***WORTH 40 POINTS*** [−3−4x≤21]

Answer:

hehehheheyeu7777777yggg

Answer:

y=2x+-4

Step-by-step explanation:

Answer:

The equation in slope intercept form (y = mx + b) is y = 2x - 4

m = the slope

b = the y intercept

The line cross the y-axis at -4 so the y-intercept (b) is -4.

You can use the slope formula \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\) since you have plotted points (0, -4) and (2, 0) on the graph that you can plug in.

\(\frac{0--4}{2-0}\) = \(\frac{4}{2}\) = 2

So the slope (m) is 2. Now you can make the slope-intercept form using these values. So, the equation for the line is y = 2x - 4

Susan has one gallon of 25% acid solution and needs to know how much pure acid she should add to make it a 75% acid solution.

To solve the problem, we will use the following formula:
(V1 x C1) + (V2 x C2) = V3 x C3
Where:
V1 = Volume of the first solution
C1 = Concentration of the first solution
V2 = Volume of the second solution
C2 = Concentration of the second solution
V3 = Final volume of the mixture
C3 = Final concentration of the mixture
Now, let's plug in the values we know:
V1 = 1 gallon
C1 = 25%
C2 = x (unknown)
V3 = 1 gallon
C3 = 75%
(1 x 0.25) + (x) = (1) (0.75)
0.25 + x = 0.75
x = 0.5
Therefore, Susan needs to add 0.5 gallons of pure acid to her one gallon of 25% acid solution to make a 75% acid solution.

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Answer:

13

Step-by-step explanation:

180-96=84

(4x-10)+(4x-10)= 84

X=13

Answer:

6

Step-by-step explanation:

floor(11/5) = 2

ceil(-15/4) = -3

2-(-3) + 1 = 6

If the value of x increases then the value of y decreases. Then the correct option is B.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

For the inverse variation function

\(\rm y = \dfrac{k}{x}\)    (where x, k > 0),

We know that the y is inversely proportional to the x.

Thus, if the value of x increases then the value of y decreases.

Therefore, the correct option is B.

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Answer:

\(a_n = -11-14n\)

Step-by-step explanation:

Given

\(a_1 = -25\)

\(a_n = a_{n-1}-14\)

Required

The explicit formula

First, calculate \(a_2\)

Set n=2; So:

\(a_2 = a_{2-1}-14\)

\(a_2 = a_{1}-14\)

Substitute -25 for \(a_1\)

\(a_2 = -25-14\)

\(a_2 = -39\)

Calculate the common difference (d)

\(d = a_2 - a_1\)

\(d = -39 --25\)

\(d = -14\)

So, the nth term is:

\(a_n = a_1 + (n - 1)d\)

\(a_n = -25+ (n - 1)*-14\)

Open bracket

\(a_n = -25-14n + 14\)

Collect like terms

\(a_n = 14-25-14n\)

\(a_n = -11-14n\)

\(\qquad \textit{power of a complex number} \\\\\ [\quad r[\cos(\theta)+i\sin(\theta)]\quad ]^n\implies r^n[\cos(n\cdot \theta)+i\sin(n\cdot \theta)] \\\\[-0.35em] ~\dotfill\\\\ z=4\left[ \cos\left( \frac{\pi }{2} \right)+i\sin\left( \frac{\pi }{2} \right)\right] \\\\\\ z^3=4^3\left[ \cos\left( 3\cdot \frac{\pi }{2} \right)+i\sin\left( 3\cdot \frac{\pi }{2} \right)\right]\implies z^3=64\left[ \cos\left( \frac{3\pi }{2} \right)+i\sin\left( \frac{3\pi }{2} \right)\right]\)

\( \blue{\boxed{\sf z^3 = 64[cos(\dfrac{3\pi}{2}) + isin(\dfrac{3\pi}{2}) ]}} \)

\( \\ \)

We are given a complex number, z, in its trigonometric form.

To find the trigonometric form of z³, we will apply De Moivre's Theorem.

