proverbs 21:5 encourages us to be diligent in our work. what is given as an outcome of practicing diligence? luoa

The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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Answer:

approx. 68%

Step-by-step explanation:

this is a normal distribution.

in a normal distribution, approximately 68% of the data is within one standard deviation of the mean (we also have 95% of data is within two standard deviations of the mean, and 99.7% of data is within three standard deviations of the mean).

one standard deviation in our question is 113.

315 is one standard deviation below the mean because 428 - 113 = 315.

541 is one standard deviation above the mean because 428 + 113 = 541.

so we expect approx. 68% of the data to be between 315 and 541.

Answer:

15(a)(b)(c)

Step-by-step explanation:

I don't know what your asking for

Answer: Step 4

Step-by-step explanation:

1. Define variable x as student signatures still needed  (Correct)

\(2)\ \dfrac{x+82}{426}\)              (Correct)

3. 25% = 0.25      (Correct)

\(4)\ \dfrac{x+82}{426}\leq 0.25\)      (Error)!

The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).

Answer:

In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.

                                         ¯\_     _/¯

      ( ﾉ ﾟｰﾟ)ﾉ                                                                                     ＼(ﾟｰﾟ＼)

The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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Answer:

Earlier we found that:

If we put y on one side by itself the equation is:

This is same as the equation of the red line.

Any right triangle using this line will be similar to each other.

It's easier

We know the slope formula for origin crossing line

Here

m is 2

So

Answer:

y = -2x + 7

Step-by-step explanation:

If you roll a fair 6-sided die, each of the 6 outcomes (1, 2, 3, 4, 5, 6) is equally likely, with a probability of 1/6. This means that the probability of rolling a particular number, such as 6, is 1/6.

Rolling the die 4 times gives 6 to the power of 4 = 1296 possible outcomes. The probability of not rolling a 6 in one roll is 5/6, so the probability of not rolling a 6 in four rolls is (5/6)^4. This can be calculated as: 5/6 × 5/6 × 5/6 × 5/6 = 625/1296. To find the probability of rolling at least one 6, we can use the principle of imputed probability.

This means that the probability that an event will occur is equal to 1 minus the probability that the event will not occur. In this case, the probability of rolling at least one 6 is 1 - (the probability of rolling no 6). So 1 - 625/1296 = 671/1296 = about 0.518.

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The difference between the area of the garden and the perimeter is \(x^{2}\) -10x + 21

A square is a polygon with 4 sides and 4 angles.

The four angles are right angles and it has four lines of symmetry.

The diagonals form right-angled triangles with equal adjacent sides.

The side of the squares are equal = x - 3

so that perimeter = 4 x side of the square

                           = 4 x ( x - 3)

                            = 4x - 12

Area of the square = side of square x side of square

                                = (x - 3) x ( x - 3)

                                 = \(x^{2}\) -3x -3x + 9

                                 = \(x^{2}\) -6x + 9

Difference between the area of garden and the perimeter of the garden =  \(x^{2}\) -6x + 9 - (4x -12)

=   \(x^{2}\) -6x -4x +9 + 12

=   \(x^{2}\)  -10x + 21

In conclusion the difference between the area of the square garden and its perimeter is   \(x^{2}\)  -10x + 21

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Answer:

28.125 degrees

Step-by-step explanation:

3/8 of 45 is 16.875

45-16.875=28.125

Draw a plane, showing the three (non-linear) points that define it.\(\boxed{\large{\bold{\blue{ANSWER~:) }}}}\)

See this attachment

Answer:

\(\frac{1}{32^{7} }\)

Step-by-step explanation:

\(32^{-1}\)÷\(32^{6}\)

First is combine exponents.  -1 + -6=-7

Next is to multiply. The answer becomes,  

=\(\frac{1}{32^{7} }\)

Answer:

whats the question

Step-by-step explanation:

Answer:

[45]

hope this helps

Answer:

4.0

Step-by-step explanation:

Given that

3.9931

Now rounded to one decimal places

3.9931 = 4.0

So the above value would be rounded to one decimal places after rounded off it comes 4.0

Check the picture below.

