Rama is stringing beads whose lengths are each 0.19 inches. How can rounding be used to estimate the length of a row of 9 beads?

The constant of proportionality on this case is 3.2

What is constant of proportionality?

The ratio between any two given values that establishes what is referred to as a proportional relationship is the constant of proportionality.

Main body:

Total amount spent by Mom = $ 72

total gallon bought = 22.5

So constant of proportionality can be found by finding value of 1 gallon of gasoline, which can be found by dividing as follows,

Price of 1 gallon = total spent/ total gasoline bought

                           = 72/22.5

                           = 3.2

Hence constant of  proportionality is 3.2.

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The height of each of the two students is 64

The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

Let the heights of each of the two students be x,

so that x, x, 68 and 62 are the heights of the four students

Average height which is 64.5 = [tex]\frac{x + x + 62 + 68}{4}[/tex]

[tex]\frac{x + x + 62 + 68}{4}[/tex] = 64.5

by cross multiplying,

x + x + 62 + 68 = 4 x 64.5

2x + 130 = 258

collecting like terms,

2x = 258 - 130

2x = 128

x = 128/2

x = 64 inches

In conclusion the height of each of the 2 students with equal height is 64 inches.

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By using the concept of confidence interval, it is obtained that

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

What is Confidence interval?

Let the quantity which is to be estimated is [tex]\theta[/tex].  A confidence interval for the parameter θ, with confidence level [tex]\alpha[/tex] is the interval (a, b), where

P(a < [tex]\theta[/tex] < b) = [tex]\alpha[/tex], P is the probability

Here the  average commute time in minutes ([tex]\mu[/tex]) is to be calculated

95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25)

This means that it is 95% confident that the interval (15.75, 28.25) contains the population mean commute time in minutes using public transit

So the correct interpretation is

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

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Complete Question

A researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). What is the correct interpretation of this interval?

A) There is a 95% chance commute time in minutes using public transit is between 15.75 and 28.25 minutes.

B) We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

C) We are 95% confident that all commute time in minutes for the population using public transit is between 15.75 and 28.25 minutes.

D) We are 95% confident that the interval 15.75 < μ < 28.25 contains the sample mean commute time in minutes using public transportation.

Answer:

[tex]3^{1.5}[/tex]

Step-by-step explanation:

[tex]3 = 3^1[/tex]

[tex]\sqrt{3} = x^{0.5}[/tex]

[tex]3*\sqrt{3} = 3^{1} * 3^{0.5} = 3^{1 + 0.5} = 3^{1.5}[/tex]

x < 2 and x > 12 are the answers to the inequality expressions supplied.

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression. One-variable inequalities can have solutions that can be graphed on a number line or on a coordinate plane.

Given the inequality expressions below:

2<-2x+6 or -18>-2x+6

Solve individually;

2 < -2x + 6

2-  6 < -2x

-4 < -2x

-2x > -4

x < 4/2

x <2

For the inequality  -18>-2x+6

-18 - 6 > -2x

-24 > -2x

-2x < -24

x  > 24/2

x > 12

Hence the solution to the given inequality expressions are x < 2 and x > 12

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The dependent variable in the function g(t) = - t - 10 is g .

In the given function g(t) = - t - 10 , we have t which is the independent variable. It makes up the domain of the function.

The independent variable is the one whose value is mapped by all and any particular t.

And 10 is the constant.

Dependent variables get their name since their values are examined throughout an experiment under the assumption or requirement that they are likewise dependent on the value of the dependent variable pursuant to some regulation .

Independent variables are those that, in relation to anything having to do with the experiment in question, are not considered to be reliant on any other factors.

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9 students made at least 3 picture frames.

An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.

Given:

The plot shows picture frames made by students last week.

Number of Frames     Number of students

              0                               6

              1                                4

              2                               1

              3                               2

              4                               7

So, the students made at least 3 picture frames

= 2+ 7

= 9

Hence, 9 students made at least 3 picture frames.

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75% of the eruptions lasted between 1.77 and 4.93 minutes.

Chebyshev's Theorem calculates the proportion of observations that are within a given number of standard deviations of the mean. This theorem is applicable to many different probability distributions. Chebyshev's inequality is another name for Chebyshev's theorem.

According to Chebyshev’s theorem, the proportion of the data lying within k standard deviations of the mean is always at least 1 – 1/k^2, where k>1.

Given

Mean = 3.35

SD = 0.79

Mean – 1*SD = 3.35 – 1*0.79

= 3.35 – 0.79

= 2.56

Mean + 1*SD =3.35 + 1*0.79

= 3.35 + 0.79

= 4.14

Mean – 2*SD =3.35 – 2*0.79

= 3.35 – 1.58

= 1.77

Mean + 2*SD =3.35 + 2*0.79

= 3.35 + 1.58

= 4.93

Here, we have k = 2

For k = 2,

= 1- (1/k2)

= 1- (1/(2)2

= 1- ¼

= ¾

at least ¾ or 75% of all values lie within 2 standard deviations of the mean.

Therefore 75% of the eruptions lasted between 1.77 and 4.93 minutes.

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Answer:

  (d)  HA

Step-by-step explanation:

You have two right triangles with the hypotenuse and one angle marked as congruent. You want to know the applicable theorem for claiming the triangles are congruent.

When two triangles are known to be right triangles, the known angle is opposite the longest side (hypotenuse), and the two legs are the sides that form that known angle. Hence, some special theorems can be invoked for right triangles:

  LA — leg, angle; equivalent to ASA

  LL — leg, leg; equivalent to SAS

  HA — hypotenuse, angle; equivalent to AAS

  HL — hypotenuse, leg; no equivalent for non-right triangles

The given triangles have the hypotenuse (H) and an acute angle (A) marked, so the HA theorem can be used to prove congruence.

__

Additional comment

The HL condition described above refers two two consecutive sides and the angle not between them (SSA). This set of descriptors will create a unique triangle if and only if the angle is opposite the longest side. In general, that will not be the case, but it is guaranteed to be the case for a right triangle.

The solution to the inequality expression is f >-3

From the question, we have the following parameter that can be used in our computation:

-2f - 3.7 < 2.3

Add 3.7 to both sides of the expression

This gives

-2f < 6

Divide both sides of the expression by -2

So, we have the following representation

f >-3

Hence, the solution is f >-3

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Answer:

Its the average of the numbers, and its the sum of all values divided by the total number of values.

Answer:

mean median and mode song rap helps me remember

no question;;;;;;;;;;;;;;;;;;;;;;

The solution to the inequality −17 + 2x ≤ 19 − 4x is x ≤ k. The value of k is 6.

In mathematics, the relationship between two values that are not equal is defined by inequalities.

Therefore, the inequality can be solved as follows:

−17 + 2x ≤ 19 − 4x is  x ≤ k .

Let's solve for k

−17 + 2x ≤ 19 − 4x

subtract 2x from both sides of the inequalities

−17 + 2x ≤ 19 − 4x

−17 + 2x - 2x ≤ 19 − 4x - 2x

- 17 ≤ 19 - 6x

Subtract 19 from both sides of the equation

- 17 ≤ 19 - 6x

- 17 - 19 ≤ 19 - 19 - 6x

- 36 ≤ - 6x

divide both sides by -6

- 36 / -6 ≤ - 6x / -6

6 ≥ x

x ≤ 6

Therefore, k = 6

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Answer:

Tens place: 8

Tenths place: 5

Ten thousandths place: 2

Answers:

tenths place = 5

ten-thousandths place = 2

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

Explanation:

Refer to the place value chart shown below.

The 5 is in the tenths place which is one spot to the right of the decimal point. The ten-thousandths place is four spots to the right of the decimal point.

Answer:

Step-by-step explanation:

[tex]\left[\begin{array}{cc}2&7\\1&3&\end{array}\right] \left[\begin{array}{cc}-3&7\\1&-2&\end{array}\right] =\left[\begin{array}{cc}2(-3)+7(1)&2(7)+7(-2)\\1(-3)+3(1)&1(7)+3(-2)&\end{array}\right] =\left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]

Answer:

x = 4

Step-by-step explanation:

assuming you require to find the value of x

Δ ADE and Δ ACB are similar ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AD}{AC}[/tex] = [tex]\frac{AE}{AB}[/tex] ( substitute values )

[tex]\frac{x}{x+x-2}[/tex] = [tex]\frac{x+2}{x+2+x -1}[/tex]

[tex]\frac{x}{2x-2}[/tex] = [tex]\frac{x+2}{2x+1}[/tex] ( cross- multiply )

(2x - 2)(x + 2) = x(2x + 1) ← expand left side using FOIL

2x² + 2x - 4 = 2x² + x ( subtract 2x² + x from both sides )

x - 4 = 0 ( add 4 to both sides )

x = 4

The statement best describes the depth of the fish is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second

In order to know which statement best describes the depth of the fish, we have to first understand what the equation means:

Given: the equation y = -5x – 9

This can be likened to the equation of a straight line, which is of the form y =mx +c,

where m is the slope and c is the y-intercept

Comparing the given equation with the equation of a line :

y = -5x – 9

Slope(m) = -5 and  y-intercept(c) = -9

The y-intercept represents the starting while the slope is the rate of descend

Therefore, what this means is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second.

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Answer:

Step-by-step explanation:

weekend 1 : 3+2= 5

weekend 2 : 5.5+3.5=9

difference: 9-5=4

increase/initial value [times] 100

4/5(100)= 80%

The weighted average of the weighted points on the number line is -0.2.

A weighted average refers to the average of a data set that considers certain numbers as more important. Weighted averages are commonly used in statistical analysis, stock portfolios and teacher grading averages. In order to determine the weighted average of the weight points on the number line:

Hence, the average weight is -0.2.

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She has to do at least 8.6 hours walking (and then 7.5 hours dog walking) for the minimum of $80 earning

Keilantra is working two summer jobs, making $12 per hour lifeguarding and $6 per hour walking dogs. Last week Keilantra worked a total of 11 hours and earned a total of $108.

x = number hours dog walking

y = number hours Lifeguarding

x + y <= 11

12x + 6y >= 80

The solution is the common area below the first line and above the second line.

The first line is above the second line (due to the y-intercept of 11 vs. 8) until the crossing point.

for the crossing point we use the regular equations :

from the first we get

x = 11 - y

using this in the second

12×(11 - y) + 6y = 80

132 - 12y + 6y = 80

6y = 52

y = 52/6 = 26/3 = 8.6

x = 11 - y = 11 - 8.6 = 2.4

So, she has to do at least 8.6 hours lifeguarding (and then 7.5 hours dog walking) for the minimum of $80 earning, all the way up to the maximum of 11 hours lifeguarding (and 0 dog walking).

Hence the answer is she has to do at least 8.6 hours lifeguarding (and then 7.5 hours dog walking) for the minimum of $80 earning.

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Answer: (3,2)

Step-by-step explanation:

[tex]7x-7y=7\\\-4x-7y=-26[/tex]

subtract second equation from the first

[tex]11x=33\\x= 3[/tex]

plug x = 3 back into first equation

[tex]7(3) - 7y = 721 - 7y = 7-7y = -14\\y = -2[/tex]

Answer:

x=3 y=2

Step-by-step explanation:

Answer:

i dont see image..

Step-by-step explanation:

The tick marks on the two sides mean those two lengths are the same, which also means the angles opposite them are the same measure.  (AKA It's an isosceles triangle.)

Since the two missing angles are equal, we can solve:

    28 + x + x = 180

to find that x = 76.

The two angles are 76 degrees.

And since LM = LN, we know LN = 18 in.

Answer:

soda=30g

juice=40g

2 juice than soda=430g

Step-by-step explanation:

Since Keven bought 12 total drinks, we have the equation S + J = 12. We also know how much sugar is in each drink, as well as the total amount of sugar in all the drinks purchased. The equation 30S + 40J = 450 represents this scenario in terms of S and J. Now we have two equations with two unknowns (S and J) that make up the following linear system of equations:

S+J =12

30S+40J =450

We can solve this system by using either elimination or substitution (I will use substitution here):

S+J = 12

S=12- J

Now we can substitute the expression 12- J in for S in the second equation, and then solve for J:

30(12- J) +40J = 450

360- 30J +40J = 450

10J = 90

J = 9

Finally, we can substitute 9 in for J in either of the two original equations to solve for S:

S + 9 = 12

S = 3

So Keven bought three bottles of soda and nine bottles of juice. Hope this helps. Let me know if you have any questions.

The system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each bottle of juice contains 40 grams of sugar, compared to 30 grams per bottle of soda. Wyatt bought 2 more bottles of juice than soda, and they all have 430 grams of sugar in total.

If Wyatt purchased 2 more bottles of juice than bottles of Soda

J =2+S ------------(1)

J-S=2

Each bottle of Soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar and they all collectively contain 430 grams of sugar.

30S+40J =430

Substitute the value of J in equation 2 as

30S+40(2+S)=430

30S+80+40S=430

70S=430-80

70S=350

S=5

The number of juice is,

J=S+2

J=5+2

J=7

Thus, the system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.

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Answer:

A

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

i did the quize good luck

Answer: Write an equation in standard form that has a y-intercept at (0,-3) and also contains the point (4,5)

Step-by-step explanation:

The area of the given triangle is 21.33 cm²

This formula is understood for its simple calculation supporting the length of three sides of a triangle, if the length of three sides are a, b, and c, then its semi-perimeter is. s=a+b+c2. Thus, the area is given by,

A=√s(s−a)(s−b)(s−c)

Given a triangle, with lengths 8 cm, 6 cm and 12 cm

Perimeter = 8+6+12 = 26 cm

Semi perimeter = 26/2 = 13 cm

Area = √s(s−a)(s−b)(s−c)

Area = √13(13-8)(13-6)(13-12)

Area = √455

Area =  21.33 cm²

Hence, The area of the given triangle is 21.33 cm²

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Isolating the variable x we will get the simplified inequality (which is equivalent to the given one)

3 < x ≤ 5.2

Sadly, the options are not given, so we can get a trivial equivalent inequality which is the one where the variable x is isolated, and it gives the solution set for the inequality.

So let's isolate the variable:

-22 > -5x - 7 ≥ −33

First, we can add 7 everywhere, so we get:

-22 + 7 > -5x - 7 + 7  ≥ −33 + 7

-15 > -5x  ≥ −26

Now we can divide everywhere by -5, because it is a negative number, it changes the direction of the symbols.

-15/-5 < -5x/-5 ≤ -26/-5

3 < x ≤ 5.2

That is the equivalent inequality, and the solution set is:

(3, 5.2]

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The equation that finds the number of dimes he will pay you after the 7th study session [tex]a_7=5\times5^{7-1}[/tex].

Given that, Your friend asks you to help him study and will pay you 5 dimes the first time you help him.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The formula to find nth term of the geometric sequence is [tex]a_n=ar^{n-1}[/tex].

According to the question,

The geometric sequence is 5, 25, 125,.....

So, r=25/5 =5

Now, [tex]a_7=5\times5^{7-1}[/tex]

= 5×15625

= 78125 dimes

Therefore, the equation that finds the number of dimes he will pay you after the 7th study session [tex]a_7=5\times5^{7-1}[/tex].

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