\( \\ \)

\( \Large{\boxed{\boxed{\sf [cos(\theta) + isin(\theta)]^n = cos(n\theta) + isin(n\theta)}}} \)

\( \\ \\ \)

\( \sf z^3 = \Bigg(4[cos( \dfrac{\pi}{2}) + isin( \dfrac{\pi}{2})]\Bigg) ^{3} \\ \\ \Longleftrightarrow \sf z^3 = 4^3 \times [cos( \dfrac{\pi}{2}) + isin( \dfrac{\pi}{2})]^3 \\ \\ \Longleftrightarrow \sf z^3 = 64[cos(\dfrac{\pi}{2}) + isin(\dfrac{\pi}{2})]^3 \)

Let's apply the theorem with our values:

\( \: \star \: \theta = \dfrac{\pi}{2} \\ \\ \star \: \sf n = 3 \)

\( \\ \)

\( \sf z^3 = 64[cos(3 \times \dfrac{\pi}{2}) + isin(3 \times \dfrac{\pi}{2})] \\ \\ \Longleftrightarrow \boxed{\sf z^3 = 64[cos(\dfrac{3\pi}{2}) + isin(\dfrac{3\pi}{2})]} \)

\( \\ \\ \)

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Answer: 19/25

Step-by-step explanation:

There are 25 markers in total and 6 of them are green. The odds of a student not getting a green marker would be the number of markers that aren’t green out of 25

25 - 6 = 19

19/25

The probability that event will not occur is 0.68 (1-0.32). The odds for event are 32:68 or simplified to 8:17 (divide both sides by 4). The odds against event are 68:32 or simplified to 17:8 (divide both sides by 4).

Given that the probability of the event occurring is 0.32, we can find the probability of the event not occurring by subtracting this value from 1:

Probability (Event Not Occurring) = 1 - Probability (Event Occurring) = 1 - 0.32 = 0.68

So, the probability that the event will not occur is 0.68.

Now, let's find the odds for the event. Odds for an event is calculated as:

Odds For = Probability (Event Occurring) / Probability (Event Not Occurring) = 0.32 / 0.68 ≈ 0.47

So, the odds for the event are approximately 0.47 to 1.

Lastly, let's calculate the odds against the event:

Odds Against = Probability (Event Not Occurring) / Probability (Event Occurring) = 0.68 / 0.32 ≈ 2.13

Therefore, the odds against the event are approximately 2.13 to 1.

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Answer:

1,3,7,13

Step-by-step explanation:

utilizar el teorema de Pythagorus.

hipotenusa² = 3² + 4²

= 9 + 16

= 25

hipotenusa = √25 = 5 cm

Answer: 6^4+10^3−4^2−15+5

6x^4 + 14x^3 + 4x^2 -15x - 5

Step-by-step explanation:

(3x-1)(2x^3 + 4x^2 - 5)

we simply distribute and collect like terms

6x^4 + 14x^3 + 4x^2 -15x - 5

Match the Data Visualisation terms as follows:

1. Numpy: Working with arrays and matrices.

2. Bar chart: Representing categorical data with rectangular bars.

3. Pip: Package installer for Python.

4. S: Statistical library for Python.

The following are the meanings of the given terms:

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-2x + 8 = 3x + 14

-2x - 3x = 14 - 8

-5x = 6 / : (-5)

x = -1,2

Answer: x = -6/5

Step-by-step explanation:

Given equation

-2x + 8 = 3x + 14

Subtract 3x on both sides

-2x + 8 - 3x = 3x + 14 - 3x

-5x + 8 = 14

Subtract 8 on both sides

-5x + 8 - 8 = 14 - 8

-5x = 6

Divide -5 on both sides

-5x / -5 = 6 / -5

\(\boxed{x = -\frac{6}{5} }\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

I think infinite since it goes on past these numbers.

Step-by-step explanation:

Answer:

Infinity solutions

Step-by-step explanation:

This inequality has infinite solutions because the number line goes from 3 to infinity. this means that there is an uncountable number of solution which means the answer to this question is E.