Inverse function of f(x) 8√ x for x > 0 is  f^-1(y)is 8√y for y > 0. The inverse of a function is a function that "undoes" the original function.

In order for a function to have an inverse, it must be one-to-one, meaning that each input value must correspond to a.

if the original function maps input values to output values, the inverse function maps the output values back to the input values.

To find the inverse of the function f(x) = 8√x for x > 0, we can use the following steps:

Replace f(x) with y. This gives us y = 8√x for x > 0.

Replace x with f^-1(y). This gives us f^-1(y) = 8√y.

Solve for y. To solve for y, we can square both sides of the equation:

y^2 = (8√y)^2

y^2 = 64y

y^2 - 64y = 0

y(y - 64) = 0

This equation has two solutions: y = 0 or y = 64. However, the original function is only defined for x > 0, so the inverse function is only defined for y > 0. This means that the inverse function is f^-1(y) = 8√y for y > 0.

Therefore, the inverse of the function f(x) = 8√x for x > 0 is f^-1(y) = 8√y for y > 0.

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Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency using algebra.

First, let's calculate how much money Kathy will withdraw in pounds and euros. She wants to withdraw half of her $300$ US dollars in each currency, so that would be $150$ US dollars for each.

To find the amount in pounds, we can divide $150$ US dollars by the exchange rate of $1.64$ USD per pound:

Amount in pounds = $\frac{150}{1.64} \approx 91.46$ pounds.

To find the amount in euros, we can divide $150$ US dollars by the exchange rate of $1.32$ USD per euro:

Amount in euros = $\frac{150}{1.32} \approx 113.64$ euros.

Rounding both amounts to the nearest whole number, Kathy will have approximately $91$ pounds and $114$ euros.

To determine how many more euros than pounds she will have, we subtract the amount in pounds from the amount in euros:

$114$ euros - $91$ pounds = $23$ more euros than pounds.

Therefore, Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer: Imaginary number

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

(5 / 12) * (1 hour) =25 minutes

Both linear functions will intersect at the same point, meaning, the x y coordinates are the same. So you have to equate both equations and clear the value of x:

Now using either function you have to calculate the value of the corresponding y-coordinate, for explanation purposes I'll do it with both:

As you see, using either function to calculate the y-coordinate is the same.

The functions intersect in point (-3/5, 11/5)

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

The statement "There is a strong positive correlation between studying and grades" best describes the meaning of a correlation coefficient of 0.93. The correct answer is A.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of 0.93 indicates a strong positive correlation between studying and grades.

A positive correlation means that as the value of one variable (study time) increases, the value of the other variable (grades) also tends to increase. A correlation coefficient close to +1 indicates a strong positive relationship, suggesting that an increase in study time is associated with higher grades. e correct answer is A.

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Answer:

8

Step-by-step explanation:

To find f(1), substitute x = 1 into the given function f(x)

(output values from an absolute value become positive)

\(f(1) = |1-4|+5\\f(1)=|-3|+5\\f(1)=3+5\\f(1)=8\)

Hope this helps!

Answer:

mean: 28.73

median: 30

Mode: 42

Range: 36

Step-by-step explanation:

Took the test on edge2020

Answer:

Students from Grover Middle School are recycling aluminum cans. The table shows the total number of cans brought in each school day for a period of six weeks. They collected a total of 862 cans. Use the drop-down menus to define the terms.

Mean:  

✔ 28.73

Median:  

✔ 30

Mode:  

✔ 42

Range:  

✔ 36

Step-by-step explanation:

Correct answers

The measure of the minor arc intercepted by the inscribed angle is 228 degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

In a circle, the measure of an inscribed angle is equal to half the measure of the intercepted arc.

Therefore, if the inscribed angle measures 114 degrees, then the minor arc it intercepts has a measure of twice that, or:

2 × 114 = 228 degrees

Hence, the measure of the minor arc intercepted by the inscribed angle is 228 degrees.

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The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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