A rectangle hasan area of 100 square yards and a perimeter of 58 yds. What is the length of the longer side of the rectangle?

Mate's car can travel 1 minute farther per gallons of gas than Jenna's car.

We know that Mate's car gets 30 miles per gallon and Jenna's car gets 25 miles per gallon. We can convert miles to kilometers by multiplying by 1.609344.

This gives us 48 kilometers per gallon for Mate's car and 40 kilometers per gallon for Jenna's car.

If we assume that both cars are traveling at the same speed, then Mate's car will travel 8 kilometers farther than Jenna's car in one gallon of gas. We can convert kilometers to minutes by dividing by 60.

This gives us 5 minutes per gallon for Mate's car and 4 minutes per gallon for Jenna's car.

Therefore, Mate's car can travel 1 minute farther per gallon of gas than Jenna's car.

For such more question on gallons:

https://brainly.com/question/17004258

#SPJ8

Answer:

55 Degrees

Step-by-step explanation:

The measure of angle {x}, between the tops of two steel beams in front and on top of the building is 54.46°.

There are six major trigonometric functions as -

We can write the relation between them as -

Also the following trigonometry relations hold true -

Given is to find the angle {x}, between the tops of two steel beams in front and on top of the building.

We can write the measure of angle {x} as -

tan(x) = (7.5 - 0.5)/5

tan(x) = 7/5

tan(x) = 1.4

x = tan⁻¹(1.4)

{x} = 54.46°

Therefore, the measure of angle {x}, between the tops of two steel beams in front and on top of the building is 54.46°.

To solve more questions on trigonometric functions, visit the link below-

https://brainly.com/question/30672622

#SPJ2

Answer:

(x,y,z)= (0,1,0)

Step-by-step explanation:

Explanation:

Given

[1]XXXx=−1−t

[2]XXXy=2+t

[3]XXXz=1+t

[4]XXX3x+y+3z=1

Substitute the expressions for x,y,z from [1], [2], and [3] into [4]

[5]XXX3(−1−t)+2+t+3(1+t)=1

Simplify [5]

[6]XXX2+t=1

[7]XXXt=−1

(x,y,z)=(−1−(−1),2+−1,1+−1)

XXXX=(0,1,0)

Removing the point (64, 40,786) from the dataset and conducting a new regression analysis may impact the slope of the least-squares line and the correlation coefficient, depending on whether the point is an outlier or follows the overall trend of the data.

If the point representing 64 wins and attendance of 40,786 people per game is removed from the set of data and a new regression analysis is conducted, the following would be impacted:

(i) The slope of the least-squares line would be impacted. This is because the slope of the line is calculated based on the data points and removing a point from the dataset would change the overall trend of the data. The slope would be recalculated based on the remaining data points, and it would be different from the original slope.

(ii) The correlation coefficient would also be impacted. The correlation coefficient measures the strength and direction of the linear relationship between two variables. Removing a point from the dataset would change the overall pattern of the data, which would in turn affect the correlation coefficient. The new coefficient would reflect the revised relationship between the remaining data points.

Let's consider how the removal of the point representing 64 wins and an attendance of 40,786 people per game would impact the regression analysis.

(i) The slope of the least-squares line:

When you remove a point from a dataset, it may cause the least-squares line to change. If the point is an outlier or significantly different from the other points in the dataset, it may have a substantial impact on the slope. If the point is close to the overall trend of the data, its removal might not affect the slope as much. In this case, if the point (64, 40,786) is an outlier, removing it could cause the slope of the least-squares line to change. If it is not an outlier, the change in slope may be minimal.

(ii) The correlation coefficient:

The correlation coefficient measures the strength and direction of the relationship between two variables. If the removed point is an outlier, its removal can impact the correlation coefficient. If the point is closely following the overall trend of the data, removing it might not have a significant effect on the correlation coefficient. In this case, if the point (64, 40,786) is an outlier, removing it could cause the correlation coefficient to increase or decrease in magnitude, depending on how it deviates from the trend. If it is not an outlier, the change in the correlation coefficient may be minimal.

