A homeowner is designing a rectangular pool for her backyard. Due to the size of the yard, the width of the pool will be one-third its length, and the pool will have a uniform depth of 5 feet. Which of the following equations can be used to describe l, the length of the pool, in terms of its volume, V?

Answer:

9800Joules

Step by step Explanations

Before we can set the integral up, let the upper half the aquarium be divided into horizontal slices for easy calculation

Then we will represent distance from the top of the tank as X and also

2 its thickness as ∆x

We will be working on the horizontal slices , since in the horizontal slices each drop of water in a given slice will be have the same distance from the top of the tank.

Given that An aquarium has;

Length = 8 m long,

Width = 1 m wide,

Dept =1 m deep

And ∆x m,

density of water is 1000 kg/m3

g = 9.8 m/s2

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

x = 20

Step-by-step explanation:

3x - 10 = x + 30

2x = 40

x = 20

Answer:

if he wants to have $400000 on gis bank in 30 years at 4 %rate then he needs to deposit $15151.5 per month

Answer:

The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.

Step-by-step explanation:

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]

In this question:

[tex]p = 0.75, n = 30[/tex]

So

[tex]\mu = 0.75, s = \sqrt{\frac{0.75*0.25}{30}} = 0.0791[/tex]

The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.

Answer: x<69

Step-by-step explanation:

For this problem, we solve is just as we would if it was an equal sign.

x+9<78       [subtract 9 on both sides]

x<69

Answer:

2b + 3t = 60

Step-by-step explanation:

2b is the number of wheels on a bicycle

3t is the number of wheels on a tricycle

and 60 is the total number of wheels

Answer:

[tex]Salary = Rs23000[/tex]

Step-by-step explanation:

Given

[tex]Shopping = \frac{1}{5}[/tex]

[tex]Sister = \frac{2}{5}R[/tex]

[tex]Left over = Rs11,040[/tex]

Required

Her salary in that month

Given that she spent [tex]\frac{1}{5}[/tex] of her salary on shopping, this implies that she has [tex]\frac{4}{5}[/tex] of her salary left

From what's left, she gave her sister [tex]\frac{2}{5}[/tex]

This means she gave her sister [tex]\frac{2}{5} * \frac{4}{5}[/tex]

Sister = [tex]\frac{8}{25}[/tex]

Calculating a fraction of what's left

[tex]Left over = 1 -Shopping - Sister[/tex]

[tex]Left over = 1 - \frac{1}{5}- \frac{8}{25}[/tex]

[tex]Left over = \frac{25 - 5 - 8}{25}[/tex]

[tex]Left over = \frac{12}{25}[/tex]

Recall that she has Rs11,040

This means that

[tex]\frac{12}{25} of Salary = Rs11,040[/tex]

Multiply both sides by [tex]\frac{25}{12}[/tex]

[tex]\frac{12}{25} * \frac{25}{12} * Salary = Rs11,040 * \frac{25}{12}[/tex]

[tex]Salary = Rs11,040 * \frac{25}{12}[/tex]

[tex]Salary = \frac{Rs276000}{12}[/tex]

[tex]Salary = Rs23000[/tex]

Hence, her salary for that month was Rs23000

Answer:

Her salary = Rs 23000

Step-by-step explanation:

In a month, Ezhil spent 1/5 of her salary on shopping.

Let

Her salary = a

she spent 1/5 of a on shopping

Amount spent on shopping = 1a/5

She gave 2/5 of the remaining to her sister .

The remaining money = a - 1a/5 = 5a - a/5 = 4a/5

She gave 2/5 of 4a/5 to her sister. Therefore,

The amount she gave to her sister = 2/5 × 4a/5 = 8a/25

Out of her salary she is left with Rs 11040 .Therefore,

a - 1a/5 - 8a/25 = 11040

25a - 5a - 8a/25 = 11040

12a/25 = 11040

12a = 11040 × 25

12a = 276000

divide both sides by 12

a = 276000/12

a = 23000

Her salary = Rs 23000

Answer: d) 23

Step-by-step explanation:

Consider matrix [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]. The determinant is: ad - bc

In the matrix given, a = 5, b = -1, c = 3, d = 4

det A = ad - bc

        = 5(4) - 3(-1)

        = 20 - (-3)

        = 20 + 3

        = 23

Answer:

99 robberies

Step-by-step explanation:

What you are basically doing is taking the discount.

1 + 14% = 1.14

113 / 1.14 = 99.12

Answer:

brittany is 42

Step-by-step explanation:

if he is 40 years older than her and the sum of there ages is 82

82-40 = 42

Answer:

the answer is A

Step-by-step explanation:

Answer:

Correct answer is A

Step-by-step explanation:

Hope this helps you

Answer:

The answer is "[tex]\bold{\frac{(m-1)(m-2)}{(m-n)}}[/tex]"

Step-by-step explanation:

Given:

[tex]\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\[/tex]

let,  ? = x then,

[tex]\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\[/tex]

[tex]\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\[/tex]

Answer:

This line can be represented by the line y = 3/4x + 2.

Step-by-step explanation:

The slope is identified as the m in y = mx + b. The slope is the rise/run of your line (AKA how many units it goes upwards/downwards and then goes to the right/left to meet the second given point).

In this case, the line rises 3 units from 2 to 5, and then goes to the right by 4 units to meet the coordinate (4, 5).

B in the equation refers to the y-intercept, or where the line intersects/crosses the y-axis. In this case, it is the coordinate (0, 2).

Finally, x is irrelevant and is placed in the equation for no reason (at least that I am aware of in my several years of high school math).

Therefore, your final equation is y = 3/4x + 2.

Answer:

Width (x) = 160ft

See explanation below

Step-by-step explanation:

The information given is incomplete as we are not told if the shape of the pond. This is about determining the surface area of a water body.

Looking at the question, we can tell we are to find the width of a pond whose shape wasn't given.

Assuming the shape of the pond is either a rectangular or square pond, let's consider the following question:

The acreage of a rectangular pond is 1.54 acres and the length is 420ft. The width of the pond shown is x ft. What is the value of x.

Find attached the diagram used for solving the question.

Formula for calculating the acreage of

a Square or Rectangular Ponds is multiplying average length (in feet) times average width (in feet) and dividing the result by 43,560 to derive our answer in acres.

That is: Average Length (ft) × Average Width (ft) ÷ 43,560 = Acres

Since we have been given acreage and length, we would make width subject of formula.

Width = (Acreage × 43500)/length

Width (x) = (1.54 × 43,560)/420

=67082.4 ÷ 420 = 159.72

Width (x) = 160ft (nearest feet)

Answer:

the answer would be (4b)/(a^4)

Step-by-step explanation:

Answer:

4.35 rounded to the nearest hundredth

4.3 rounded to the nearest tenth

4 rounded to the nearest whole number.

Step-by-step explanation:

[tex]8\frac{1}{6}[/tex] ÷ [tex]1 \frac{7}{8}[/tex] =

[tex]\frac{49}6}[/tex] ÷ [tex]\frac{15}{8} =[/tex]

[tex]\frac{49}{6} *\frac{8}{15} =[/tex]

[tex]\frac{392}{90} =[/tex]

[tex]4 \frac{32}{90} =[/tex]

[tex]4\frac{16}{45}[/tex] ≈ 4.35

Answer:

  8 minutes

Step-by-step explanation:

Let t represent the time for one mile. We are told the ratio of minutes to miles is constant, so we have the proportion ...

  time / distance = t/(1 mi) = (208 min)/(26 mi)

Multiplying both sides of the equation by (1 mi), we have ...

  t = (208/26) min = 8 min

Geri's average pace was 8 minutes to run 1 mile.

Answer:

The score that separates the lower 5% of the class from the rest of the class is 55.6.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 73, \sigma = 10.6[/tex]

Find the score that separates the lower 5% of the class from the rest of the class.

This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

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

[tex]-1.645 = \frac{X - 73}{10.6}[/tex]

[tex]X - 73 = -1.645*10.6[/tex]

[tex]X = 55.6[/tex]

The score that separates the lower 5% of the class from the rest of the class is 55.6.

Answer:

Yes. There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.

P-value = 0.00013.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

The significance level is 0.05.

The sample 1 (Group 1), of size n1=145 has a proportion of p1=0.124.

[tex]p_1=X_1/n_1=18/145=0.124[/tex]

The sample 2 (Group 2), of size n2=355 has a proportion of p2=0.037.

[tex]p_2=X_2/n_2=13/355=0.037[/tex]

The difference between proportions is (p1-p2)=0.088.

[tex]p_d=p_1-p_2=0.124-0.037=0.088[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{18+13.135}{145+355}=\dfrac{31}{500}=0.062[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.062*0.938}{145}+\dfrac{0.062*0.938}{355}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0.001}=0.024[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.088-0}{0.024}=\dfrac{0.088}{0.024}=3.68[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=P(z>3.68)=0.00013[/tex]

As the P-value (0.00013) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.

Answer:

Step-by-step explanation:

  This particular permutation  deals with words that have repeated letters.

Given word = "ONGOING"

the formula for the permutation is

[tex]= \frac{n!}{mA! mB!.....mZ!}[/tex]

where   n   is the amount of letters in the word, and  m A , m B , ... , m Z  are the occurrences of repeated letters in the word. Each   m  equals the amount of times the letter appears in the word.

So in the word  "ONGOING"

n= 7

mO= 2

mN= 2

mG=2

[tex]permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}[/tex]

[tex]permutations= \frac{52920}{8} \\permutation = 6,615[/tex]

Answer:

80 g

Step-by-step explanation:

mass of sanitizer = 400 g

percentage of alcohol = 24%

mass of alcohol in the sanitizer = 24% of 400 g = 0.24 x 400 = 96 g

this means that the mass of other chemicals = 400 - 96 = 304 g

If alcohol content is increased to 30% by removing more of the other chemicals, then mass of alcohol will still remain 96 g

this means that 96 g becomes 30% of the resulting hand sanitizer, we write mathematically as

96 g = 30% of y

where y is the new mass of the sanitizer

96 = 0.3y

y = 96/0.3 = 320 g

The remaining mass of other chemicals  = 320 - 96 = 224 g

the total mass of other chemical lost is

304 - 224 = 80 g

25.

Look at this:

There are 5 digits in 46987.

There will be 5 combinations.

5 times 5 = 25.

You have your answer.

A total of 31 possible combinations are there for number 46987.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a 5 - digit number 46987.

Assume that there are [y] possible combinations. For a [x] digit number, the total possible combinations are -

y = 2ˣ - 1

So, for [x] = 5, we will have -

y = 32 - 1

y = 31

Therefore, a total of 31 possible combinations are there for number 46987.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

cosФ = 0.97

sinФ = 0.292

tanФ = -4

Step-by-step explanation:

A general point P(x,y) with an angle Ф has the following trigonometrical functions:

[tex]sin\phi=\frac{y}{r}\\\\cos\phi=\frac{x}{r}\\\\tan\phi=\frac{y}{x}\\\\r=\sqrt{(x)^2+(y)^2}[/tex]

For the point P(-1 , 4) you obtain:

[tex]r=\sqrt{(-1)^2+(4)^2}=\sqrt{17}\approx 4.123[/tex]

[tex]sin\phi=\frac{4}{4.123}=0.97\\\\cos\phi=\frac{-1}{4.123}=0.242\\\\tan\phi=\frac{4}{-1}=-4[/tex]

The 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.

Given information:

An artist bought 5 yards of rope.

We know that one yard is equal to 3 feet.

So, here it is required to find the equivalent of 5 yards in the form of feet.

The value of 5 yards in the form of feet can be calculated as,

[tex]5\times 3=15\rm\;feet[/tex]

Therefore, the 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.

For more details, refer to the link:

https://brainly.com/question/22316471

Answer:

b

Step-by-step explanation:

Answer:

2.5

Round this up to 3

Step-by-step explanation:

Add all the numbers of the graph together

1+4+3+2 = 10

Divide by 4 because it has 4 categories in total

= 2.5

Round up because its asking for puppets and theres not 1/2 of a puppet.

Answer:

22cm

See explanation below

Step by step explanation:

The question is incomplete without the diagram of the shape or its dimensions.

From the question, we are to determine the perimeter of the circle.

Let's consider the following question by determining the perimeter of a circle. If diameter is 7cm. Use pi as 3.14.

Perimeter of circle = circumference of circle

circumference of circle = 2πr

Radius = diameter/2 = (7/2)cm

circumference of circle = 2πr

= 2×π×(7/2) = (14/2)×3.14

= 7×3.14

=21.98cm

circumference of circle = 22cm (nearest tenth)

Perimeter of circle = 22cm

Answer:

The value of a is -1.

Step-by-step explanation:

The line of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

For a quadratic function in standard form, [tex]y=ax^2+bx+c[/tex], the line of symmetry is a vertical line given by [tex]x=-\frac{b}{2a}[/tex].

We know that the quadratic equation, [tex]y=ax^2+8x-3[/tex], has x = 4 as line of symmetry. Therefore, the value of a is:

                                                         [tex]4=-\frac{8}{2a}\\\\4=-\frac{4}{a}\\\\4a=-4\\\\a=-1[/tex]

Answer:

a=-1

Step-by-step explanation:

so that the other person could get brainliest

Answer:

x = 3

area = 6

Step-by-step explanation:

using phytagoras's. theorem

a² + b² = c² (with c is the longest one)

x² + (x+1)² = 5²

x² + x² + 2x + 1 = 25

2x² + 2x - 24 = 0 (divide all by 2)

x² + x -12 = 0 then factorize

(x-3)(x+4) = 0

we get x = 3 and x = -4. Take the positive one.

so now we have x = 3 then x + 1 must be 4.

the area is

A = ½ . 3 . 4 = 6

Answer: i am pretty sure it is C dont get your hopes up but

Step-by-step explanation:

from what i see if you take the y=3 over 2 and make that a decimal you can now take y = that number and make a line and so on then after that step you want to now take your final answer which is x and subtract it by 3 i MIGHT be wrong but i tried.

Answer:

The Answer is C I hope this helped

Step-by-step explanation:

I did it on my quiz!

Answer:

14×7=98

188-98=90 so she had 90 left