Which fraction is less than 1/2, not equal to 3/10, greater than 0. 1 and not equal to 1/5

0. 3, 7/10, 1/2, 0,8
0. 6, 2/5, 0. 2, 1/10

The angles in the triangle are as follows:

m∠S = m∠Q = 58°

m∠T = 64°

The unknown angles in the triangle can be found as follows:

In the triangle STQ, ST = TQ and SD is perpendicular to TQ.

Therefore, let's find the unknown angles as follows:

Hence, base on ST = TQ, STQ is an isosceles triangle. Therefore,

m∠S = m∠Q

Therefore,

m∠Q = 180 - 90 - 32

m∠Q = 58 degrees

m∠S = m∠Q = 58 degrees

Finally,

m∠T = 180 - 58 - 58

m∠T = 64 degrees

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To find the average mark of the boy, we need to add up all of his scores and divide by the total number of subjects.

Average mark = (89% + 60% + 80% + 96% + 89%) / 5

= 414% / 5

= 82.8%

Therefore, the boy's average mark is 82.8%. It's worth noting that this calculation assumes that all subjects have equal weight, which may not always be the case in real-life scenarios. If different subjects have different weightings, the calculation of the average mark would need to take this into account.

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Answer:

6/55

Step-by-step explanation:

4 red + 7 blue = 11 marbles in total

P(first red) = 4/11.

we now have 10 marbles left. 3 of them are red.

P(second red) = 3/10

P(both red) = 4/11 X 3/10 = 12/110 = 6/55

Answer:

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

Let the dimensions be x and y.

The area is:

When sides have changed we get:

The new area is:

The difference in areas is:

It represents 17% increase.

Answer:

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

The first step involves addition of 7 to both sides and the second step involves division of both sides by 9.

They indicate the addition and division property of equality respectively.

Therefore correct choice is A.

V = 1000

Put the sides together: 4/6

Cube the sides (for volume you cube): 64/216

Then put the volume across from the side that has that volume: 64 x

----- = -----

216 3375

Cross multiply.

It should then equal this: 216x=216000

Divide by 216 and then you find x, which in other words the volume

x = 1000

[tex]D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0[/tex]

[tex]\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]

[tex]-4\not\in D[/tex]

Therefore [tex]x=2[/tex].

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex]= 19/25

What is proportion?

In statistics, proportion typically refers to the proportion or percentage of individuals or items in a population that have a specific characteristic or belong to a certain category.

In this scenario, the population proportion refers to the proportion of all Prime members' packages that arrive within two business days. The claim made by Amazon is that this population proportion is 85%.

Let's denote the population proportion as p.

a. The population proportion:

p = 0.85

The sample proportion, on the other hand, refers to the proportion of packages that arrived within two business days among the 25 students in the random sample. We can calculate the sample proportion using the number of students who claimed their packages arrived within two business days.

Let's denote the sample proportion as [tex]\hat p[/tex] (pronounced "p-hat").

Given:

Number of students in the sample (n) = 25

Number of students who claimed their packages arrived within two business days (x) = 19

b. The sample proportion:

[tex]\hat p[/tex] = x / n

[tex]\hat p[/tex] = 19 / 25

Therefore, the sample proportion is 19/25.

To summarize:

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex] = 19/25

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Answer: THE TOTAL AMOUNT TAKEN BY KEVIN IN MIXING, BAKING, AND COOLING THE MUFFINS IS 30 MINUTES.

Step-by-step explanation:

1. AMOUNT TAKEN BY KEVIN FOR MIXING=8MIN.

2. AMOUNT TAKEN BY KEVIN FOR BAKING=17 MIN.

3. AMOUNT TAKEN BY KEVIN FOR COOLING=5MIN.

IN TOTAL, (8+17+5)MIN. = 30 MIN.

Answer:

30 minutes

Step-by-step explanation:

8+7  =15 +5=20+ another 10 = 30

Answer:

6 books

6 packages of mints

It would cost $240.00 is carpet was purchased.

Step-by-step explanation:

If 2 books cost 16.40, then one book costs 16.40/2 = 8.20 each.

50/8.20 = 6.1 rounded. You cannot buy part of a book, so 6 books may be purchases.

If 2 packages of mints cost .69, then I package costs .69/2 = .345

2.25/ .345 = 6.5 rounded.  You cannot buy .5 of a package, so you can purchases 6 packages.

192/16 = 12

There are 12 square meters of flooring

12 x 20 = 240

Helping in the name of Jesus.

The probability that a student who passed the test did not complete the homework is 1 / 6.

This is a conditional probability problem and we are looking for the probability that a student who passed the test did not complete the homework.