Learn more about variables at: brainly.com/question/17344045

#SPJ11

Answer:

√61

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Prime numbers have to be only divisible by one and themselves (2 numbers), but one is,\(1*1\) so it is only divisible by one number, thus it is not prime.

The algebraic expression for the given phrase would be: c + 6, where c represents the unknown quantity (number of cars in the garage) and 6 represents the number of cars outside.

To translate the following phrase into an algebraic expression, we need to use the variable c to represent the unknown quantity. The phrase is "the total of the number of cars in the garage and the 6 cars outside."

So, the algebraic expression is: c + 6Where "c" represents the number of cars in the garage.

The expression c + 6 represents the total number of cars, which is the sum of the number of cars in the garage and the 6 cars outside.

Example: If there are 10 cars in the garage, then the total number of cars would be: c + 6= 10 + 6= 16.

So, there would be 16 cars in total.

The expression c + 6 would always give us the total number of cars, regardless of the value of "c."

For more such questions on algebraic expression

https://brainly.com/question/4344214

#SPJ8

Answer:

Step-by-step explanation:

Answer: they will each get 1/8 of the pan of brownies

Step-by-step explanation:

She only has 1/2 the pan.

Herself plus 3 friends are 4 people.

1/2= 4/8

So, they will each get 1/8 of the pan of brownies.

Note:

You missed adding the answer options.

But, I am solving the given expression to determine its equivalent so that you could get an idea and could easily determine all the options which would be equivalent to the result we would get.

Answer:

\(5^{\frac{1}{3}}\:\times 25^{\frac{1}{3}}=5\)

Step-by-step explanation:

Given the expression

\(5^{\frac{1}{3}}\times \:25^{\frac{1}{3}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\)

\(5^{\frac{1}{3}}\times \:25^{\frac{1}{3}}=\left(5\times \:25\right)^{\frac{1}{3}}\)

               \(=125^{\frac{1}{3}}\)

\(\mathrm{Factor\:the\:number:\:}\:125=5^3\)

               \(=\left(5^3\right)^{\frac{1}{3}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\)

               \(=\left(5^3\right)^{\frac{1}{3}}=5^{3\times \frac{1}{3}}=5\)

Thus,

\(5^{\frac{1}{3}}\:\times 25^{\frac{1}{3}}=5\)

Answer:

C. 3x - y = -2

Step-by-step explanation:

We know that lines with the same slope are usually parallel

3x - y = -2

-y = -3x - 2

y = 3x + 2

They have the same slope so we can assume that they're parallel

You can also graph to check this

Answer:

\(102^\circ\)

Step-by-step explanation:

Given that:

\(\angle 5\) is a supplement of \(\angle 6\).

m\(\angle 5\) = 78°

To find:

m\(\angle 6\) = ?

Solution:

First of all, let us learn about the concept of an angle being a supplement of the other angle.

\(\angle B\) is known as supplement of \(\angle A\), if sum of the two angles is equal to 180°.

\(i.e. \angle A +\angle B=180^\circ\).

For example, angle made on one side by a line intersecting the other line are supplement of each other.

Here, we are given that \(\angle 5\) is a supplement of \(\angle 6\).

In other words:

\(\angle 5+\angle 6=180^\circ\)

Putting value of \(\angle 5\):

\(\Rightarrow 78^\circ+\angle 6=180^\circ\\\Rightarrow \angle 6 =180^\circ-78^\circ\\\Rightarrow \bold{\angle 6 =102^\circ\\}\)

So, the answer is: \(102^\circ\)

The height of the arch, measured 3 inches from the left side of the arch is 30 inches.

Given

A sculptor creates an arch in the shape of a parabola.

When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x.

The path of a projectile under the influence of gravity follows a curve of this shape.

Therefore,

The height of the arch, measured 3 inches from the left side of the arch is;

\(\rm f(x) = -2(x)(x - 8)\\\\f(3) = -2(3)(3-8)\\\\f(-3)=(-6)(-5)\\\\f(-3)=30\)

Hence, the height of the arch, measured 3 inches from the left side of the arch is 30 inches.

To know more about Parabola click the link given below.

https://brainly.com/question/8495268

Answer:30 inches

Step-by-step explanation:

just took test

Answer:

no choise

Step-by-step explanation:

=54/8-73/8

=-19/8

so no choise

Answer:

The answer is:  D

Y-c=x

Step-by-step explanation:

just did it

a) Looking at the given graph, at 40 degrees Fahrenheit, the corresponding temperature in degree Celsius is: 4.5°C

b) At a temperature of 0 degree Fahrenheit, the corresponding temperature in degree Celsius is: -18°C

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the given linear graph shows us that the x-axis is represented by degree Celsius while the y-axis is represented by degree farenheit.

a) Looking at the given graph, at 40 degrees Fahrenheit, the corresponding temperature in degree Celsius is: 4.5°C

b) At a temperature of 0 degree Fahrenheit, the corresponding temperature in degree Celsius is: -18°C

Read more about Linear Equation Graph at: https://brainly.com/question/28732353

#SPJ1

Answer:

Step-by-step explanation:

G

Option a, adjacency matrix. An adjacency matrix is a two-dimensional array that represents a graph's edges, where the rows and columns correspond to the vertices of the graph. If there is an edge between two vertices, the corresponding element in the matrix is set to 1, otherwise it is set to 0. This implementation is useful for dense graphs, where the number of edges is close to the maximum possible number of edges.

An adjacency matrix is a simple and efficient way to represent graphs that have a large number of vertices and edges. It allows for fast lookups of the existence of an edge and is useful for various algorithms that require graph representation. However, it is not suitable for sparse graphs, where the number of edges is much smaller than the maximum possible number of edges. In such cases, an adjacency list would be more appropriate.

The common implementation of a graph that uses a two-dimensional array to represent the graph's edges is called an adjacency matrix.

To know more about array representation,visit:

https://brainly.in/question/5489688

#SPJ11

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

1023 distinct color groupings, can be made out of 10 tubes of paint.

Permutations and combinations. A variety of ways to select objects from a set that form subsets that typically have no replacements. This subset selection is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. French mathematicians Blaise Pascal and Pierre de Fermat used many of the 17th-century odds in games to study combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets. explained. encouraged the development of theory.

= 2¹⁰ - 1

= 1024 - 1

= 1023

To know more about combination and permutation, visit:

https://brainly.com/question/28720645

#SPJ4

Answer:

7a

Step-by-step explanation:

your multiplying a 7 times so this is how you right it

\( \qquad \qquad \large\overbrace{  \underbrace{\underline{ \boxed{ \sf \:Answer \: }}}}\)

\(\green{ \qquad{ \sf{ \dashrightarrow{}}}} \sf a \: • \: a \: • \: a \: • \: a \: • \: a \: • \: a \: • \: a\)

\(\green{ \qquad{ \sf{ \dashrightarrow{}}}} \sf a {}^{7} \)

The weight of the cable Dustin is using would be 58.67 pounds.

As per the given statement, Dustin is using a cable to lift heavy equipment.

His company has a table of the weights of various lengths of cable.

If Dustin needs to use 88 feet of cable, Pounds will this cable weigh:

Let us find the solution to the problem given in the question.

The length of the cable Dustin is using is 88 feet.

Using the table given by his company, the weight of the 88 feet long cable can be determined.

Using the terms given in the question, the solution is as follows:

Dustin needs to use 88 feet of cable, and the weight of this cable can be found from the table given by the company.

If we look at the table, it is evident that there is a weight of 2 pounds for every 3 feet of cable, so the weight of the 88 feet of cable Dustin is using would be:

Pounds of 3 feet of cable = 2 pounds of 3 feet of cable.

Pounds of 1 foot of cable = (2/3) pounds of 1 foot of cable

So, the weight of 88 feet of cable = (2/3) × 88 = 58.67 pounds.

For similar question on Word problem

https://brainly.com/question/21405634

#SPJ11.

Question: Dustin is using cable to lift heavy equipment. his company has a table of the weights of various lengths of cable. if dustin needs to use 88 feet of cable, how many pounds will this cable weigh?

Length of cable in feet: 5 15 25 35

Weight of cable in pounds: 24.4 73.2 122.0 170.0

The series of transformations correctly shows that △ABC≅△XYZ is D

a translation 2 units left and a reflection over the x-axis.

if a translation happens to each point of △ABC horizontally to the left by 2 units, which means  subtracting 2 from the x-coordinate of each vertex, we notice that a transformation of ABC to coordinates that are almost identical to XYZ but let it be called it A'B'C'

A(3, 0) ⇒ A'(1, 0)

B(2, -3) ⇒ B'(0, -3)

C(0, 3) ⇒ C'(-2, 3)

Secondly, if a reflection happens to A'B'C' at the x axis the transformation becomes identical to △XYZ

A'(1, 0) ⇒ X(1, 0)

B'(0, -3) ⇒ Y(0, 3)

C'(-2, 3) ⇒ Z(-2, -3)

Find more exercises on transformation;

https://brainly.com/question/13801312

#SPJ1

Answer:

Step-by-step explanation:

Term Definition

Linear regression line The line that goes through a set of points either exactly or approximately.

Difference The result of a subtraction operation is called a difference.

Answer:

18 m

Step-by-step explanation:

The given situation is equivalent to a right angled triangle as shown in the diagram attached.

AB is the height at which tree was cut.

And the top touches the ground at a point C.

So,

AB = 5 m and

AC = 12 m

Here, we have to find original height of the tree.

Original height of Tree = AB + BC OR AB + BC' (Because B is the point in height AC' of tree)

Let us consider the \(\triangle ABC\).

As per pythagorean theorem:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow BC^{2} = AB^{2} + AC^{2}\\\Rightarrow BC ^2=5^2+12^2\\\Rightarrow BC = \sqrt{169}\\\Rightarrow BC = 13\ m\)

Therefore the answer is :

Height of tree = 5+13 = 18 m

Mass of O₂ produced is: B. 144

Mass of H₂O produced is: C. 180 g

The balanced chemical equation is:

2 KClO3 → 2 KCl + 3 O₂

From the equation, we can see that 2 moles of KClO₃ produce 3 moles of O2. So, 1 mole of KClO₃ produces (3/2) moles of O₂.

Therefore, 3.0 mol of KClO₃ will produce (3/2) × 3.0 = 4.5 moles of O₂.

To convert moles of O₂ to grams of O₂, we need to use the molar mass of O2, which is 32 g/mol.

So, the mass of O₂ produced is:

4.5 mol × 32 g/mol = 144 g

Answer: B. 144

The balanced chemical equation is:

2 H₂ + O₂ → 2 H₂O

We can see that 1 mole of O₂ reacts with 2 moles of H2 and produces 2 moles of H₂O.

So, 5.0 moles of O₂ will react with (2/1) × 5.0 = 10.0 moles of H₂ to produce (2/1) × 5.0 = 10.0 moles of H₂O.

To convert moles of H₂O to grams of H₂O, we need to use the molar mass of H₂O, which is 18 g/mol.

So, the mass of H₂O produced is:

10.0 mol × 18 g/mol = 180 g

Answer: C. 180

Learn more about mass of O₂.

brainly.com/question/12127540

#SPJ11

Answer:

The value for X is 25

Step-by-step explanation:

I hope this helps you out!

Answer:

the answer is ____

Step-by-step explanation:

first study more

then clean that computer

and then dont ask on here okau

Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

Learn more about the demand curve at:

brainly.com/question/1139186

#SPJ11