Out of 1,000 students, 80 were asked by random sampling what color they would prefer for their first car. Their responses are shown in the table below.

Answer:

The expression that equivalent to  \(\frac{12x^{4}}{4x^{16}}\)  is 3\(x^{4-16}\) ⇒ C

Step-by-step explanation:

Let us revise some rule of exponents

Let us solve the question

∵ The expression is \(\frac{12x^{4}}{4x^{16}}\)

→ Simplify the fraction 12/4 first

∵ 12/4 = 3

∴  \(\frac{12x^{4}}{4x^{16}}\) = 3 ( \(\frac{x^{4}}{x^{16}}\))

→ By using the second rule above to simplify the variable

∵  \(\frac{x^{4}}{x^{16}}\) = \(x^{4-16}\)

∴  \(\frac{12x^{4}}{4x^{16}}\) = 3\(x^{4-16}\)

∴ The expression that equivalent to  \(\frac{12x^{4}}{4x^{16}}\)  is 3\(x^{4-16}\)

The polynomial P(x) with the given properties is -4x⁵ + 24x⁴ - 46x³ + 36x² + 32x - 48.

To find the polynomial P(x) with real coefficients, overall degree 5, zeros at -1, 3, and -2i, and a zero of multiplicity 2 at -1, and leading coefficient -4, we can use the factored form of the polynomial:

P(x) = -4(x+1)²(x-3)(x+2i)(x-2i)

Expanding this expression, we get:

P(x) = -4(x²+2x+1)(x-3)(x²+4)

Multiplying out the terms, we get:

P(x) = -4x⁵ + 24x⁴ - 46x³ + 36x² + 32x - 48

Therefore, the polynomial P(x) with the given properties is -4x⁵ + 24x⁴ - 46x³ + 36x² + 32x - 48.

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(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

It depends what x is equal to.

Step-by-step explanation:

For example, the expressions 2x+3 and 3x-6 are equal when x=9.

They can be expressed by 2x+3=3x-6

(2×9)+3=21

(3×9)-6=21

Answer:

11

Step-by-step explanation:

Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.

Solution:

Let x be the larger number and y be the smaller number such that;

From equation 1, we have;

Substitute equation3 in equation2, we have;

Then, substitute the value of y in equation3;

Thus, the larger number is 20 and the smaller number is -13

Answer:

297

Step-by-step explanation:

Since we have to make 9 as the whole, and 33 is the denominator to make 9, we need to multiply 9*33=297.

This makes no sense if you hear it. But trust me it is the right answer i think.

Answer:

Mia spent 68 dollars.

Step-by-step explanation:

The equation would be 2(13.50) + 4(10.25) = x

Solving for the first part, you get 27 for adult tickets and 41 for the children tickets. When you add the two values, you get 68.

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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(a) To have exactly one solution, the discriminant of the quadratic equation must be equal to zero.b² - 4ac = 1 - 4(1)(_) = 0

⇒ 1 - 4_ = 0

⇒ _ = 1/4

Substituting the value of _ in the original equation, we get:

x² + x + 1/4 = (x + 1/2)² = 0

⇒ x = -1/2 (as square of a number is always non-negative)

(b) Following the same approach as in part (a), we get:

(-_)² - 4(1)(1) = _² - 4 = 0

⇒ _ = ± 2

Substituting the values of _ in the original equation, we get:

For _ = 2: x² + 2x + 1 = (x + 1)² = 0

⇒ x = -1

For _ = -2: x² - 2x + 1 = (x - 1)² = 0

⇒ x = 1

(c) Following the same approach as in part (a), we get:

1 - 4(_) = 0

⇒ _ = 1/4

Substituting the value of _ in the original equation, we get:

x² + x + 1/4 = (x + 1/2)² = 0

⇒ x = -1/2

(d) Following the same approach as in part (a), we get:

(-_)² - 4(1)(4_) = _² - 16_ - 4 = 0

⇒ _ = 2 ± √5

Substituting the values of _ in the original equation, we get:

For _ = 2 + √5: x² + (2 + √5)x + 5 + 2√5 = (x + (1 + √5))² = 0

⇒ x = -1 - √5

For _ = 2 - √5: x² + (2 - √5)x + 5 - 2√5 = (x + (1 - √5))² = 0

⇒ x = -1 + √5

Hence, we have found the values of the constant _ for each of the given quadratic equations to have exactly one solution and determined the solution for each value.

