Consider the following Grouped data regarding the ages at which a sample of
20 people were married:
Class Class Class
18-21 2
22-25 5
26-29 6
30-33 4
34-37 3
Limits Boundaries Mark Frequency

Equations are expressions that have equal values, while inequalities are used to represent unequal expressions

From the question,

The number of meters (x) Skyler must add is represented using the following equation

\(x + 1.48 = 1.57\)

Solve for x

\(x = 0.09\)

To break the record, the number of meters added to his personal best must be greater than 1.57.

So, we have:

\(x + 1.48>1.57\)

Solve for x

\(x > 0.09\)

Hence, the number of meters Skyler must be greater than is 0.09 meters

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Answer:

10 sqrt7 / 7

Step-by-step explanation:

convert mixed fraction to improper fraction.

this gives 107/49. Now find the square root of the numerator and denominator individually.

10 sqrt7 / 7

Graphing functions is the process of drawing a curve on the reference system that represents a function, and its calculation can be defined as follows:

Graph function:

\(\to F(x)=\frac{3}{8} (x-1)(x-9)\)

solving the above given function:

\(\to F(x)=\frac{3}{8} (x^2 -9x-x+9)\\\\\to F(x)=\frac{3}{8} (x^2 -10x+9)\\\\\to F(x)=\frac{3}{8} \times x^2 - \frac{3}{8} \times 10x+ \frac{3}{8} \times 9\\\\\to F(x)=\frac{3}{8} \times x^2 - \frac{3}{4} \times 5x+ \frac{3}{8} \times 9\\\\\)

Please find the graph function in the attached file.

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Answer:

a)160

b)300

Step-by-step explanation:

Answer:

Would diagonal mean triangle so: 9/2 which is

4.5? Sorry if it is wrong!

Answer:

f(2)=3

Step-by-step explanation:

Replace x with 2. 5-2=3

Answer:

27/28

Step-by-step explanation:

A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Answer: i am a person

Step-by-step explanation:

Answer:

heloo

i am a person

or am I.

If Susan stands 300 m away from the lighthouse and looks up at it with an angle of elevation of 5 degrees, the height of the lighthouse is approximately 26 meters. This calculation is important for navigation and other purposes.

To determine the height of the lighthouse, we can use trigonometry. We know that the angle of elevation, which is the angle between Susan's line of sight and the ground, is 5'. We also know the distance between Susan and the lighthouse, which is 300 m.

We can use the tangent function to find the height of the lighthouse:

tan(5') = height/300

To solve for height, we can cross-multiply and simplify:

height = 300 x tan(5')

Using a calculator, we get that the height of the lighthouse is approximately 26.2 m.

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Answer:

yes

It follows the y=mx+b format so it’s linear

Hopes this helps

Answer:

This is a test, please refer to the Academic Integrity and Honor Code

Answer:

0.625 years = 7.5 months

Step-by-step explanation:

Simple interest formula = rxtxp divided by 100

R x T x P / 100 = 30

Substitute all the values we know

3.2 x T x 1500/100 = 30

Simplify and rearrange =

3.2 x T x 1500 = 3000

3.2 x T = 2

T = 2/3.2

T = 0.625

The fraction of the volume of the larger cone occupied is 1/3.

Draw the cones. If the large cone has height H and radius R, the small cone has height h and radius r, so that

r/R = 1 - h/H

The ratio of the two volumes is v/V = r²h/R²H = (r/R)² h/H

if we maximize that ratio as a function of u = h/H, we get

f(u) = (1-u)² × u

= (u - 2u² + u³)

f'(u) = (1-4u+3u²)

= (h-1)(3h-1)

Clearly, when u=1, f(u) = 0 a minimum

when u = 1/3, f(h) = 4/9×1/3 = 4/27

so, h/H = 1/3 for max volume ratio.

Hence we get the required answer.

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Given that each roll is independent and that the odds of rolling a 2 are 1/6, the probability of receiving three 2s in a row is 1/216.

a. We can apply the multiplication principle to determine how many outcomes there are overall in the sample space.

There are 666 = 216 possible outcomes in the sample space because there are six outcomes for each die roll and we are rolling the die three times.

b. As each die roll is independent of the others, there is a 1/6 chance that any particular roll will result in a 2.

Therefore, the probability of getting three 2's in a row is (1/6)(1/6)(1/6) = 1/216.

So the probability of all three rolls being 2 is 1/216.

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Given:

Given the equation y = x - 2

Required: Classify it as direct variation, inverse variation or neither.

Explanation:

Two variables x and y show direct variation when they satisfies y = ax or y/x = a, where a is non-zero.

Similarly, two variables x and y show inverse variation when they satisfies y = a/x or xy = a, where a is non-zero.

Here, the equation y = x - 2 is in neither of the form y = ax or y = a/x.

So, y = x - 2 show neither direct nor inverse variation.

Final Answer: y = x - 2 show neither direct nor inverse variation.

The values of x for which the series converges is (-4,4)

The sum of the series for these values of x is x/(4-x)

The question stated can be solved by using concept of Geometric series converges .

By the geometric series theorem , we can say ,

if |r| < 1 , series converges

if |r| >= 1 , series diverges

∑\((x/4)^{n}\)  n ranges from (1,∞)

r=x/4

By geometric series converge theorem,

|r| < 1

|x/4| < 1

|x|<4

-4 < x < 4

Therefore , the mentioned series converges when x lies between (-4,4)

Now to find sum we have a formula ,

(r^(lower limit))/1-r

Now substituting the values that is r=x/4 and lower limit=1 , we have

\(\frac{x/4 }{1-x/4} }\)

After solving this , we have the required sum as x/(4-x)

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Answer: The x intercept is (-14/9,0)  which means the x intercept is -14/9. The y intercept is -14.

Step-by-step explanation:

the x intercept is when y is 0  so using the equation we could solve for x by putting in 0 for y.

0=--9x - 14

+ 14        +14

14= -9x  

x= -14/9

The y intercept is when x is zero so using the same method we will put in 0 for x in the equation and solve for y.

y= -9(0) - 14

y= 0-14

y= -14

Answer:

Step-by-step explanation:

Solve the linear system, X ′

=AX where A=( 1

1

​

5

−3

​

), and X=( x(t)

y(t)

​

) Give the general solution. c 1

​

( −1

1

​

)e 4t

+c 2

​

( 5

1

​

)e −2t

c 1

​

( 1

1

​

)e 4t

+c 2

​

( 5

−1

​

)e −2t

c 1

​

( 1

1

​

)e −4t

+c 2

​

( 5

−1

​

)e 2t

c 1

​

( −1

1

​

)e −4t

+c 2

​

( 5

1

​

)e 2t

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

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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When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to of those invited. The total number of invited guests is 18 by Linear equations

What was the total number of invited guests?

There are different methods of solving the problem, and we will use the following steps to get the solution of the problem: Let the total number of invited guests be x.Let's solve the problem with a step-by-step explanation.

Step 1: At the time Cedric arrived, two-thirds of the guests were already present.Let the number of guests present at the party when Cedric arrived be A. Therefore, A = (2/3)x

Step 2: Six more people arrived after Cedric got there. Therefore, the total number of guests after the six people arrived is A + 6.

Step 3: The total number of guests present was also x, which is the total number of guests invited. Therefore A + 6 = x.

Step 4: Substitute A = (2/3)x from Step 1 into A + 6 = x from Step 3 to obtain: (2/3)x + 6 = xStep 5: To solve for x, we will get rid of the fraction by multiplying every term by 3x.

Then we will simplify. 3x * (2/3)x + 3x * 6 = 3x * x Simplifying further  2x + 18 = 3x Subtracting 2x from both sides of the equation 18 = x.

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To determine the gross production of each industry to meet the market demand, we can set up a system of linear equations based on the given information and solve it using the Gauss-Jordan method.

Let's represent the gas production, oil production, and gasoline production as variables G, O, and A, respectively.

From the information provided, we can write the following equations:

1/5G + 2/5O + 1/5A = 100 (equation 1)

2/5G + 1/5O = 100 (equation 2)

1/5G + 1/5O = 100 (equation 3)

We can rearrange equation 2 to get G in terms of O: G = 250 - O/5. Then substitute this expression into equations 1 and 3. This will eliminate G, leaving only O and A in the equations.

After performing the necessary operations using the Gauss-Jordan method, we can find the values of O and A. The resulting values will represent the gross production of oil and gasoline, respectively, needed to meet the market demand.

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Answer:

a fraction with 100 as the denominator and the other fractions denominator 100 and input the other two numbers.

Step-by-step explanation:

Answer:

i only know 4 number only

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

The simplest form of 108/648 is 16

For the given condition 108 as a fraction of 648 will be 108/648.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have to write 108 as a fraction of 648, in simplified form.

p as the fraction of q in the simplified form can be written as,

=p/q

For the given condition we have to write the 108 as a fraction of 648 in the simplified form.

Write the fraction's numerator, hyphenate it, and then spell out the denominator to represent it verbally. The phrase p/q would be used to represent the fraction 108/648.

Thus, for the given condition 108 as a fraction of 648 will be 108/648.

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