Answer:

a.4

Step-by-step explanation:

Because 10 is greater than 6 so, it turns into a positive instead of a negative. and of course 10 + 6 = 4

The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²

f(x) = 3x² + 4x³ + 8x⁴

g(x) = -3x + 12x² - 5x³

h(x) = 12x + 6

Therefore,

(f.h)(x) = f(x).h(x)

Hence,

f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)

f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴

(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ +  36x³ + 42x³ + 18x²

(f.h)(x) =  96x⁵ + 132x⁴ + 78x³ + 18x²

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Answer:

i dont know sorry

Step-by-step explanation:

i  dont understand i just watch anime all day

Answer:

Free points? idek sorry.

Step-by-step explanation:

As per the mathematical operation both Jillian and Samuel are correct.

Given expression = 30+40+70,

The methodology by Jillian = added 30 and 40 and then 70

The methodology by Samuel = added 30 and 70 and then 40.

Determining the result of the given equation:

30 + 40 + 70

= 140

Reviewing the operations of both Jillian and Samuel

Jillian

He added 30 and 40 and then 70:

30 + 40 = 70

70 + 70 = 140

Samuel

He added 30 and 70 and then 40

30 + 70 = 100

100 + 40 = 140

The result of both mathematical operations is 140. Thus, it can be stated that both are correct.

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We can calculate the experimental probability of selling a can of tomato soup, and then use that probability to predict the number of tomato soup cans sold in the next 20 cans.

Step 1: Calculate the experimental probability of selling a can of tomato soup.
Probability = (Number of tomato soup cans sold) / (Total number of cans sold)
Probability = 6 / 12 = 0.5

Step 2: Use the probability to predict the number of tomato soup cans sold in the next 20 cans.
Expected number of tomato soup cans = Probability × Total number of cans
Expected number of tomato soup cans = 0.5 × 20 = 10

Based on the experimental probability, you should expect 10 of the next 20 cans sold to be tomato soup.

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No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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A unit vector in a normalized vector space is a vector of length 1. A unit vector is often denoted by a lowercase letter with a caret, or "hat". We have the answer:

\(\begin{pmatrix} \bold-\dfrac{ \bold4}{ \bold5}& \bold-\dfrac{ \bold3}{ \bold5}\end{pmatrix}\)

Vector of a Vector

A vector is a quantity that has magnitude and direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector. Learn vectors in detail here.

For example, the vector v = (1,3) is not a unit vector, because its magnitude is not equal to 1, that is, |v| = √(1²+3²) ≠ 1. Any vector can be made a unit vector by dividing it by the magnitude of the given vector.

Let's calculate the vector AB = B-A = (-2, 6) - (2, 9) = (-4, -3)

\(\mathrm{ \bold{Calculating\:the\:unit\:vector\:of\:}}\left|\vec{ \bold{a\:}}\right|:\quad \hat{ \bold{a\:}}=\dfrac{\vec{ \bold{a \:}}}{\left|\vec{ \bold{a\:}}\right|} \: \)

\(\hat{ \bold{a\:}}= \bold{\dfrac{\begin{pmatrix} \bold- \bold4& \bold- \bold3\end{pmatrix}}{5}}\)

\(\begin{pmatrix}-\dfrac{ \bold4}{ \bold5}&-\dfrac{ \bold3}{ \bold5}\end{pmatrix}\)

Answer:

Versors are unit modulus vectors. They serve to write the equation of other vectors as a function of them. Like vectors, vectors have three different directions in the plane. Determine the vector defined between points A(2,9) and B(-2,6)

Answer:

Step-by-step explanation:

It is given that the area of a circle is 36.43cm² and we have to find the length of the radius.

So, first of we must know this formula :

⇒ πr² = Area(Circle)

Now, Substituting the given values in the formula :

⇒ 3.14 × r² = 36.43

⇒ r² = 36.43/3.14

⇒ r² = 11.60

⇒ r = √11.60

⇒ r = 3.40

Therefore,

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with area of circle that is 36.43 cm² . And we are asked to find the length of radius of circle rounded to two decimal points .

