Need help for math! Open the picture above number 7 thank you

Answer:

drop out dog

Step-by-step explanatiopensin:

The factorized expressions are t^2 + 8t – 9 = (t - 1)(t + 9), 2b^2 – 16b – 18 = (2b - 1)8(b + 1), 36f^2 – 21f – 36 = (9f - 12)(4f + 3) and 24x^2 – 6 = 6(2x – 1)(2x + 1)

Expression 1

Here, we have

t^2 + 8t – 9

Expand the expression

t^2 + 8t – 9 = t^2 + 9t - t – 9

Factorize the expression

t^2 + 8t – 9 = t(t + 9) - 1(t + 9)

This gives

t^2 + 8t – 9 = (t - 1)(t + 9)

Expression 2

Here, we have

2b^2 – 16b – 18

Expand the expression

2b^2 – 16b – 18 = 2b^2  + 2b – 18b – 18

Factorize the expression

2b^2 – 16b – 18 = 2b(b + 1) – 18(b + 1)

This gives

2b^2 – 16b – 18 = (2b - 1)8(b + 1)

Expression 3

Here, we have

36f^2 – 21f – 36

Expand the expression

36f^2 – 21f – 36 = 36f^2 + 27f - 48f - 36

Factorize the expression

36f^2 – 21f – 36 = 9f(4f + 3) - 12(4f + 3)

This gives

36f^2 – 21f – 36 = (9f - 12)(4f + 3)

Expression 4.

Here, we have

15m^2 – 42m – 3

The expression cannot be factorized

Expression 5.

Here, we have

24x^2 – 6

Factor out 5

24x^2 – 6 = 6(4x^2 – 1)

Apply the difference of two squares

24x^2 – 6 = 6(2x – 1)(2x + 1)

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Answer:

Please refer to the attached image in the answer area.

Step-by-step explanation:

The given inequality is:

\(0.3(x -4) > -0.3\)

To find:

The graph of inequality on the number line.

Solution:

First of all, let us simplify the inequality.

\(0.3(x -4) > -0.3\)

Dividing it with 0.3 on the both sides:

\(x -4 > -1\\\text{Adding 4 on both sides}\\\Rightarrow x > 3\)

i.e. all the values x > 3 will be our solution. There is no equal sign in the inequality so 3 will not be included in the solution.

Please refer to the attached image for the solution graph of the given inequality.

3 has an empty circle drawn over it which signifies that 3 is not included in the solution set.

Red line shows that all the values greater than 3 are included in the solution.

It looks like the system of ODEs is

\(\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}\)

Differentiate both sides of both equations with respect to \(t\).

\(\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}\)

Eliminating the exponential terms, we have

\((2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0\)

\((x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0\)

Now we can eliminate \(y\) and it derivatives.

\(\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0\)

Solve for \(x\). The characteristic equation is \(r^2 + 4 = 0\) with roots at \(r=\pm2i\), hence the characteristic solution is

\(\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}\)

Solve for \(y\). Substituting \(x\) into the second ODE gives

\(x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)\)

The characteristic equation this time is \(r + 1 = 0\) with a root at \(r=-1\), hence the characteristic solution is

\(y(t) = C_3 e^{-t}\)

Assume a particular solution with unknown coefficients \(a,b,c\) of the form

\(y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)\)

Substituting into the ODE gives

\(5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5\)

so that the general solution is

\(\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}\)

Answer:   \(\bold{b)\quad \dfrac{2\pi}{3},\dfrac{4\pi}{3},0}\)

Step-by-step explanation:

Note the following identities: tan² x = sec²x - 1

                                                 \(\sec x=\dfrac{1}{\cos}\)

tan² x + sec x = 1

(sec² x -1) + sec x = 1

sec² x + sec x - 2 = 0

(sec x + 2)(sec x - 1) = 0

sec x + 2 = 0     sec x - 1 = 0

sec x = -2          sec x = 1

\(\dfrac{1}{\cos x}=-2\qquad \dfrac{1}{\cos x}=1\\\\\cos x=-\dfrac{1}{2}\qquad \cos x=1\\\\x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}\qquad x=0\)

Answer:

Option B

Step-by-step explanation:

We have tan^2( x ) + sec( x ) = 1.

