The perimeter of a rectangle is 84 cm. If the length is 17 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation

B) Solve your equation in part [A] to find the width of the rectangle.
Answer: The rectangle is
cm wide.

PLS HELP I NEED THIS ASAP

Cześć odpowiedź byłaby 790,997 do punktu i do przecinka dziesiętnego.

Answer:

Justin's salary is $400/month.  His commission is 25% of his sales.

Step-by-step explanation:

Let y be Justin's income for one month.  His salary is made up of a monthly base pay, which we'll call x, and a commission on the sales, S, he makes in that month.  We will assume the commission is a fixed ratio of sales every month, which we will call b.  b is the percentage his commission is based on.

Justin's total monthly salary is therefore:

y = x + b(S)

where y is monthly salary, x is monthly base pay, b is the rate of commission, and S are his merchandise sales in that month.

We are told in one month Justin earned a total of $500 in a month he sold $400 of merchandise.  

We have y = $500, and S = $400, so we can write:

500 = x + b(400)  

In another month, Justin earns a total of $575 when he sold $700 of merchandise.  We can write:

575 = x + b(700)

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

We have two unknowns (x and b) and two equations.  If we substitute one equation into another, we will eventually find the values of x and b.

Take the first equation and rearrange it to isolate x:

500 = x + b(400)

x = 500 - b(400)

Now take the second equation and substitute this definition of x:

575 = x + b(700)

575 = (500 - b(400)) + b(700)

575 = 500 + 300b

75 = 300b

b = (75/300)

b = 0.25

The rate of commission Justin receives on the merchandise he sells is 0.25 or 25%.  Nice.

575 = x + b(700)

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

Now take either equation and set b = 0.25, then solve for x, Justin's monthly base pay:

575 = x + b(700)

575 = x + (0.25)(700)

575 = x + 175

x = 400

Justin's base pay is $400/month.

CHECK

Do the values of x ($400) and b(0.25) result in the pay amounts for the months discussed?

y = $400 + (0.25)b

Month  Sales(S) Base Pay  Commission (0.25)*(S)  Total($)   Actual($)

    1        400           400             (0.25)*(400)= $100      $500          $500

    2        700           400             (0.25)*(700)= $175     $575          $575

Answer:

I select the third option and the last linear equation

a) One example of a relation on the set {1,2,3,4} that is reflexive and symmetric, but not transitive is {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3), (3,2)}.

b) One example of a relation on the set {1,2,3,4} that is reflexive and transitive, but not symmetric is {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (1,3)}.

c) One example of a relation on the set {1,2,3,4} that is transitive and symmetric, but not reflexive is {(1,2), (2,1), (2,3), (3,2), (3,4), (4,3)}.

d) One example of a relation on the set {1,2,3,4} that is not transitive, symmetric, or reflexive is {(1,2), (2,3), (3,4)}.

(a) One example of a relation on the set {1,2,3,4} that is reflexive and symmetric, but not transitive is {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3), (3,2)}. This relation is reflexive because each element is related to itself, and symmetric because if (a,b) is in the relation, then (b,a) is also in the relation. However, it is not transitive because (1,2) and (2,3) are in the relation, but (1,3) is not.

(b) One example of a relation on the set {1,2,3,4} that is reflexive and transitive, but not symmetric is {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (1,3)}. This relation is reflexive because each element is related to itself, and transitive because if (a,b) and (b,c) are in the relation, then (a,c) is also in the relation. However, it is not symmetric because (1,2) is in the relation, but (2,1) is not.

(c) One example of a relation on the set {1,2,3,4} that is transitive and symmetric, but not reflexive is {(1,2), (2,1), (2,3), (3,2), (3,4), (4,3)}. This relation is transitive because if (a,b) and (b,c) are in the relation, then (a,c) is also in the relation, and symmetric because if (a,b) is in the relation, then (b,a) is also in the relation. However, it is not reflexive because there are no elements related to themselves in the relation.

(d) One example of a relation on the set {1,2,3,4} that is not transitive, symmetric, or reflexive is {(1,2), (2,3), (3,4)}. This relation is not reflexive because there are no elements related to themselves, not symmetric because (1,2) is in the relation, but (2,1) is not, and not transitive because (1,2) and (2,3) are in the relation, but (1,3) is not.

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Answer:

r ≈ 12 cm

Step-by-step explanation:

arc length = circumference × fraction of circle, that is

2πr ×\(\frac{60}{360}\) = 12.57 ( multiply both sides by 360 to clear the fraction )

2πr × 60 = 4525.2

120πr = 4525.2 ( divide both sides by 120π )

r = \(\frac{4525.2}{120\pi }\) ≈ 12 cm

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

6.2 feet

Step-by-step explanation:

Joe must attempt approximately 14.93 free throws in a game to be expected to make 10 of them. Since he cannot attempt a fraction of a free throw, he would need to round this up to 15 attempts.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

We can use the binomial distribution to solve this problem. Let X be the number of successful free throws that Joe makes in a game, then X follows a binomial distribution with n trials and probability of success p = 0.67.

We want to find the value of n such that the expected number of successful free throws is 10. The expected value of X is given by E(X) = np, so we have:

E(X) = np = 10

Solving for n, we get:

n = 10/p = 10/0.67 ≈ 14.93

Therefore, Joe must attempt approximately 14.93 free throws in a game to be expected to make 10 of them. Since he cannot attempt a fraction of a free throw, he would need to round this up to 15 attempts.

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Answer:

Step-by-step explanation:

the longest length is always the hypotenuse

Use Pythagorean theorem

a^2+b^2=c^2

5^2+10^2=c^2

c=11.18

Note: if c=13 than it is a right triangle

since 11.18 not=13

not right triangle

Answer:

It is not a right triangle

Step-by-step explanation:

a(squared) + b(squared) = c(sqaured)

a = 13, b = 5, c = 10

13 times 13 is 169

5 times 5 is 25

169 + 25 = 194

but that's not all.

10 times 10 is 100.

the problem is 169 + 25 is 194, not 100. for the triange to be a right triangle, all the numbers have to make sense. i don't know if this helps but again, it is not a right triangle.

Answer:

Step-by-step explanation:no you should not

-9x+27=-13

-9x-27=13

-9x=18

-2=x

To prove that the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in a compact space x is compact, we need to show that any open cover of this sequence has a finite subcover. Here is the step-by-step explanation of the proof:

1. Let {Uα} be an open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x.
2. Since z1 is a closed subset of x, its complement, x - z1, is open.
3. Since {Uα} is an open cover of the sequence, there must exist an α1 such that z1 ⊆ Uα1.
4. Now, consider the set z2. It is a closed subset of x, so its complement, x - z2, is open.
5. Since {Uα} is an open cover of the sequence, there must exist an α2 such that z2 ⊆ Uα2.
6. By continuing this process, we can find α3, α4, and so on, such that z3 ⊆ Uα3, z4 ⊆ Uα4, and so on.
7. Since the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... is decreasing, we have z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN for any positive integer N.
8. Now, consider the subcover {Uα1, Uα2, ..., UαN} of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
9. Since {Uα} is an open cover of the sequence, each zN is covered by at least one Uα.
10. Therefore, the subcover {Uα1, Uα2, ..., UαN} is a finite subcover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
11. Thus, we have shown that any open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... has a finite subcover.
12. Therefore, the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x is compact.
In summary, the proof demonstrates that in a compact space x, any sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... is also compact.

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Step-by-step explanation:

\(\sf \leadsto \dfrac{5y - 2}{4(y + 2)} = \dfrac{1}{3}\)

\(\sf \leadsto \dfrac{5y - 2}{4y + 8} = \dfrac{1}{3}\)

\(\sf \leadsto 3(5y - 2) = 1(4y + 8)\)

\(\sf \leadsto 15y - 6 = 4y + 8\)

\(\sf \leadsto 15y - 4y = 8 + 6\)

\(\sf \leadsto 11y = 14\)

\(\sf \leadsto y = \dfrac{14}{11}\)

Answer:y=14/11

Step-by-step explanation:

Answer:

y=7x-19

Step-by-step explanation:

slope equation is y=mx+b

plug in the coordinate

2=7(3)+b

b=-19

Answer:

y=3x-13

Step-by-step explanation:

this is the answer

Including all relevant disciplines and considering various disciplinary perspectives are important aspects of integration, they do not directly address the completeness of the integration process itself.

The difference between partial integration and full integration is whether or not all insights have been integrated to form a single theory. Partial integration refers to the process of integrating some of the insights or components into a cohesive whole, but not necessarily incorporating all of them. On the other hand, full integration implies that all relevant insights or components have been brought together to create a comprehensive and unified theory or understanding.

The other two answer choices mentioned, whether all relevant disciplines are included as part of the investigation and whether all disciplinary perspectives have produced alternative integrations, are not the defining factors that differentiate partial integration from full integration. While including all relevant disciplines and considering various disciplinary perspectives are important aspects of integration, they do not directly address the completeness of the integration process itself.

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Answer:

$13.00 per person

Step-by-step explanation: you divide $26 by 2

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.

A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).

It is suitable when we want to understand how changes in the explanatory variable affect the response variable.

In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.

This means that the relationship between y and x can be adequately described by a straight line.

The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.

If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.

Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.

Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.

Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.

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The Cartesian coordinates are (-2√2, -2√2). Plot this point on the graph as well.

(a) To convert polar coordinates (5, π) to Cartesian coordinates, we use the formulas x = r * cos(θ) and y = r * sin(θ). Plugging in the values, we get x = 5 * cos(π) = -5 and y = 5 * sin(π) = 0.

The Cartesian coordinates are (-5, 0). To plot this point, mark the position (-5, 0) on the x-axis.

(b) For polar coordinates (4, -2π/3), we calculate x = 4 * cos(-2π/3) = 4 * (-1/2) = -2 and y = 4 * sin(-2π/3) = 4 * (√3/2) = 2√3. Hence, the Cartesian coordinates are (-2, 2√3). Plot this point on the graph.

(c) Given polar coordinates (-4, 3π/4), x = -4 * cos(3π/4) = -4 * (√2/2) = -2√2 and y = -4 * sin(3π/4) = -4 * (√2/2) = -2√2. The Cartesian coordinates are (-2√2, -2√2). Plot this point on the graph as well.

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Answer:

98

Step-by-step explanation:

The formula for this situation = Cube volume - cone volume

Cube volume = 5.1 * 5.1 * 5.1 = 132.7 ( rounded )
Cone volume = pi × r^2 × h/3 = pi × 2.55^2 × 5.1/3 = 3.14 × 6.5025 × 1.7 = 34.7 ( rounded )

Total volume = 132.6 - 34.7 = 98

Notes for myself: Cube = 5.1 * 5.1 * 5.1
Problem Description:
the volume of the cube with the empty cone-shaped indentation is ___ cubic meters.

Use 3.14 for pi and round your answer to the nearest hundredth.
Hope this helped

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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Answer:

1 only

Step-by-step explanation:

because it talks about a coin and a dice and the rest is about cards

Answer:

Priya practiced for: 75 x 152% = 114 minutes or 1 hour and 54 minutes

Hope this helps!

Answer:

A rational number is a nonterminating, nonrepeating number. this is false

Answer: 12x^6+104x^5-319x^4-2890x^3+4661x^2+14000x-19600 sorry I don't have enough time to explain I got to go hope that helps tell me if I was right or not bye!

Step-by-step explanation:

Answer:

\(\dfrac{1}{6561}\)

Step-by-step explanation:

Given the expression \([(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}\), Using the laws of indices to simplify the expression. The following laws will be applicable;

\(a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\\)

\(a^{-m} = 1/a^m\)

Given \([(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}\)

open the parenthesis

\(= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}\)

To find the probability of Sarah cleaning her room or doing her homework, we can use the addition rule for probabilities. However, we need to be careful not to count the probability of Sarah cleaning her room and doing her homework twice. Therefore, we need to subtract the probability of Sarah cleaning her room and doing her homework from the sum of the probabilities of Sarah cleaning her room and doing her homework separately.

Let C be the event that Sarah cleans her room, and let H be the event that Sarah does her homework. Then we know:

P(C) = 0.40 (the probability that Sarah cleans her room)

P(H) = 0.70 (the probability that Sarah does her homework)

P(C and H) = 0.24 (the probability that Sarah cleans her room and does her homework)

Using the addition rule, we can find the probability of Sarah cleaning her room or doing her homework as follows:

P(C or H) = P(C) + P(H) - P(C and H)

          = 0.40 + 0.70 - 0.24

          = 0.86

Therefore, the probability of Sarah cleaning her room or doing her homework is 0.86, or 86%.

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Answer:

The length of the segment GI is 30.5 units

Step-by-step explanation:

In any triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length

In ΔFHJ

∵ G is the mid-point of the side FH

∵ I is the mid-point of the side JH

∵ FJ is the 3rd side of the triangle

→ From the rule above

∴ GI // FJ

∴ GI = \(\frac{1}{2}\) FJ

∵ FJ = 61 units

∴ GI = \(\frac{1}{2}\) (61)

∴ GI = 30.5

∴ The length of the segment GI is 30.5 units

Median length of time required to review an application = (45 + 100)/2= 72.50 Hence, the correct option is A, 72.50

Given times (in minutes) that several underwriters took to review applications for similar insurance coverage are 100, 110, 42, and 45 and we need to find the median length of time required to review an application.What is the median?The median is the middle value when a data set is ordered from least to greatest.To find the median of a data set, the first step is to write the data set in order from least to greatest. In the above given dataset,Let's first order these numbers from least to greatest;42, 45, 100, 110 Now we can see the median will be between 45 and 100, so we just need to find the mean of these two numbers. the correct option is A

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The period of the voltage signal can be calculated using the formula T = 1/f, where T is the period in seconds and f is the frequency in hertz.

In this case, the frequency can be found by noting that the argument of the sine function is 30nt, where n is a constant. This means that the frequency is 30n Hz. Therefore, the period can be calculated as T = 1/(30n) seconds.

Voltage, also known as electric potential difference, is a measure of the difference in electric potential energy between two points in an electric circuit. It is typically measured in volts (V) and is the driving force that pushes electric charges through a circuit.

The voltage between two points in a circuit can be calculated using Ohm's law, which states that voltage (V) equals current (I) times resistance (R): V = I * R. In other words, the voltage across a circuit element is proportional to the current flowing through it and the resistance of the element.

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Answer:

42

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

42/60 = 70%

(Hope I helped)