Assuming event A is the event that a student passed the test and B is  event that a student completed the assignment.

We have :

P ( B' | A ) = P ( A ∩ B ' ) / P (A)

P ( B' | A ) = ( 3 / 27 ) / ( 18 / 27 )

P ( B' | A ) = 3 / 18

P (B' | A ) = 1 / 6

In conclusion, the probability that a student who passed the test did not complete the assignment is 1/6.

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To determine Cody's total revenue if he charges $20 for each mailbox, we need to know the number of mailboxes he sells. Let's denote the number of mailboxes as 'n'.

Cody's total revenue can be calculated by multiplying the price per mailbox ($20) by the number of mailboxes sold (n):

Total revenue = Price per mailbox × Number of mailboxes sold

Total revenue = $20 × n

Therefore, Cody's total revenue will be $20n, where 'n' represents the number of mailboxes he sells.

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For the sample of n sludge specimens is selected and the conclusion and the pH of each one is determined.

The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.

A) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

B) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

C) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

D) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

E) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

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[tex]|\Omega|=6+4+2=12\\|A|=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}\approx33.3\%[/tex]

Answer:

Step-by-step explanation: 6 + 4 + 2 = 12 (denominator)

Put 4 (blue beads) in numerator

4/12 reduces to 1/3

Final answer is 1/3

Answer:58

Step-by-step explanation:

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

To find the range of the following set of numbers: 68, 56, 40, 10, 51, 15

First, we need to find the largest and smallest numbers in the set.

The largest number is 68 and the smallest number is 10.

So, the range is:

68 - 10 = 58

Therefore, the range of the set of numbers is 58.

The solution to the given absolute value problems is:

1) x > 0 and x < 0

2) x > 0 and x < 0

3) y = |x| + 2

The absolute value which is also referred to as modulus | x | of a real number x is the non-negative value of x without any regard given  to its sign. For example, the absolute value of 4 is 4, and the absolute value of −4 is also 4. The absolute value of a number may be referred to as its distance from zero along real number line.

1) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

2) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

3) When we translate a function by two units upwards, then it means that we add 2 to the function.

Thus, we have:

y = |x| + 2

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The specific form of the function G(t) and the limits of integration would depend on the available data or assumptions about gas consumption during the specified months.

To express the average monthly U.S. gas consumption during the part of the year between the beginning of April and the end of September, we can set up an integral to calculate the average value of a function over a specific interval.

Let's denote the gas consumption as a function of time, G(t), where t represents the months from April to September. We'll integrate this function over the interval [April, September] to find the average gas consumption.

The integral that represents the average monthly U.S. gas consumption is:

(1 / (September - April)) ∫[April, September] G(t) dt

In this integral, G(t) represents the gas consumption in a given month, and the integration is taken over the interval from April to September. The average gas consumption is obtained by dividing the integral by the length of the interval (September - April).

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1. The value of x in the expression is 3

2. The value of y in the expression is -9/16

3. The value of d in the expression is -16 / 25

4. The value of x in the expression is 1

The value of x in the expression can be obtained as follow:

x + 5 = 3x - 1

Collect like terms

5 + 1 = 3x - x

6 = 2x

Divide both sides by 2

x = 6 / 2

Value of x = 3

The value of y in the expression can be obtained as follow:

5y/6 + 1 = -1y/2 + 1/4

Collect like terms

5y/6 + y/2 = 1/4 - 1

(5y + 3y)/6 = (1 - 4)/4

8y/6 = -3/4

Cross multiply

8y × 4 = 6 × -3

32y = -18

Divide both sides by 32

y = -18 / 32

Value of y = -9/16

The value of d in the expression can be obtained as follow:

20 + 3d = 36 + 28d

Collect like terms

20 - 36 = 28d - 3d

-16 = 25d

Divide both sides by 25

d = -16 / 25

Value of d = -16 / 25

The value of x in the expression can be obtained as follow:

4(x + 8) - 4 = 34 - 2x

Clear bracket

4x + 32 - 4 = 34 - 2x

4x + 28 = 34 - 2x

Collect like terms

4x + 2x = 34 - 28

6x = 6

Divide both sides by 6

x = 6 / 6

Value of x = 1

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In trapezoid MNPQ shown below, MN || QP ,

m < P = 85°

and

m < Q = 45°.

Find the measures of angles N and M.MNPQ is a trapezoid and therefore its opposite angles are supplementary.

We can use this fact and find the measures of angles N and M as follows: First, we notice that angles P and Q are supplementary since MN || QP. Therefore,

m∠Q + m∠P = 180°45° + m∠P = 180°m∠P = 180° - 45° = 135°.

We can use this information to find the measures of angles N and M. Let's call

m∠N = x

and

m∠M = y.

We can write two equations using the fact that opposite angles of a trapezoid are supplementary:

x + 135° = 180°

(opposite angles)

y + 45° = 180° (opposite angles)

Solving for x and y, we get:

x = 45° y = 135°

Therefore, m∠N = 45° and m∠M = 135°.

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Answer:

(x + 2)² + (y - 5)² = 13

Step-by-step explanation:

equation of circle is (x - a)² + (y - b)² = r²

where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.

(-2, 5) is centre.

radius = √((7 - 5)² + (1 - -2)²)

= √(4 + 9)

=√13

equation of our circle is (x - -2)² + (y - 5)² = (√13)²

(x + 2)² + (y - 5)² = 13

because their sides were corresponding.

answers:

1. aas (g).

2. sas (h).

3. sss (n).

4. asa (s).

5. hl (c).

6. none - aaa (t).

7. asa (0).

8. none - ssa (d).

9. aas (i).

10. sas (w).

11. sss (p).

12. hl (r).

13. asa (e).

The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

[tex]S = 4\pi r^2,[/tex]

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

[tex]V = (4/3)\pi r^3.[/tex]

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

[tex]dV/dt = d/dt [(4/3)\pi r^3].[/tex]

Using the power rule of differentiation, we get:

[tex]dV/dt = (4/3)\pi * 3r^2 * (dr/dt).[/tex]

Simplifying further, we have:

[tex]dV/dt = 4\pi r^2 * (dr/dt).[/tex]

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

[tex]100\pi = 4\pi r^2.[/tex]

Dividing both sides by 4π, we get:

[tex]r^2 = 25.[/tex]

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

[tex]dV/dt = 4\pi(5^2) * (0.3).[/tex]

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

The history class started at 2:35 pm

Step-by-step explanation:

To find the before time or starting time, we need to subtract 55 min from 3:30.

We cannot subtract 55 min from 30 min.

1 hour = 60 minutes. 3 : 30 can be written as 2: 90 minutes

Now subtract,

               2 : 90

          -      : 55

               2 : 35

The history class started at 2:35 pm

Answer:

(C) 297

Step-by-step explanation:

Write a proportion. 45 miles is to 5 gallons as x miles is to 33 gallons.

45 / 5 = x / 33

9 = x / 33

x = 297

The length of the line is given as follows:

B. 12 units.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the length of the line is given as follows:

l² = 10² + 6²

[tex]l = \sqrt{10^2 + 6^2}[/tex]

l = 12 units. (rounded up).

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The equivalent expressions are 32, 27, 64, 36, 1/16, 1/9 respectively.

Given are the numbers we need to simplify them,

2⁵ = 2·2·2·2·2 = 32

3³ = 3·3·3 = 27

4³ = 4·4·4 = 64

6² = 6·6 = 36

(1/2)⁴ = 1/2·1/2·1/2·1/2 = 1/16

(1/3)² = 1/3·1/3 = 1/9

Hence the equivalent expressions are 32, 27, 64, 36, 1/16, 1/9 respectively.

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10 liters of water was drained out of the tank in one minute and it would take 80 minutes to completely drain the water

This is the slope of the graph

From the graph, we have

(x, y) = (0, 800) and (40, 400)

So, we have

Slope = (400 - 800)/(40 - 0)

Evaluate

Slope = -10

This means that 10 liters of water was drained out of the tank in one minute

From (a), the equation of the line would be

y = -10x + 800

When the water is completely out, we have

-10x + 800 = 0

So, we have

x = 80

This means that it would take 80 minutes

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Using the given information, the measure of each exterior angle in the polygon is 20°

From the question, we are to determine the measure of each exterior angle in the polygon

Let the number of sides in the polygon be n.

Sum of exterior angles in a polygon = 360°

Thus,

Measure of one exterior angle = 360°/n

From the given information,

The measure of each exterior angle is 12.5% of the measure of each interior angle

The measure of each interior angle = (n - 2)180° / n

Thus,

360°/n = 12.5% of (n - 2)180° / n

360° = 12.5% of (n - 2)180°

Solve for n

360° = 0.125 × (n - 2)180°

360° =  (n - 2)22.5°

360° = 22.5n° - 45°

22.5n° = 360° + 45°

22.5n° = 405°

n = 405°/22.5°

n = 18

Then,

Measure of each exterior angle = 360° / 18

Measure of each exterior angle = 20°

Hence, the measure of each exterior angle is 20°

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