Solve the equation for a. 10= 1/5a+2

Answer:

8,9,11

Step-by-step explanation:

A-1

B-2

C-3

D-4

E-5

F-6

G-7

H-8

I-9

J-10

K-11

L-12

M-13

N-14

O-15

Answer:

A. y=-5/3x+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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About 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).

To determine the percentage of students who failed the course, we need to find the proportion of students who scored 59.99 or lower on the exam, and then convert this proportion to a percentage.
First, we need to standardize the cutoff score of 59.99 using the formula:
z = (x - μ) / σ
where x is the cutoff score, μ is the mean, and σ is the standard deviation.
Plugging in the values given in the question, we get:
z = (59.99 - 73) / 11 = -1.18
Next, we look up the proportion of scores below a z-score of -1.18 in a standard normal distribution table (or use a calculator or software). This proportion is approximately 0.1190.
Therefore, about 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).
In other words, roughly 12% of the students failed the course based on the given criteria.

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dy/dx by implicit differentiation of sin(x) cos(y) = 7x − 4ydy/dx is (7 - cos(y) × cos(x)) / (sin(x) × sin(y) - 4).

To find dy/dx using implicit differentiation for the given equation sin(x)cos(y) = 7x - 4y, follow these steps:

1. Differentiate both sides of the equation with respect to x, remembering to apply the chain rule for trigonometric functions and implicit differentiation for y terms.

d/dx [sin(x)cos(y)] = d/dx [7x - 4y]

2. Differentiate each term individually:

d/dx [sin(x)] × cos(y) + sin(x) × d/dx [cos(y)] = 7 - 4 × d/dx [y]

3. Apply the chain rule for the cos(y) term:

cos(y) × d/dx [sin(x)] + sin(x) × (-sin(y) × dy/dx) = 7 - 4 × dy/dx

4. Simplify the equation:

cos(y) × cos(x) - sin(x) × sin(y) × dy/dx = 7 - 4 × dy/dx

5. Solve for dy/dx:

sin(x) × sin(y) × dy/dx - 4 × dy/dx = 7 - cos(y) × cos(x)

Factor dy/dx:

dy/dx × (sin(x) × sin(y) - 4) = 7 - cos(y) × cos(x)

Finally, divide both sides by (sin(x) × sin(y) - 4) to isolate dy/dx:

dy/dx = (7 - cos(y) × cos(x)) / (sin(x) × sin(y) - 4)

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Answer:

72 + 7x + 24 = 180

7x + 96 = 180

7x = 84

x = 12

Step-by-step explanation:

4x³ = 36x

4x³ - 36x = 0

4x(x² - 9) = 0

4x(x + 3)(x - 3) = 0

Hence x = 0, x = -3 or x = 3.

The measures of the angles are: 64°  and 26°.

Recall: Two angles are complement of each other if they add up to the sum of 90° .

Thus,

Let \(x\) represent the first angle

The second angle = \((x-38)^{o}\)

Therefore:

\(x + (x - 38) = 90\)

Solve for x

\(x + x - 38 = 90\\2x - 38 = 90\\2x - 38 + 38 = 90 + 38\\2x = 128\\x = 64\)

The first angle, x, is 64°

The second angle = \(x - 38\)

Plug in the value of x

\(= 64 - 38\\= 26\)

Therefore, the measures of the two angles are 64°  and 26°

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It is appropriate to take a pulse by counting the heart rate for 30 seconds and multiplying by two when a rapid or irregular pulse is suspected, or when it is difficult to count the pulse for a full minute.

Counting the heart rate for a full minute is the most accurate way to determine the heart rate. However, there are situations when it may be more appropriate to count the heart rate for 30 seconds and multiply by two.

For example, if a person's pulse is rapid or irregular, it may be difficult to accurately count the pulse for a full minute. In such cases, it may be more appropriate to count the pulse for 30 seconds and multiply by two to get an estimate of the heart rate.

Another situation where it may be appropriate to count the pulse for 30 seconds is when time is limited, such as in an emergency situation. In such cases, counting the pulse for 30 seconds and multiplying by two can provide a quick estimate of the heart rate.

However, it is important to note that counting the pulse for 30 seconds and multiplying by two may not be as accurate as counting the pulse for a full minute.

Therefore, if possible, it is recommended to count the pulse for a full minute to obtain the most accurate measurement of the heart rate.

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Using trigonometric identity, cos(A-B) is:

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If sin A = 1/3 and A terminates in Quadrant 1. All trigonometric functions in Quadrant 1  are positive

sin A = 1/3 (sine = opposite/hypotenuse)

adjacent = √(3² - 1²)

               = √8 units

cosine = adjacent/hypotenuse. Thus,

\(cos A = \frac{\sqrt{8} }{3}\)

If cos B = 2/3 and B terminates in Quadrant 4.

opposite = √(3² - 2²)

                = √5

In  Quadrant 4, sine is negative. Thus:

\(sin B = \frac{\sqrt{5} }{3}\)

We have:

cos(A-B) = cosA CosB + sinA sinB

\(cos (A-B) = \frac{\sqrt{8} }{3} * \frac{2}{3} + \left \frac{1}{3} * \frac{\sqrt{5} }{3}\)

\(cos (A-B) = \frac{2\sqrt{8} }{9} + \left\frac{\sqrt{5} }{9}\)

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

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The lab should budget for the next year's rat orders be $63,700.00.

The lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.

The prices for 100 rats follow the given distribution:

Price ($): 10.00, 12.50 , 15.00

Probability: 0.35 0.40 0.25

Mean price per 100 rats can be calculated using the expected value formula,

μx = ∑ [ xi × P(xi) ]

where

μx = mean value,

xi = price,

P(xi) = probability of xi

Mean price per 100 rats:

μx = (10.00 × 0.35) + (12.50 × 0.40) + (15.00 × 0.25)

μx = 3.50 + 5.00 + 3.75

μx = $12.25

The mean price per 100 rats is $12.25.

Hence, the cost of 100 rats is $12.25.

Therefore, the lab should budget for the next year's rat orders:

$12.25 × 100 × 52

= $63,700.00

The lab should budget for the next year's rat orders be $63,700.00.

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Answer:

The answer is "C. 84"

Step-by-step explanation:

Divide 12 by 3 which gets 4. Then, multiply 4 by 21.

The statement is true. There exists a real number x such that for every real number y that is not negative, x is greater than y.

The statement is expressing the existence of a real number x that is greater than any other real number y, excluding the negative real numbers. In other words, there is at least one positive real number that is larger than any non-negative real number.

To prove this, we can consider x = 1. For any non-negative real number y, we have x = 1 > y. Therefore, the condition of the statement is satisfied, and the statement is true.

In general, this statement reflects the fact that among all the non-negative real numbers, there is always a larger positive real number. This can be visualized on a number line where the positive real numbers extend infinitely to the right, surpassing any non-negative real number.

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The ounces of cheese Ellie uses to make tacos is 2

What is a unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Calculation :

1 pound = 16 ounces

Total cheese Ellie has = \(\frac{2}{8}\) pound

Cheese required to make tacos = \(\frac{2}{8}\)×\(\frac{1}{2}\) = \(\frac{1}{8}\) pounds

Ounces of cheese required to make cheese are \(\frac{1}{8}\) × 16 = 2 ounces

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Answer:

1

Step-by-step explanation:

Using the general exponent rule, that

\(a^{0}\) = 1, so

\(7^{0}\) = 1

Answer:

D) $115

Step-by-step explanation:

15x + 40 = y

15 (5) + 40 = 115

15 x 5 = 75

75 + 40 = 115

Answer:

D is the answer

Step-by-step explanation:

15x5=75

75+40=115

Answer:

5.236

Step-by-step explanation:

Answer:

d. 325

If 20 percent of the animals are amphibians and yiu are trying to find the total amound of numbers in the zoo you first have to realize that 20% is equal to 1/5. Then since you are trying to find the total and not decrease the number, you get the reciprical of 1\5, which is 5/1 and multiply it by 65/1 . 5 × 65 equals 325.

Answer:

the value of Celsius temperature is 100

o

 when Fahrenheit temperature is 212

o

.

Step-by-step explanation:

Answer:

Step-by-step explanation:

he height of the storage unit is equal to twice its radius (since the diameter is twice the radius), so the height is 2 x 8 = 16 feet.

The storage unit is in the shape of a cylinder, so we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height:

V = π(8^2)(16)

V = π(64)(16)

V = 3,218.69 cubic feet (rounded to two decimal places)

Therefore, the volume of the storage unit is approximately 3,218.69 cubic feet.

According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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The sum of the three even positive integers is 18.

A whole number that is greater than zero is what is meant by the term "positive integer." All counting numbers are included in the set of positive integers (that is, the natural numbers).

A set (collection of objects) whose components are numbers is known as a number set. All whole numbers on the number line to the right of zero are included in the set of positive integers. The Z, the superscript asterisk (*), and the subscript plus sign (+) all stand for the set of all positive numbers.

The  Z was chosen because it derives from the German word for numbers and signifies integers in general (positive, negative, and zero) (Zahlen). The plus sign indicates that negative numbers are eliminated, while the asterisk indicates that zero is excluded from the set of integers.

here it is given in the question that,

the product of the first and the third is 8 more than 4 times the second,

then Let x,x+2,x+4

Product of 1st nd 2nd= x*(x+4)

Therefore,

x*(x+4)= 4(x+2)+8

x^2+4x= 4x+8+8

x^2=16

x=4

Three consecutive positive integers is 4,6,8

Sum of three consecutive integers=4+6+8=18

Hence, The sum of the three even positive integers is 18.

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The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

\(h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}\)

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You can add the distance she travelled upwards to her new distance to get her old distance.

Essentially, 21.6 + 61.9 = 83.5.

This means she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.

Answer: she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.

Step-by-step explanation:

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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2x + 1 = 5x - 44

3x = 45

x = 15

Thus PQ = 2*(15) + 1 = 31

PQ = 31

Answer:

x=71 degrees

Step-by-step explanation:

The value of x from the given equation is 7.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is ∛(4x-1)-7=-4.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, ∛(4x-1)-7=-4

∛(4x-1)=3

Cubing on both side of an equation, we get

(∛(4x-1))³=3³

4x-1=27

4x=28

x=7

Therefore, the value of x is 7.

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Answer:

Step-by-step explanation:

4 + 6z - 15 = 6z - 11

2(3z -4) = 6z - 8

Here's the tricky part. You are only taking 8 away from 6z

The result is going to be larger than when you take away 11 from 6x

Try it

suppose z = 7

6*7 - 8 = 42 - 8 = 34

6*7 - 11 = 42 - 11 = 31

34>31