First subtract 1 from either side, applying the identity tan^2( x ) = - 1 + sec^2( x ) = - 2 + sec( x ) + sec^2( x ) = 0

One key method that you should use to solve like problems, is to substitute a rather large value with a variable, such as say a. Let sec( x ) = a,

- 2 + a + a^2 = 0,

By the zero product property, a = 1, a = - 2. Substitute this value of a back into sec( x ) -

sec( x ) = 1, sec( x ) = - 2

From this we can create inequality( s ) as follows -

sec( x ) = 1, 0 ≤ x ≤ 2π, x = 0 and x = 2π

sec( x ) = - 2, 0 ≤ x ≤ 2π, x = 2π / 3 and x = 4π / 3

As you can see, x is the following solutions -

0, 2π, 2π / 3, 4π / 3

Eliminate 2π, and it should be that your solution is option B

Answer:

1/3x^2+1/8

Step-by-step explanation:

simplify the equation to 1/8+1/3x^2

Statistically meaningful results that make it possible for researchers to feel confident that they have confirmed their hypotheses is known as a statistically significant outcome.

statistically meaningful results that make it possible for researchers to feel confident that they have confirmed their hypotheses is known as statistical significance.

This means that the results are unlikely to be explained solely by chance or random factors. The p value, or probability value, tells you the statistical significance of a finding.

In most studies, a p value of 0.05 or less is considered statistically significant, but this threshold can also be set higher or lower depending on the context.

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To solve this problem, we can use a system of equations. Let's denote the amount of 0.72 beans as x and the amount of 0.52 beans as y.

From the given information, we have two equations:
Equation 1: x + y = 110  (since 110 pounds of beans are used in total)
Equation 2: (0.72x + 0.52y) / 110 = 0.74  (since the mixture is worth 0.74 a pound)
To solve this system of equations, we can use the method of substitution. Let's solve Equation 1 for x:

x = 110 - y.
Now we substitute x in Equation 2 with 110 - y:
(0.72(110 - y) + 0.52y) / 110 = 0.74
Simplifying this equation, we get:
79.2 - 0.72y + 0.52y = 81.4
Combine like terms:
0.52y - 0.72y = 81.4 - 79.2
-0.20y = 2.2
Divide both sides by -0.20:
y = -2.2 / -0.20
y = 11
Substituting the value of y back into Equation 1:
x + 11 = 110
x = 110 - 11
x = 99
Therefore, 99 pounds of 0.72 beans and 11 pounds of 0.52 beans are used in the mixture.
99 pounds of 0.72 beans and 11 pounds of 0.52 beans are used in the mixture.
To solve this problem, we used a system of equations to represent the given information. We assigned variables to the amounts of 0.72 beans and 0.52 beans used in the mixture.

By setting up two equations based on the total weight of the beans and the average price per pound, we were able to solve for the values of x and y.

Using the method of substitution, we substituted the value of x in Equation 2, simplified the equation, and solved for y. Then, we substituted the value of y back into Equation 1 to solve for x.

The final solution showed that 99 pounds of 0.72 beans and 11 pounds of 0.52 beans were used in the mixture.
The solution we obtained is reasonable because it satisfies both equations and meets the given conditions.

The total weight of the beans (99 + 11 = 110) matches the given total weight, and the average price per pound

(0.72 × 99 + 0.52 × 11) / 110 = 0.74 matches the given average price.

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We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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Answer: 7/40x + 19

Step-by-step explanation:

---Distribute the negative sign

4/5x + 13 - 5/8x + 6

---Get common denominators on the fractions

32/40x + 13 - 25/40x + 6

---Combine like terms

(32/40x - 25/40x) + (13 + 6)

7/40x + 19

Answer: 7/40x + 19

Hope this helps!

The point on the plane closest to the origin is P(49, 0, 0).

To find the point on the plane that is closest to the origin, we need to minimize the distance from the origin to any point on the plane. Let's call the point on the plane that is closest to the origin P.

We can use the formula for the distance between a point and a plane to set up an equation:

distance = |ax + by + cz - d| / sqrt(a^2 + b^2 + c^2)

where a, b, and c are the coefficients of the plane equation (2, 3, and 6), d is the constant term (98), and x, y, and z are the coordinates of any point on the plane.

Since we want to minimize the distance, we can ignore the absolute value and just focus on the numerator. We can also use the fact that the vector [2, 3, 6] is perpendicular to the plane to simplify the equation:

distance = (2x + 3y + 6z - 98) / sqrt(2^2 + 3^2 + 6^2)
distance = (2x + 3y + 6z - 98) / 7

To minimize this distance, we need to find the point on the plane where (2x + 3y + 6z - 98) is as small as possible. This occurs when the plane equation is satisfied and x, y, and z are as small as possible. Since the plane equation has three variables, we can fix two of them and solve for the third. Let's fix y and z at zero:

2x + 0 + 0 = 98
x = 49

So the point on the plane closest to the origin is P(49, 0, 0).

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Answer:

0.02941176...

— Used a calculator for this, so it is guarantied correct! Hope this helps. Brainliest appreciated (and very much needed)

Answer: 118

Step-by-step explanation: The reason why is because all of the angles at then end should equal up to 180 degrees. So you would have to add those two angles first then subtract that by 180.

Answer:

I think the equation is this

a_n = -n^2/2 + 13n/2 - 5

If this helps the 5th term is 15

Hope this helps :)

Answer:

c=5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = \(\frac{\sqrt{3} }{2}\) and sin30° = \(\frac{1}{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{x}{18}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 18\(\sqrt{3}\) ( divide both sides by 2 )

x = 9\(\sqrt{3}\)

----------------------------------------------------------

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{y}{18}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9\(\sqrt{3}\) and y = 9 → C

Answer:

please mark brainliest

as it's not in root form and root 1 Is 1 it is a rational number

Step-by-step explanation:

you can easily find if a number is rational or not for eg root 4

root 4 is 2 so it will be rational where as root 3 there is no answer.for root 3 unless it decimal so it irrational as well as pie is irrational

Answer:

If f=5 pounds of pressure, l=5.4 feet long

Step-by-step explanation:

Force needed to break a board varies inversely with the length of the board

Let

Force to break the board=f

Length of the board=l

f=k/l

Where k is a constant

If f=9 pounds of pressure and l=3 feet long

f=k/l

9=k/3

Cross product

9*3=k

27=k

If k=27, f=5 pounds of pressure. Find l?

f=k/l

5=27/l

Cross product

5l=27

l=27/5

=5.4

l=5.4 feet long

Using proportions, it is found that the board that requires 5 pounds of pressure to break is 1.67 inches long.

The rule of three is:

9 pounds - 3 feet

5 pounds - x feet

Applying cross multiplication:

\(9x = 3(5)\)

\(x = \frac{15}{9}\)

\(x = 1.67\)

The board that requires 5 pounds of pressure to break is 1.67 inches long.

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Answer:

18.18%

Step-by-step explanation:

(65000-55000)/55000×100

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

----------------------------

Use the formula:

We know that John drives a distance of 16 miles to work at a rate of m miles per hour.

So, the time it takes him to travel the full distance is:

On a certain day, the car stops after only v miles. So, the distance John still needs to travel is:

We also know that he will be traveling at the same rate, so we can use the formula again:

To find the time left, we can rearrange the formula:

The taxicab distance formula between two points (x1, y1) and (x2, y2) is expressed as

distance = Ix1 - x2I + Iy1 - y2I

From the information given,

x1 = 7, y1 = 5

x2 = 8, y2 = 6

Distance = I7 - 8I + I5 - 6)

Distance = I- 1I + I- 1I = 1 + 1

Distance = 2

The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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Answer:

\(Longer\ leg = 8\)

Step-by-step explanation:

Given

30-60-90 triangle

\(Shorter = \frac{8}{\sqrt 3}\)

Required

The longer leg

The following relationship exists in a 30-60-90 triangle.

\(Longer\ leg = \sqrt 3 * Shorter\ Leg\)

This gives:

\(Longer\ leg = \sqrt 3 * \frac{8}{\sqrt 3}\)

\(Longer\ leg = 1* \frac{8}{1}\)

\(Longer\ leg = 1* 8\)

\(Longer\ leg = 8\)

Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

Based on the given system equation y[n] = x[2n], the system is linear, time-invariant, causal, and stable.

Based on the given system equation y[n] = x[2n], we can determine the following properties:

1. Linearity: The system is linear because the output is a linear function of the input signal.

2. Time-Invariance (TI): The system is time-invariant, as the output does not depend on the specific time "n". A time shift in the input signal results in the same time shift in the output signal.

3. Causality: The system is causal because the output at time "n" only depends on the input at time "2n" and not on any future inputs.

4. Stability: The system is stable, as the output is bounded for any bounded input signal. A change in the input signal will not cause the output to become unbounded.

So, the system is linear, time-invariant, causal, and stable.

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Answer:

Step-by-step explanation: