Y varies inversely as x: y=13, when x=3

Answer:

83°

Step-by-step explanation:

Fund the diagram attached. The sum of the ange in the triangle given is 180°, hence;

2x+1+x+15+x = 180

Collect like terms

2x+x+x+1+15 = 180

4x+16 = 180

4x = 180-16

4x = 164

x= 164/4

x =41

Out of the angles the largest angle is 2X+1

Get the largest angle;

2x+1 = 2(41)+1

=82 +1

= 83°

Hence the measure of the largest angle is 83°

Answer:

Substitute x for 8

23-8=15

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Answer:

Step-by-step explanation:

?

Answer:

a) 53.33 miles per hour

b) 1.7 pages per minute

c)2.25 $ per avocado

Step-by-step explanation:

a) 320/6 = 53.33333

b) 68/40 = 1.7

c) 27 /12 = 2.25

Answer:

Step-by-step explanation:

16:45 + 14:00

= 30:45

30:45 - 14

= 06:45.

Two or more expressions with an equal sign is Equation.-76(x-61)=x-89 is the equation for −76 times the difference between a number and 61 is equal to the number plus −89.

Two or more expressions with an equal sign is called as Equation.

The sentence −76 times the difference between a number and 61 is equal to the number plus −89. We have to express in the form of equation.

−76 times the difference between a number

Let the number be 'x', times means multiplication and difference is subtraction.

-76(x-61)

the number plus −89

x+(-89)

−76 times the difference between a number and 61 is equal to the number plus −89.

-76(x-61)=x+(-89)

-76(x-61)=x-89

Therefore -76(x-61)=x-89 is the required equation.

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Answer:

\(y' = 5x + 4\)

Step-by-step explanation:

Given

\(f(x) = \frac{1}{5}x - \frac{4}{5}\)

Required

The inverse relation

\(f(x) = \frac{1}{5}x - \frac{4}{5}\)

Rewrite as:

\(y = \frac{1}{5}x - \frac{4}{5}\)

Swap x and y

\(x = \frac{1}{5}y - \frac{4}{5}\)

Multiply through  by 5

\(5x = y - 4\)

\(y = 5x +4\)

Rewrite the new function as:

\(y' = 5x + 4\)

This question is incomplete, the complete question is;

You have two strains of mice, one is inbred and the other is genetically heterogeneous. You examine weight differences for the mice when they are raised in the same environment. If the total variance for the inbred strain is 0.5 square ounces and total variance for the heterogeneous strain is 0.7 square ounces, what is the relative amount of variance due to genetic variation ?

Multiple Choice

A. 0.2 square ounces

B. 0.5 square ounces

C. 0.7 square ounces

D. 1.2 square ounces

Answer:

Option  A) 0.2 square ounces  is the correct answer

Step-by-step explanation:

Given that;

two strains of mice where raised in the environment and while one is inbred, the other is genetically heterogeneous.

The total variance for the inbred strain =  0.5 square ounces

total variance for the heterogeneous strain = 0.7 square ounces

relative amount of variance due to genetic variation = ?

The relative amount of variance due to genetic variation can be gotten by taking the difference of the total variance of both mice

so;

relative amount of variance due to genetic variation = variance for the heterogeneous strain - total variance for the inbred strain

we substitute our values

relative amount of variance due to genetic variation = 0.7 - 0.5

relative amount of variance due to genetic variation = 0.2 square ounces.

Therefore Option  A) 0.2 square ounces  is the correct answer

"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.

Relation:

In math relation means the relationship between sets of values of ordered pairs.

Given,

Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.

As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.

Here we have to identify the type of relation between a an b.

Here we have given that the relation a uniquely determines the value in b.

So, this type primarily refers the dependency of the relation.

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Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Answer:

The probability that at least one of the three smoke detectors functions properly = 0.996625

Step-by-step explanation:

Given that:

a certain brand of smoke detector functions properly 85 percent of the time

Let X represent the certain brand of smoke detector

X = 85%

X = 0.85

Let the probability that at least one of the three smoke detectors functions properly be P(Y)

P(Y) = 1-  (1 - X)³

P(Y) =1 -  (1 - 0.85)³

P(Y) = 1 -  0.003375

P(Y) = 0.996625

∴

The probability that at least one of the three smoke detectors functions properly = 0.996625

Answer:

rational numbers

Step-by-step explanation:

According to the binomial distribution, there is a 0.128 = 12.8% chance that it will take her precisely 3 pushes to start the mower.

It has a 20% chance of starting on any given pull, therefore

Item

a:This probability is P(X = 0) when n = 2, multiplied by 0.2, which is the probability that it starts on the third, and it is that it doesn't start on the first two. Hence:

It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.

Item b:When n = 10, this probability is none on the first 10 and is hence P(X = 0):

Her chances of needing more than 10 pushes to start the mower are 0.1074, or 10.74%.

It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.

Item b:On the first, there is no chance in this.

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Answer: 147.2

Step-by-step explanation:

(8+15) = 23

23 x 6.4= 147.2

Answer: 147.2

Step-by-step explanation: 8+15= 23 so 23*6.4 is 147.2

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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ANSWER

33.5 cubic inches

EXPLANATION

This is a cone with radius r = 2 in and height h = 8 in. The volume of a cone is,

Replace the known values and solve,

Hence, the volume of the cone is 33.5 in³, rounded to the nearest tenth.

Answer:

3 > x * 8 = 6

Step-by-step explanation:

three (3) more than ( > ) the product ( * ) of a number (x) and 8 (8) is (=) 6

Hope this helps :)

Answer:

x=\(\frac{3}{8}\)

Step-by-step explanation:

The sentence in number form is 8x+3=6

Solving for x.

You use inverse operations to cancel out the 3 on the left side.

What you do on one side of the equal sign you must do to the other side.

8x+3-3=6-3

Thus, you are left with 8x=3.

The inverse operation you use next to get x by itself is division. This cancels out  the 8 on the left.

\(\frac{8x}{8}\)=\(\frac{3}{8}\)

You are left with x=\(\frac{3}{8}\)

We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =\(10^1\) + 2

Therefore, we can write 98 in exponential form as:

98 = \(10^3\)

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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Answer:

8x+64

Step-by-step explanation:

The area of a parallelogram is found by multiplying its base length by its perpendicular height (marked by red line):

(8)(x+8)

(8)(x)+(8)(8)

8x+64

Step 1: Calculate the total number times the experiment was carried out

Step 2: Write out the formula for probability of an event to occur

Step 3: Find the experimental probability of landing on B

Hence, the experimental probability of landing on B is 8/30

Answer:

7

Step-by-step explanation:

-6 + 13

7

-*-=+

The answer is 12, 15, 30

A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125

ii)  solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.

C) See the description of the solution below.

Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.

The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:

0.80b + 65 ≤ 125

Now we can solve for b:

0.80b + 65 ≤ 125

0.80b ≤ 125 - 65

0.80b ≤ 60

b ≤ 75

Therefore, the dance committee can buy up to 75 balloons to stay within their budget.

To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.

The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.

As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.

Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.

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Full Question:


Since the above question is incomplete, it appears you are referring to the question below.


The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.

A) Write and solve an inequality to show the number of balloons that the dance committee could buy.

B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.

Answer:

7 to 10 or 70%

Step-by-step explanation: