A rectangular box has a square base. Its height is half the width of the base. Find a function that models its volume v in terms of its width w.

Alto earned $200 while Sheryl earned $300 over the summer.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider x represent the amount of money earned by Alto and y represent the amount of money earned by Sheryl

Together they earned a total of $500.

Hence the system of equations for the situation

x + y = 500 (1)

Sheryl earned $100 more than Alto:

y = x + 100

-x + y = 100(2)

Using Substitution to solve the system.

Solving equations 1 and 2 simultaneously gives:

x = 200 , y = 300

Therefore Alto earned $200 while Sheryl earned $300 over the summer.

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Answer:

[tex]\textsf{1)\quad 48\;inches}[/tex]

[tex]\textsf{2)\quad$2\sqrt[3]{3}$\; inches}[/tex]

Step-by-step explanation:

Define the variables:

The rate of vibration of a string under constant tension varies inversely with the length of the string:

[tex]\boxed{y \propto \dfrac{1}{x} \implies y=\dfrac{k}{x}\quad\text{for a constant $k$}}[/tex]

Given values:

Substitute the given values of x and y into the formula and solve for k:

[tex]\implies 128=\dfrac{k}{24}[/tex]

[tex]\implies k=128 \cdot 24[/tex]

[tex]\implies k=3072[/tex]

Therefore, the equation is:

[tex]y=\dfrac{3072}{x}[/tex]

To find the length of a string that vibrates 64 times per second, substitute y = 64 into the equation and solve for x:

[tex]\implies 64=\dfrac{3072}{x}[/tex]

[tex]\implies x=\dfrac{3072}{64}[/tex]

[tex]\implies x=48[/tex]

Therefore, the length of a string that vibrates 64 times per second is 48 inches.

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

Define the variables:

The horsepower that a shaft can safely transmit varies jointly with its speed and the cube of the diameter:

[tex]\boxed{y \propto vd^3 \implies y=kvd^3\quad\text{for a constant $k$}}[/tex]

Given values:

Substitute the given values of y, v and d into the formula and solve for k:

[tex]\implies 45=k \cdot 100 \cdot 3^3[/tex]

[tex]\implies 45=k \cdot 100 \cdot 27[/tex]

[tex]\implies 45=2700k[/tex]

[tex]\implies k=\dfrac{45}{2700}=\dfrac{1}{60}[/tex]

Therefore, the equation is:

[tex]y=\dfrac{vd^3}{60}[/tex]

To find the diameter of the shaft in order to transmit 60 hp at 150 rpm, substitute y = 60 and v = 150 into the equation and solve for d:

[tex]\implies 60=\dfrac{150d^3}{60}[/tex]

[tex]\implies 3600=150d^3[/tex]

[tex]\implies d^3=\dfrac{3600}{150}[/tex]

[tex]\implies d^3=24[/tex]

[tex]\implies d=\sqrt[3]{24}[/tex]

[tex]\implies d=\sqrt[3]{8 \cdot 3}[/tex]

[tex]\implies d=\sqrt[3]{8} \sqrt[3]{3}[/tex]

[tex]\implies d=\sqrt[3]{2^3} \cdot \sqrt[3]{3}[/tex]

[tex]\implies d=2\sqrt[3]{3}[/tex]

Therefore, the diameter of a shaft that transmits 60 hp at 150 rpm is 2³√3 inches.

the mean absolute deviation is 4.24

Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. Similar to standard deviation, MAD is a parameter or statistic that measures the spread, or variation, in your data.

the given mean absolute deviation 5,11,2,7,16

mean = [tex]\frac{5+11+2+7+16}{5}[/tex]

mean = 8.2

Hence, the mean absolute deviation is given by:

[tex]M_{d}[/tex] = |5-8.2| + |11-8.2| +|2-8.2| +|7-8.2|+|16-8.2| / 5

     = 4.24

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With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).

A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).

A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.

Given in the question:

n = 46

x = 8.90

σ = 6

α = 0.95

As we know that:

[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]

putting the values we get,

  8.90 ± Z (0.95/2) ×6/√46

Now, considering the positive sign, we get,

=  8.90 + 3.52

= 12.42

Now considering the negative sign,

8.90 ± Z (0.95/2) ×6/√46

= 8.90 - 3.52

= 5.38

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The number of child ticket were sold on Wednesday is 236

The cost of child admission ticket = $6.10

The cost of adult admission ticket = $9.20

Consider the number of child ticket as x and the number of adult ticket as y

Twice times as many adult tickets as child tickets were sold

y = 2x

Then the equation will be

x + y = 707.70

Substitute the value of y in the equation

x + 2x = 707.70

Add the like terms

3x = 707.70

x = 707.70/3

Divide the terms

x = 235.9

x ≈ 236

Therefore, 236 child ticket were sold on that day

I have answered the question in general, as the given question is incomplete

The complete question is:

At the movie theatre, child admission is $6.10 and adult admission is $9.20 . On Wednesday, twice times as many adult tickets as child tickets were sold, for a total sales of $707.70 . How many child tickets were sold that day?

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Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer: 2

Step-by-step explanation:

solve in parentesis than divide by 0.5 or 1/2 then 2^3= 4 so

that minus 4 equals 2

Answer:

A Acute angle (Give me pointssss)

Step-by-step explanation:

Its right bc im smart

Answer:

1. y=5

2. y=2x-1

3.y=-2x+1

4. y=-(1/2x)+1

Step-by-step explanation:

1. y=y-intercept. y=5.

2. 2x=mx=slope. -1=b=y-intercept

3. 2x=mx=slope. 1=b=y-intercept

4. -(1/2x)=mx=slope. 1=b=y-intercept

-Hope this helped

The path  LORAN followed is hyperbolic.

The equation of the hyperbola is x²/8100 + y²/1900 = 1

Given,

These are the coordinates:

(x, y) = (-100, 0)  (100, 0)

The hyperbola's center; (h, k) = (0, 0)

The following is the distance between the center and the focal points:

c = 100

Square both sides;

c² = 10000

The following is the distance between the transmitters and the receiver:

2a = 180

Divide 2 from both sides.

a = 90

Square both sides;

a² = 8100

We possess;

b² = c² - a²

This results in;

b² = 10000 - 8100

b² = 1900

A hyperbola's equation is as follows:

(x - h)²/a²  + (y - k)²/b² = 1

We thus have:

(x - 0)²/8100 + (y - 0)²/1900 = 1

x²/8100 + y²/1900 = 1

As a result, the hyperbola's equation is: x²/8100 + y²/1900 = 1

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Answer:

4p³z - 14z +13

Step-by-step explanation:

(5p³z -9z +9) - (p³z +5z -4)

the - multiplies the bracket

5p³z -9z +9 -p³z -5z +4

collect like terms

5p³z -p³z -9z -5z +9+4

4p³z - 14z +13

Qualitative data is used to represents the qualities , intention of human behavior and is basically based on observations and interview using open ended questions where as quantitative data is based on the statistical and mathematical data.

Explanation:

Difference between Quantitative and Qualitative data sources:

Qualitative data sources:

Quantitative data sources:

Therefore, qualitative data is used to represent the human behavior while quantitative data is for statistical and mathematical data.

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To compare result to hypothesis, we will start by providing the key result from the each model and then compare and contrast them.

A hypothesis is usually a prediction based on some evidence. Hypothesis must be tested and once tested they can be supported by evidence if a statement is made that cannot be tested or disproof then it is not hypothesis

To compare we will start by providing the key result from the each model and then compare and contrast them then you can then provide any interpretation or future direction to some of the comparison

To prove or disprove your hypothesis you need to be able to do an experiment and take that measurement or make observation to see how two things are related

If you have hypothesis is not supported by the result of the experiment you should really realize the data in order to figure out why your result disprove your hypothesis

You should not alter the observation or experiment so that you reserve proof your hypothesis

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In four digits number, if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.

In the given question, we have to find the value of underlined 5 in four digit numbers.

As we know that,

Place value labels like tens and ones notify us of a number appear digit's value. More than one digit can be used to create a number. As a result, to better understand the value of each digit, we employ place value labels such as ones, tens, hundreds, and thousands.

As we know that we count the numbers as ones, tens, hundreds and so on.

So if a 4 digit number is given and we have to find the value of underline 5, and then if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.

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Answer:

Step-by-step explanation:

39.06

The length of cable that is needed for the initial rise is; 41 feet.

The given parameters are as shown in the image of the triangle attached.

Where;

A = 28 , a = 25 ft, and b = 20 ft.

Now, if A is acute and a > b, it means that one solution exists. Using the

Law of Sines to find B;

a/sin A = b/sin B

Plugging in the relevant values gives;

25/sin 28 = 20/sin B

sin B = (20 sin 28)/25

sin B = 0.3756

B = sin⁻¹0.3756

B = 22.06°

Due to the fact that the two angles are now known, it means that the angle opposite x is 180 – (28 + 22.06 ) = 129.94 . Using the Law of Sines to find x;

a/sin A = x/sin X

25/sin 28 = = x/sin 129.94

solving fir x gives;

x = 40.83 ≈ 41 feet

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Initial and terminal points of the vector [tex]\vec{PQ}[/tex] of (3., 3) and (5, 7) , and the initial and final point of the vector [tex]\vec{RS}[/tex] of (4, -5), and (1, -5), indicate that  the the difference between the vectors is; 5·i + 5·j

A vector is a quantity that has both magnitude and direction.

The specified vectors are;

The initial and terminal point on vector [tex]\vec{PQ}[/tex] are; (3, 3) and (5, 7)
The initial and terminal point of vector  [tex]\vec{RS}[/tex] are  (4, -6), and (1, -5)

Therefore, the vector  [tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] is therefore;

The vector form of [tex]\vec{PQ}[/tex] = <5 - 3, 7 - 3> = <2, 4>

The vecror form of    [tex]\vec{RS}[/tex]  = <1-4, -5 - (-6)> = <-3, -1>

The difference  between the vectors is therefore;

The vectors are therefore;

[tex]\vec{PQ}[/tex] = 2·i + 4·j

[tex]\vec{RS}[/tex] = -3·i - j

The difference between the vectors is therefore;

[tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] = (2 - (-3))·i + (4 - (-1))·j = 5·i + 5·j

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According to the model, the kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.

From the question, we are to drag and drop the correct numbers to complete the given sentence.

The given sentence is

According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.

From the given information,

The equation that fits the model is

w = 0.45n + 0.12

By comparing with the slope-intercept form a line,

y = mx + c

Where m is the slope

and c is the y-intercept

m = 0.45

and c = 0.12

This means the kitten gained approximately 0.45 kilogram every month and the initial weight of the kitten is 0.12 kilogram

Hence,

The kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.

Here is the complete question:

Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.

She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.

Drag and drop the correct numbers below to complete the sentence.

According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.

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The parallelism of the linear equations of two lines is clearly shown by the fact that both have the same slope. Due to the fact that they both have a slope of -2, they are parallel.

An equation is said to be linear if the maximum power of the variable is consistently 1.

Another name for it is a one-degree equation.

A linear equation with one variable has the conventional form Ax + B = 0.

In this case, the variables x and A are variables, while B is a constant.

So, there is a degree of 1 in these equations.

Knowing the lines' equation:

ab: 6x + 3y = 9

cd: 4x + 2y = 8

Afterward, write in slope-intercept form as follows:

ab: y = -2x + 3

cd = y = -2x +8

It is evident that both lines have the same slope, demonstrating their parallelism.

Therefore, the parallelism of the linear equations of two lines is clearly shown by the fact that both have the same slope. Due to the fact that they both have a slope of -2, they are parallel.

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Distributional semantics develops methods for measuring and classifying semantic similarity between language elements.

To quantify and classify semantic relatedness among linguistic items based on their distributional qualities in large samples of language data, distributional semantics is a field of study. The distributional hypothesis captures the fundamental principle of distributional semantics.

The semantic theory of language usage, states that terms used and occurring in comparable situations tend to have similar meanings is the basis for the distributional hypothesis in linguistics. For instance, the words "fire" and "dog" have very different meanings and aren't typically used together in a sentence. However, the terms "dog" and "cat" are occasionally used interchangeably, suggesting that they may have a similar connotation.

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He will practice 40 m on piano if he spends 64 m practicing on guitar. It can be solve by the concept of word problems on multiplication of fraction.

What is fraction?

Fraction is a part of a whole number or quantity. It is written as 3/8, 4/9, etc.

Piano practice time = 5 m

Guitar practice time = 8 m

If he spend 8 minute practicing on guitar then he will spend on piano practice = 5 m

If he spend 1 minute practicing on guitar then he will spend on piano practice = 5m/8m

If he spend 64 minute practicing on guitar then he will spend on piano practice

[tex]=\frac{5m}{8m}64m\\=40 m[/tex]

Hence, he will practice 40 m on piano if he spends 64 m practicing on guitar. It can be solve by the concept of word problems on multiplication of fraction.

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The largest area is found to be 8702.5 [tex]ft^{2}[/tex].

We know that area of rectangle

A = xy ........ (1)

Perimeter of rectangle (given) = 590 ft

Using x and y as two variables ;

5x + 2y = 590

solve yb in term of x

y = -5/2 x + 295......(2)

Now we will get area only in one variable from (1) and (2)

A = x ((-5/2)x + 295)

A = -5/2 [tex]x^{2}[/tex] + 295x

differentiate it with respect gto x

A' = -5x + 295........ (3)

find the critical point to get your minima and maxima value.

Put A' = 0,  x = 295/5 = 59

x = 59

then , from (2)

y= (-5/2 × 59) + 295 = 147.5

y = 147.5

again differentiate (3)

A'' = -5 < 0. i.e critical point x = 59 is point of maxima.

So, maximum area = 59 × 147.5

Largest area = 8702.5 [tex]ft^{2}[/tex]

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Answer: the last two situations

Step-by-step explanation:

there would be 0 students left in a school after 6 pm and the temperature in degrees fahrenheit has to be above 0 because it is a hot day and the oven is on

There are 72% percent of the seats had people sitting on them.

What are ratios and percentages?

A ratio is a comparison of two quantities that are similar. Given any two similar quantities a and b, so a:b ratio is defined as a:b = a/b, where b0. The percentage is an abbreviation for 'by the hundred' or 'divide by one hundred.' The percentage, which means 'per 100,' is also used to compare quantities.

Given data:

Ratio of adults to children = 7 : 2

The proportion of children that had sit in the stalls = 4/5

Number of children that had sit in the Circle = 124 children

Number of seats at the theatre = 3,875

Let x represent the number of children, we have;

The number of children in the stalls = (4/5).x

Then the number of children in the circle = x - (4/5).x = 124

Solving this, we get

          x = 620

Given ratio is Number of adults/Number of children = 7:2

                    Number of adults/620 = 7/2

      So the number of adults = 2,170

Total number of peoples = 2170 + 620 = 2790

The percentage of the seats had people sitting on them

                                                                                                 [tex]=\frac{2790}{3875}\times100\\\\=72\%[/tex]

Hence, 72% percent of the seats had people sitting on them.

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Answer: 11 turkey burgers

Step-by-step explanation:

1/4 = 0.25
2.93 ÷ 0.25 = 11.72
You can't have a partial burger, so round down
He can make 11 turkey burgers

Answer:

12 burgers

Step-by-step explanation:

i just did this, you round up from the fraction you get

Answer:

a = -5/4

Step-by-step explanation:

There are too many steps, it would take an hour to list it all....

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

are you sure this is correct tho?

Step-by-step explanation:

Answer: 4.278695 × 10^7

Step-by-step explanation:

Answer: 4.2786950x10^7 or 4.2x10^7

Step-by-step explanation:

To convert a number to scientific notation, move the decimal.

42,786,950

At the and of this number, there is an understood decimal. To find the scientific notation version of it, move the decimal over to the left until you have only one digit to the left of the decimal, as such...

4.2786950

To then find what the exponent you're multiplying by, you count how many places you moved the decimal.

So in the end, you get 4.2786950x10^7

Answer:

Step-by-step explanation its is 0.72

i hoped this helped

a) The area to the left of 25 is 0.63056

b) The area to the left of 16 is 0.12167

c) The area to the right of 22 is 0.56618

d) The area to the right of 28 is  0.20233

e) The area between 16 and 30 is  0.75666

Given,

The mean of the distribution = 23

Standard deviation  = 6

We have to find the following areas

(a) Entering the values

(b) Entering the values

(c) Entering the values

(d) Entering the value

(e) Entering the values

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The equations used to compare the two scenarios are as follows:

3.65x

300 + 1.35x

Identifying which variables values result in equality is part of solving a variable equation. The variables for which the equation must be solved are known as unknowns, whereas the unknown values that fulfill the equality are known as equation solutions. A mathematical expression with two equal sides separated by an equal sign is known as an equation. 4 + 6 = 10. We can see 4 + 6 on the left and 10 on the right side of the equal symbol.

We already have,

1) You often purchase a grande cafe latte from Starbucks, which costs $3.65.

This formula is:

Number of days = x

Total cost after x days = 3.65x

2) You spend $300 on an espresso machine and ingredients for lattes, which cost an extra $1.35 per day.

This formula is:

Number of days = x

Total cost after x days = 300 + 1.35x

Now, three days later,

3.65 x 3 = $10.95

300 + 1.35 x 3 = 300 + 4.05 = $304.05

Thus,

The equations used to compare the two scenarios are as follows:

3.65x

300 + 1.35x

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