is the p-value of Z when X = 0.6.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.6 - 0.73}{0.0993}[/tex]

[tex]Z = -1.31[/tex]

[tex]Z = -1.31[/tex] has a p-value of 0.0951.

So

The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.

The standard error of the sample proportion is 0.0098.

The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951

Given that,

Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it.

You randomly ask 20 Greensboro voters whether they support the bond referendum.

We have to determine,

The standard error of the sample proportion is.

The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is .

According to the question,

There is a school bond referendum in Greensboro, and 73% of voters support it.

20 Greensboro voters whether they support the bond referendum.

[tex]standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}[/tex]

Where, p = 73% = 0.73

And n = 20

Therefore,

[tex]Standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}\\\\ Standard \ deviation = \sqrt{\dfrac{0.73(1-0.73)}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.73\times 0.27}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.19}{20}}\\\\Standard \ deviation = 0.0098[/tex]

The standard error of the sample proportion is 0.0098.

[tex]\dfrac{12}{20 }= 0.6[/tex]

 This is the p-value of Z when X = 0.6.

Therefore,

[tex]Z = \dfrac{X-\mu}{\sigma}\\\\Z = \dfrac{0.6-0.73}{0.993}\\\\Z = -1.31\\\\[/tex]

Z = -1.31 has a p-value of 0.0951.

Hence, The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.

To know more about Probability click the link given below.

https://brainly.com/question/24248147

Answer:

A(2,2) _scale factor ½--(1,1)

B(4,6)_scale factor ½--(2,3)

C(6,2)_scale factor ½--(3,1)

is a required coordinate

Scale factor=1/2

Apply and get new coordinates

Answer:

A = $3,526.50

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = [tex]\frac{R}{100}[/tex]

r = [tex]\frac{3.5}{100}[/tex]

r = 0.035 rate per year,

Then solve the equation for A

A = P(1 + [tex]\frac{r}{n}[/tex])nt

A = 2,500.00(1 + [tex]\frac{0.035}{1}[/tex])(1)(10)

A = 2,500.00(1 + 0.035)(10)

A = $3,526.50

Hence:

The total amount of over 10 years is $3,526.50.

Answer: - $6.75

Step-by-step explanation:

Answer:

[tex](g\ o\ f)=-20x+10[/tex]

Step-by-step explanation:

One is given the following functions:

f(x) =5x + 2

g(x) = 4x + 2

One is asked to find the following:

[tex](g\ o\ f)(x)[/tex]

One can rewrite this operation as the following:

g(f(x))

In essence, one substitutes in function (g) in place of the parameter (x), and solves to find the new function formed.

[tex]g(f(x))\\\\=g(-5x+2)\\\\=4(-5x+2)+2[/tex]

Simplify, distribute, multiply every term in the parenthesis by the term outside of it, then simplify,

[tex]=-20x+8+2\\\\=-20x+10[/tex]

Answer:

answer is B

Step-by-step explanation:

got it right on edge :)

9 × 8 = 8 × 9 equation is true

Answer:

Step-by-step explanation:

W = 2L + 3, and:

P = 2W + 2L = 192

Substituting 2L + 3 for W, we get:

P = 2(2L + 3) + 2L = 192, or

4L + 6 + 2L = 192, or:

6L = 186

L = 186/6 = 31

The length is 31, the width is 62 + 3, or 65

Therefore, the perimeter P is P = 2(31) + 2(65) = 130 + 62  = 192 (OK!)

Answer:

I can help you via Watsapp

Answer:

Is it C. 50

Step-by-step explanation:

Answer:

Easy is 15 bc 15 and 10 are in a 5 equal to 5 x 2 10 and you take the 5 away from the 50 and so its 15 trust

Step-by-step explanation:

Answer:

53.76 cm3

Step-By-Step Explanation

Answer:

x = 1    or   x = -5   or   x = 10

Step-by-step explanation:

f(x) = x³ – 6x² – 45x + 50 = (x² + 4x -5) (x - 10) = (x - 1) (x + 5) (x - 10)

(x - 1) (x + 5) (x - 10) = 0

x = 1    or   x = -5   or   x = 10

Answer:

72

Step-by-step explanation:

6x4=24x3=72

Answer:

B

Step-by-step explanation:

MOVE TO THE RIGHT 9 TIMES!!

Answer:

x < 26

Step-by-step explanation:

Given the following algebraic expression;

x - 30 < -4

To find the value of x in its simplest form;

First of all, we would have to rearrange the algebraic expression to make the variable on one side and the integer on the other side;

Simplifying an expression simply means to collect like terms that are having the same variables or constants and combining them, so as to reduce the expression to the lowest possible value.

x < -4 + 30

x < 26

Answer:

You are t subtract both 28,176.44-$1500

Step-by-step explanation:

right after that the answer you get for subtraction you go ahead and use it to subtract with 34,083.30

Answer:

672 meters squared

Step-by-step explanation:

Area of Triangle: b*h*1/2

The isosceles triangle's height, splits the base in half.

Answer:

672

Step-by-step explanation:

Area of a triangle = [tex]\frac{bh}{2}[/tex]

where b = base length and h = height

In the triangle shown, we are only given the base length

This means that we must find the height in order to find the area.

We can do this by using the Pythagorean theorem

[tex]a^2+b^2=c^2[/tex]

where a and b = legs and c = hypotenuse

Two right triangles are formed within the isosceles triangle.

Each has a hypotenuse of 50 m, a base length of 28/2=14m ( because they are sharing the base length ) and they are both sharing the height.

So we are given the hypotenuse and a leg and we need to find the other leg

So we plug in what we are given and solve for the missing side length

[tex]50^2=a^2+14^2\\50^2=2500\\14^2=196\\2500=a^2+196[/tex]

step 1 subtract 196 from each side

2500 - 196 = 2304

196 - 196 cancels out

we now have 2304 = a²

step 2 take the square root of each side

[tex]\sqrt{a^2} =a\\\sqrt{2304} =48[/tex]

we're left with a = 48

This means that the height of the isosceles triangle is 48m

Now we can find the area.

Using the formula stated previous....

[tex]A=\frac{28*48}{2} \\28*48=1344\\\frac{1344}{2} =672[/tex]

Hence, the area is 672m²

Answer:

d

Step-by-step explanation:

Answer:

24°

Step-by-step explanation:

The sum of all interior angles of a triangle always equal to 180°.

There are two givens in the problem. Set up the equation by equaling 180 to the two given angles and the unknown.

[tex]180 = 102 + 54 + x\\180 = 156 + x\\[/tex]

Isolate x by subtracting 156 to both sides.

[tex]180 - 156 = 156 - 156 + x\\x= 180-156\\x=24\\[/tex]

Answer:

14

Step-by-step explanation:

Answer:

14 flashes.

Step-by-step explanation:

1 minute = 60 seconds

x minutes = 45 seconds.

1/x = 60/45                           Cross multiply

60x = 45                               Divide by 60

x = 45/60

x = .75

10 1/2 minutes = 10.5 minutes.

x flashes / 10.5 minutes = 1 flash / 0.75 minutes   Multiply by 10.5

x = 10.5/0.75

x = 14