We know that ,

\( \qquad \quad \frak{Area_{(Circle)} = \pi r {}^{2} } \quad \bigstar\)

Where ,

Solution : -

According to question , area of Circle is equal to 36.43 . So ,

\( \longrightarrow \qquad \: \pi r {}^{2} = 36.43\)

Step 1 : Substituting value of π :

\( \longrightarrow \qquad \:3.14 \times r {}^{2} = 36.43\)

Step 2 : Transposing 3.14 to right side :

\( \longrightarrow \qquad \: r {}^{2} = \cancel{\dfrac{36.43}{3.14} }\)

On dividing 36.43 by 3.14 , We get :

\( \longrightarrow \qquad \: r {}^{2} = 11.60\)

Step 3 : For removing square from r , We are applying root on both sides :

\( \longrightarrow \qquad \: \sqrt{r {}^{ 2 }} = \sqrt{ 11.60}\)

We get :

\( \longrightarrow \qquad \:r = \sqrt{11.60} \)

Step 4 : Finding square root of 11.60 , We get :

\( \longrightarrow \qquad \: \purple{\underline{\boxed{\frak{r = 3.40 \: cm}}}} \)

The rotation rule used in this problem is given as follows:

90º counterclockwise rotation.

The five more known rotation rules are given as follows:

The equivalent vertices for this problem are given as follows:

Hence the rule is given as follows:

(x,y) -> (-y,x).

Which is a 90º counterclockwise rotation.

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Answer:

y = 10.5x + 35

Step-by-step explanation:

Since the roof is 35 feet tall, it will be the y-intercept (since it is constant). The number of floors can change, so it will be the x variable.

The final equation is y = 10.5x+35

Answer:

21.75

Step-by-step explanation:

Change fraction to decimal

20.25 - 9.50 + 11

20.25 - 9.50 = 10.75

10.75 + 11 = 21.75

Answer:

21.75

Step-by-step explanation:

you make 9 1/2 to 9.5

20.25-9.5+11

you would do PEMDAS

Parenthesis

Exponent

Multiflicatin

Division

Addidion

Subtraction

Thus, the p-value is greater than 0.10 (the significance level α), indicating that there is not enough evidence to support the alternative hypothesis.

To find the p-value, we need to calculate the test statistic and compare it to the critical value.

Given:

Sample 1: sample size (n1) = 22, variance (\(s_{1}^2\))

= 8, mean (x1(bar))

= 51

Sample 2: sample size (n2) = 20, variance (\(s_{2}^2)\)

= 11, mean (x2(bar))

= 50.5

To calculate the test statistic, we can use the formula for the difference in means:

t = (x1(bar) - x2(bar)) / √((\(s_{1}^2\)/n1) + (\(s_{2}^2\)/n2))

Substituting the given values:

t = (51 - 50.5) / √((8/22) + (11/20))

  = 0.5 / √(0.3636 + 0.55)

  = 0.5 / √0.9136

  ≈ 0.53

Now we need to find the degrees of freedom. For independent samples with equal variance, the degrees of freedom (df) can be calculated using the formula:

df = n1 + n2 - 2

Substituting the given values:

df = 22 + 20 - 2

  = 40

With α = 0.10, the critical value for a one-tailed test (upper tail) with 40 degrees of freedom is 1.684.

Now, we can determine the p-value. Since the alternative hypothesis is μ1 - μ2 > 0, we are conducting an upper-tailed test.

The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 0.53) under the null hypothesis.

By comparing the test statistic to the critical value, we can determine the conclusion:

Since the test statistic (0.53) is less than the critical value (1.684), we fail to reject the null hypothesis.

Therefore, the conclusion is: "We don't have enough evidence to conclude that the difference in means is > 0; therefore, H0 is not rejected."

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The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

To find the curve that passes through (4, 5) and has a slope of 3√x at each point, we can integrate the derivative of y with respect to x, which gives us the original function y(x):

\(\frac{dy}{dx}\) = 3√x

Integrating both sides with respect to x, we get:

y = (\(2x^{3/2}\)) + C

where C is a constant of integration.

We can use the point (4, 5) to solve for C:

5 = 2\((4)^{3/2}\) + C

C = 5 - 2\((4)^{3/2}\)

Substituting this value of C, we get the final equation for the curve:

y =  (\(2x^{3/2}\)) + 5 -  2\((4)^{3/2}\)

Therefore, The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

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Answer:

36%

Step-by-step explanation: