54 is 120 percent of what number ?

Given:-

To find:-

Wheather the given sides form a valid triangle.

So now let,

To check we use the condition,

Substituting the values we get,

In the above condition 12+7>20 is wrong.

So the condition fails and the given sides doesnt form a triangle.

7 out of every 500 Americans are aged 13-17 years generation are vegetarian

Thus the ratio of the vegetarian is 7 : 500

In a group of 350,

Let x be the number of people who are vegetarian

So, the ratio out of 350 who are vegetarian are : x : 350

SInce the ratio is same so:

So, the number of people who are vegetarian out of 350 people is 4 people

Using the z-distribution, it is found that:

a. The 90% confidence interval to estimate of the percentage of yellow peas is: (34.04%, 41.58%).

b. The correct option is: Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.

The bounds of a confidence interval of proportions is given according to the equation presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the parameters are described as follows:

The confidence level is of 90%, hence the critical value is z = 1.645, using a z-distribution calculator.

The values of the sample size and of the estimate are given as follows:

[tex]n = 447, \pi = \frac{169}{447} = 0.3781[/tex]

Hence the lower bound of the interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 - 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.3404[/tex]

The upper bound is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 + 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.4158[/tex]

As a percentage, the interval is given as follows: (34.04%, 41.58%).

The confidence interval does not contain 0.25, hence the true percentage would not be equal to 25%, contradicting the expectation.

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The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.

The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.

a) Then, the average velocities are determined below:

Case i)

u = [f(1.05) - f(1)] / (1.05 - 1)

u = (18.748 - 18.1) / 0.05

u = 12.96 m / s

Case ii)

u = [f(1.01) - f(1)] / (1.01 - 1)

u = (18.232 - 18.1) / 0.01

u = 13.20 m / s

Case iii)

u = [f(1.005) - f(1)] / (1.005 - 1)

u = (18.166 - 18.1) / 0.005

u = 13.20 m / s

Case iv)

u = [f(1.001) - f(1)] / (1.001 - 1)

u = (18.113 - 18.1) / 0.001

u = 13 m / s

The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.

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Given:

length of the piece of string = 3/4 inches

length of the piece that we need = 1/8 inches

The number of smaller piece that we can get from the original piece of string can be calculated using the formula:

Applying this formula:

If the number of pieces is represented as n:

Answer:

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The original number is 13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 4 is an equation.

We have,

Let the number be K.

K thinks of a number, then doubles the number, and then multiplies the result by 3.

This can be written as:

(2 x k) = 2k ____(1)

3 x (2k) = 6k ____(2)

If her final number is 65 more than her original number can be written as:

6k = 65 + k _____(3)

From (3) we get,

6k = 65 + k

Subtract k on both sides.

6k - k = 65 + k - k

5k = 65

Divide both sides by 5.

5k / 5 = 65 / 5

k = 13

Thus,

The original number is 13.

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Answer:

x=13

Step-by-step explanation:

50+3x=89

89-50=3x

39=3x

13=x

Recall that the graph of the cosine function is:

Now, notice that the given graph is the above graph but with a midline

and amplitude equal to 4. The frequency is also different.

Therefore, the equation of the function given in the graph is:

We have to solve this inequality:

We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.

When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:

The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:

Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.

We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).

Answer: (-∞, -3.25) ∪ (0.75, ∞)

It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:

And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:

If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.

In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.

Given:

Amount of chocolate chips needed = 30 ounces

Amount of chocolate you have already = 8 ounces

Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.

To write the inequality, we have:

8 + x ≥ 30

Where x represents the ounces of chocolate chips you need to buy.

Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:

8 + x ≥ 30

ANSWER:

8 + x ≥ 30

Given:

At 10 gallons, the car is able to cover 310 miles.

Find: At 1 gallon, the car can travel ____ miles.

Solution:

First, let's fill in the number line with the given values.

To solve for the question mark at 1 gallon, simply divide 310 by 10.

Hence, the car uses gas at 31 miles per gallon.

Answer:

[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]

Graphs attached

Step-by-step explanation:

Your inverse function is correct.  So not sure what additional information you need

I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool

We have:

x = total pens

n = number of black pens

so:

and for black pen:

answer: 2 black pens

Given:

The function is,

Explanation:

Determine the function for f(x + h).

Determine the value of expression.

So exprression after simplification is,

-2h - 4x - 1

IN order to find the area of the shaded region, proceed as follow:

calculate the area of the right triangle:

A = b·h/2

A = (21 yd)(34 yd)/2 = 357 yd²

next, calculate the area of the circle:

A' = π r²

A' = (3.1415)(7 yd)² = 153.93 yd²

next, subtract the area of the circle to the area of the rectangle:

AT = A - A' = 357 yd² - 153.93 yd²

AT = 203.07 yd²

Hence, the area of the shaded region is 203.07 yd²

Answer

Option C is correct.

The roots of the given function include

2, -3i, (4 + i), (4 - i)

Explanation

To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression

The expression is

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

Starting with 2

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(2) = 2⁵ - 10(2)⁴ + 42(2)³ - 124(2)² + 297(2) - 306

= 32 - 160 + 336 - 496 + 594 - 306

= 0

So, 2 is a root

-3i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(-3i) = (-3i)⁵ - 10(-3i)⁴ + 42(-3i)³ - 124(-3i)² + 297(-3i) - 306

= -243i - 810 + 1134i - 1116 - 891i - 306

= 0

So, -3i is also a root

4 + i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(4 + i) = (4 + i)⁵ - 10(4 + i)⁴ + 42(4 + i)³ - 124(4 + i)² + 297(4 + i) - 306

= 0

So, we know that the right root, when inserted and expanded will reduce the expression to 0.

4 - i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(4 - i) = (4 - i)⁵ - 10(4 - i)⁴ + 42(4 - i)³ - 124(4 - i)² + 297(4 - i) - 306

= 0

Inserting any of the other answers will result in answers other than 0 and show that they aren't roots/zeros for this expression.

Hope this Helps!!!

Answer:

Step-by-step explanation:

A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.

So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.

To determine the exact value of sin A we get -2/√13

What is determinant?

the determinant is a scalar of value that is a function of to the  entries of a square matrix. It is  allows characterizing of  some  properties of to the  matrix and the linear map of represented by the matrix.

It is a scalar value which is associated with the square matrix.

Sol-Cos A =3/√13

angle A is not in quadrant I

So angle A is in quadrant IV

Thus,

Sin A =-√(√13)^2-3^2/√13

           =-√13-9/√13

           =-√4/√13

           =-2/√13

Thus the answer is -2/√13.

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The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.

A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).

During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.

Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.

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Complete Question:

Which statement best completes the diagram?

A. British leaders limit the ability of colonists to expand westward.

B. British merchants refuse to buy raw materials from the colonies.

C. British military forces are ordered to leave North America.

D. British leaders end policies that strictly controlled the colonies.

The average rate of change of the function is the average rate at which one quantity is changing with respect to another.

Average rate of change = (y2 - y1)/(x2 - x1)

y represents the output values and it is also called f(x)

x represents the input values

For the given interval,

for f(- 1), x = -1 and f(x) = 8

For f(1), x = 1, f(x) = 4

Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2

Average rate of change = - 2

Recalling the laws of exponents:

So, for the number 3^5 times 3^4, we have:

Therefore, the answer is the option b) 3^9.

What we have is a fractional division, this is following expression

For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator

In conclusion after splitting and simplifying this, the answer is 9/5

An equation of line with a slope of 1/3 and containing the point (-4,7) is

y = 1/3 x + 25/7

In this question, we have been given

slope (m) = 1/3

and a point (-4, 7)

We need to find an equation of a line with a slope of 1/3 and containing the point (-4,7)

Using the formula for the slope-point form of equation of line,

y - y1 = m(x - x1)

y - 7 = 1/3(x + 4)

y - 7 = (1/3)x + 4/3

y = (1/3)x + 4/3 + 7

y = 1/3 x + 25/7

Therefore, an equation of line with a slope of 1/3 and containing the point (-4,7) is y = 1/3 x + 25/7

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The exponential expression as required to be chosen is; 10⁴.

The expanded form of the expression is; 10 × 10 × 10 × 10.

The standard form of the expression is; 10,000.

It follows from the task content that the exponential expression is to be written in expanded and standard form.

Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.

An example of such exponential expression is therefore;

10⁴.

Hence, to write the expression in expanded form; it is written as a product of factors as follows;

10 × 10 × 10 × 10

Also, the expression can be written in standard form as the result of the multiplication above;

= 10,000.

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Answer:

Option 2

Step-by-step explanation:

hope this helps

EXPLANATION

Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:

Where the whole number is 156 and the percentage is 150%:

In conclusion, the solution is 234

Any number raised to the power of zero equals 1, then

then, we need to substitute the value 10 in the variable s. It yields,

Then, the answer is

that is, 1 / 100.

By theorem, we will have that m

m

=> m

=>2m

Then, we replace values and solve:

2m m

So, we have that m