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Answer:

35 degrees.

Step-by-step explanation:

m < TSK = 180 - 22 - 123

= 180 - 145

= 35.

1) Considering that function, we can evaluate it at x=3, i.e. find the corresponding value for f(x) when x=-3

So when we plug x=-3 into that function the corresponding y value is -15

2) Now, the other way around, we've got the y (or f(x)) value -16 let's find the corresponding value for x:

Note that looking attentively at that trinomial, we can see that this is a binomial (x+4)² or (x+4)(x+4) picking on binomial and equating to zero we can get the root. In this case, there's only value for those two roots x=-4

3) Hence the answer is f(-3)=-15, and x=-4

Answer:

0.251

Step-by-step explanation:

for a normal distribution question, we need to use the z-score formula for finding the area (probability).

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (4 - 5) / 1.5

= -0.67

in the z-table, find -0.6 down the side column and 0.07 on the top row. the number in the table where these two meet is 0.25143. this is the area to the left of z = -0.67. this is what we want for this question since we want an orange that weighs less than 4oz.

that means that the probability is 0.251 to nearest thousandth

cosine 122.2 = -0.532876276......

A= 20%

B= 33%

What is Relative Frequency?

Relative frequency is simply the number of outcomes in a particular subgroup (f) divided by the total number of outcomes in an experiment (n).

Thus, Relative frequency= f/n

In the above question, we need to find the relative frequencies of 2 subgroups- lifeguards and retail.

For lifeguards, f=3 and n=15

∴ Relative Frequency (A) = \(\frac{3}{15}\)

Since we've to express it in percentage form,

A= \(\frac{3}{15}\) * 100

  = 20%

Similarly for retail-

B= \(\frac{5}{15}\) * 100

 = 33%

Thus, A= 20% and B= 33%

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1. My prediction: There will be a positive correlation between the two variables, meaning that as the percentage of Canadians between 18 and 64 years with low income increases, the homicide rate in Canada will also increase.

2. Report Raw data and the average score for each variable:

  Year | Homicide rate per 100,000 | Percentage of Canadians with low income (18-64)

  ------|------------------------|-----------------------------------------------

  2015 | 1.45 | 13.4

  2016 | 1.68 | 13.9

  2017 | 1.80 | 13.5

  2018 | 1.80 | 12.8

  Average Score:

  Year | Homicide rate per 100,000 | Percentage of Canadians with low income (18-64)

  ------|------------------------|-----------------------------------------------

  2015 | 1.45 | 13.4

  2016 | 1.68 | 13.9

  2017 | 1.80 | 13.5

  2018 | 1.80 | 12.8

  Mean | 1.6825 | 13.4153

  Standard Deviation | 0.1919 | 0.5264

3. Scatter plot of the two variables:

  [Image]

4. The correlation coefficient value obtained is r = 0.753. This means that there is a positive correlation between the two variables. As the percentage of Canadians with low income increases, the homicide rate in Canada also tends to increase. The correlation coefficient value of 0.753 indicates a strong positive correlation between the two variables.

5. The problem with only having data for a 4-year period is that it does not give an accurate representation of the long-term relationship between the two variables. In order to make reliable generalizations about the relationship between homicide rate and the percentage of Canadians with low income, a larger sample size covering a longer time period is required.

6. There might be a correlation between these two variables because low income is associated with various stressors, such as financial hardship, inadequate housing, and poor health. These stressors, in turn, can lead to increased crime rates and other negative social outcomes. The correlation coefficient of 0.753 suggests that there may be three potential avenues of cause and effect between the two variables: (1) increased stress and hardship may lead to increased crime rates, (2) increased crime rates may lead to increased poverty, and (3) there may be some underlying factors that are causing both the increase in crime and poverty.

7. You cannot examine this relationship in an experimental study because it would be unethical to manipulate individuals' income levels or exposure to violence for the sake of a study. Furthermore, experimental studies cannot establish causation between variables, as there may be other uncontrolled factors that affect the relationship between variables.

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Answer:

7 because length times width = volume

Answer:

\(\frac{b}{a}\) is the total time taken to clean the house.

Step-by-step explanation:

Given that:

Betsy cleans \(\frac{a}{b}\) of the house.

Time taken = 1 hour

To find:

Time taken to clean the whole house = ?

Solution:

We can use unitary method here to solve this problem.

We are given that \(\frac{a}{b}\) of the house is cleaned in 1 hour.

We have to find that a total of 1 house will be cleaned in how much time.

(1 house because Betsy's house can be considered as a single unit).

To find this we will divide 1 hour with \(\frac{a}{b}\).

Now, Let us solve this mathematically:

\(\frac{a}{b}\) of the house is cleaned in = 1 hour

1 of the house will be cleaned in =  1 hour divided by \(\frac{a}{b}\)

\(\dfrac{1}{\dfrac{a}{b}}\ hours\\\Rightarrow \dfrac{1 \times b}{a}\ hours\\\Rightarrow \dfrac{b}{a}\ hours\)

So, the answer is:

\(\frac{b}{a}\) is the total time taken to clean the house.

The rules that defines the graphed function include the following: B. y = x + 2; y = 5

By critically observing the graph, we can logically deduce that the function represents a piecewise-defined function and there are two lines on this graph.

The first line has the following points;

(0, 2) and (3, 5)

Therefore, we would express 2 and 5 as a sum of 2 as follows;

(0, 0 + 2) and (3, 3 + 2)

This ultimately implies that, the y-value is the sum of 2 and the x-value:

y = x + 2

The other line has a constant y-value of 5 for any or all x-values:

y = 5

In conclusion, the rules that defines the graphed function are y = x + 2 and y = 5

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Answer:

p = 0

r = 1

Step-by-step explanation:

you can multiply the first equation by -6 to eliminate the 'r' value:

-6(r - 3p) = 1(6)

-6r + 18p = -6

now add the second equation to the new one to get:

17p = 0

p = 0

now find 'r' by setting 'p' equal to zero:

r - 3(0) = 1

r - 0 = 1

r = 1

check:

6(1) - 0 should equal 6; it does

1 - 3(0) should equal 1; it does

Answer:

this is the answer for the empty circle and rectangle

Greetings from Brasil...

Looking at the attachment we can use some properties:

(A/B) ÷ (C/D) = (A/B) · (D/C)

(M/N) · (P/Q) = (M/Q) · (P/N)

One solution:

...........................................................

another polynomial division

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Answer:so fresh and so clean

Step-by-step explanation:

its cheaper starting price and lower increase

The service with the cheaper initial fee is the graphed one, So Fresh & So Clean.

For both cases, we can write the costs as linear equations, so we want to see which linear equation has the smallest y-intercept.

We can see that for the graphed line, the y-intercept is b = 15.

For the data on the table, we can use the first two points to get the slope. The points are (1, 28) and (2, 36), so the slope is:

\(a = \frac{36 - 28}{2 - 1} = 8\)

Then we can write this line as:

y = 8*x + c

To find the y-intercept we can use the first point (1, 28), this means that:

28 = 8*1 + c

28 - 8 = c = 20

Then the y-intercept, in this case, 20.

This means that the service with the cheaper initial fee is the one where the line is graphed, which is So Fresh & So clean.

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Answer:

Since the graph looks like this, I would say solid line

Point C is located at (4,5)

It means

x= 4

y= 5

The only graph that has Point C at (4,5) is graph C.

Graph A, B, and D have point C on (5,5) , (5,4), and (4,-2)

Graph C also has the distance between A and B equal to 4 units, and the distance between B and C equal to 3 units.

Answer: C

Answer:

l think the answer is C

32.70m

Step-by-step explanation:

we all know that perimeter is the distance round the shape.

so the first step is adding 6 +6 because the other side of the shape is also 6 then add 5 and this equals to 17.

After that we find the area of the circle

which is 3.14*5= 15,7

After getting this value we add it to 17

then we get 32.70m

Answer:C

Step-by-step explanation: