solve the inequality 8 + 3x < 2 + x and 2x + 23 ≤ 11

Answer:

Step-by-step explanation:

If a helicopter flies 312 miles against the wind in 2 hours, the speed of the helicopter in air is expressed as shown;

Speed = Distance/Time

Speed = 312miles/2hours

Speed = 156miles/hr

The speed of the helicopter against the wind is 156miles/hr

If it can fly 468 miles in the same amount of time, the speed during this time at this distance will be;

speed = 468 miles/2hours

Speed = 234miles/hr

The speed of the helicopter in still air = Speed while flying - Speed while against the wind

The speed of the helicopter in still air = 234miles/hr - 156miles/hr

The speed of the helicopter in still air  = 78miles/hour

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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The measure of angle ∠H in triangle ΔFGH is approximately 47.4 degrees.

To find the measure of angle ∠H in triangle ΔFGH, we need to use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

According to the Law of Cosines, for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we have side lengths f = 830 inches, g = 460 inches, and h = 500 inches. We are interested in finding the measure of angle ∠H, which is opposite side h.

Using the Law of Cosines, we can set up the equation:

h^2 = f^2 + g^2 - 2fg * cos(H)

Plugging in the given values, we have:

500^2 = 830^2 + 460^2 - 2 * 830 * 460 * cos(H)

Simplifying the equation, we get:

250000 = 830^2 + 460^2 - 2 * 830 * 460 * cos(H)

Now, let's solve this equation to find the value of cos(H). First, we can simplify the right side of the equation:

250000 = 688900 + 211600 - 2 * 830 * 460 * cos(H)

Next, combine like terms:

250000 = 900500 - 960800 * cos(H)

Rearranging the equation to isolate cos(H):

960800 * cos(H) = 900500 - 250000

960800 * cos(H) = 650500

cos(H) = 650500 / 960800

cos(H) ≈ 0.676

To find the measure of angle ∠H, we can take the inverse cosine (cos^(-1)) of 0.676 using a calculator:

H ≈ cos^(-1)(0.676)

H ≈ 47.4 degrees

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Answer:

x = -1/3 or x = 6

Step-by-step explanation:

For this equation, you should use the FOIL method or the BOX method. Break it apart to solve it easier. Sites like mathpapa or symbolab can help break these down for you.

Answer:

9

Step-by-step explanation:

39 x 39 = 1521

1521 divided by 169

= 9    good luck bro

Answer:

Step-by-step explanation:

It's B. If you divide 15 and 12 ( The first triangle) it's 1.25. So, for the second triangle, do 5 x 1.25 and you get 6.25

Answer: ❘-168 - 115❘

you’re finding difference so we set up a subtraction problem.

We can’t have a negative answer so we must take the absolute value of that number

Answer:

Step-by-step explanation:

8y^2 - 84y

Answer:

1561.813ft32ft²

Step-by-step explanation:

To calculate the area of the wall which we will call the largest rectangle we must calculate the area of all rectangles on the wall and subtract their combined area from the total.

A = l*w

large rectangle 52.5ft * 33ft = 1732.5 ft²

rectangle A 6.25ft * 5.75ft = 35.9375ft²

rectangle B 3.125ft * 4ft = 12.5ft²

square C (9.5ft)² = 90.25ft²

rectangle D 4ft * 8ft = 32ft²

the total area of the wall needed to be painted

1732.5 ft² - 35.9375ft² - 12.5ft² - 90.25ft² - 32ft² = 1561.813ft32ft²

True, a researcher wants to compare performance scores for men versus women on a motor skills task. it would not be possible to use a repeated measures design for this study.

What is a performance comparison?

They are frequently used while benchmarking, which is the practice of evaluating an organization's performance versus that of the best-performing businesses.

                 The measures are employed in productivity improvement projects to monitor changes in productivity over time.

Why is performance measurement important?

Comparing is one of the most important growth drivers. Only when we contrast our development with that of our rivals or our current performance with our former performance do we get motivated to advance and accomplish greater feats.

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Answer:

175 is the answer the percentage is 75

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

Rounding up to the nearest whole number, we need a sample size of 25 water specimens to achieve a sampling error of 1 mg/L with 95% confidence.

To determine the number of water specimens required in the sample with a sampling error of 1 mg/L, we can use the formula:

n = (zα/2 * σ / E)^2

where:

n = the required sample size

zα/2 = the z-score associated with the level of confidence (for example, at 95% confidence, zα/2 = 1.96)

σ = the standard deviation of the pollution readings (given as 5 mg/L)

E = the desired sampling error (given as 1 mg/L)

Substituting the given values, we get:

n = (1.96 * 5 / 1)^2

n = 24.01

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Answer:

3,036

Step-by-step explanation:

x=12*253

Answer: 20 cards.

Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.

Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.

Answer:

Step-by-step explanation:

I'm assuming you're trying to solve this for x. We use the difference identity for cosine and rewrite:

\(cos(x-30)=cosxcos30+sinxsin30\) and simplify using the unit circle to help.

\(cosx(\frac{\sqrt{3} }{2})+sinx(\frac{1}{2})=0\\cosx(\frac{\sqrt{3} }{2})=-\frac{1}{2} sinx\\cosx=-\frac{1}{2}(\frac{2}{\sqrt{3} })sinx\\cosx=-\frac{1}{\sqrt{3} }sinx\\1=-\frac{1}{\sqrt{3} }\frac{sinx}{cosx}\\1=-\frac{1}{\sqrt{3} }tanx\\-\sqrt{3} =tanx\)

and on the unit circle, the angle where the tangent is negative square root of 3 is -60° which is also a positive 300°

Answer:

x = n*360° + 120°      or     x = n*360° + 300°

Step-by-step explanation:

cos(x-30°)=0

x-30° = 90° or x-30° = 270°

it means can be : x-30° = n*360° + 90°    or    x-30° =n*360° + 270°

x = n*360° + 120°      or     x = n*360° + 300°   n is integers

In conclusion for a. If the system is homogeneous , every solution is trivial true. b. If there exists a trivial solution, the system is homogeneous false. c. If there exists a nontrivial solution, there is no trivial solution false.

How to solve?

a. If the system is homogeneous, every solution is trivial.

This statement is true. A homogeneous system of linear equations has the form Ax = 0, where A is the coefficient matrix and x is the vector of variables. The trivial solution is always x = 0, which satisfies the equation. Any other solution would require a nonzero x vector, but then Ax would be nonzero, contradicting the fact that it equals zero in a homogeneous system.

b. If there exists a trivial solution, the system is homogeneous.

This statement is false. A system of linear equations can have a trivial solution (i.e., all variables are equal to zero) without being homogeneous. For example, the system

x + y = 0

2x + 2y = 0

has a trivial solution (x = 0, y = 0) but is not homogeneous.

c. If there exists a nontrivial solution, there is no trivial solution.

This statement is false. A homogeneous system of linear equations can have both trivial and nontrivial solutions. For example, the system

x + y = 0

2x + 2y = 0

has both a trivial solution (x = 0, y = 0) and a nontrivial solution (x = 1, y = -1).

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Rounding to two decimal places, the obtained chi-square statistic is 6.67.

We can use the chi-square goodness-of-fit test to determine if there is a significant difference in the preference for class format. We need to calculate the expected frequencies under the assumption that all groups have an equal preference. The total sample size is 90, so each group would be expected to have 30 students.

Observed frequencies:

Online: 50

In-person: 18

Hybrid: 22

Expected frequencies:

Online: 30

In-person: 30

Hybrid: 30

We can use the chi-square formula to calculate the test statistic:

χ^2 = Σ [(O - E)^2 / E]

where Σ is the sum of all the cells, O is the observed frequency, E is the expected frequency.

Plugging in the values:

χ^2 = [(50 - 30)^2 / 30] + [(18 - 30)^2 / 30] + [(22 - 30)^2 / 30]

χ^2 = 6.67

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Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

x = -1

Step-by-step explanation:

-2(3x - 5) = 16

3x - 5 = -8

3x = -8 + 5

3x = -3

x = -1

Hope this helps! :)

Answer:

x = -1

Step-by-step explanation:

-2 (3x-5) = 16

-6x + 10 = 16

-6x = 16-10

-6x = 6

x = 6 ÷ -6

x = -1

Answer:

y = f(x) = 7.

The output for the equation is 7 when x=2.

Step-by-step explanation:

First, let's transform y = 3x + 1 into a function (f(x)) form.

f(x) = 3x + 1

When the Input, or x, equals to 2, we have:

f(x) = 3x + 1

f(2) = 3(2) + 1

f(2) = 6 + 1

f(2) = 7.

Given that y = f(x),

The output for the equation is 7 when x=2.

The volume of a spherical tank with a radius of 15 m is calculated as 4/3πr3, or 4/3π × 153 = 14,137 m3.

The volume of a sphere is calculated using the formula V = 4/3πr³, where r is the radius.The volume of a cylindrical tank with a radius of 15 m and a height of 20 m is calculated as πr2h, or π × 152 × 20 = 11,309 m3.

Therefore, the ratio of the volume of the spherical tank to the volume of the cylindrical tank is 14,137/11,309 = 1.24.

This means that the spherical tank has 24% more volume than the cylindrical tank.

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Answer:

\(r = \sqrt{ \frac{v}{20\pi?} ?} \)

Answer:

Step-by-step explanation:

oh thats easy its 2

Answer:

The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.

Step-by-step explanation:

You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x

=> x = 50 m / tan(86°)

x = 50 m / 14.30 = 0.98 m

The value of the sides are;

CB = 13.8

CD = 6. 9

To determine the value of the sides of the triangle, we need to know the different trigonometric identities are;

From the information given, we have that;

Using the sine identity, we have that;

tan 60 = CD/4

cross multiply the values, we have;

CD = 4(1.73)

multiply the values

CD = 6.9

To determine the value;

sin 30 = 6.9/CB

CB = 13.8

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The equation that describes the simple harmonic motion of the particle is:

x = 7 * sin(2t + φ)

The equation that describes the simple harmonic motion of a particle moving uniformly around a circle can be represented as:

x = A * sin(ωt + φ)

In this equation:

x represents the displacement of the particle at time t.

A represents the amplitude of the motion.

ω represents the angular frequency or angular speed of the motion.

t represents time.

φ represents the phase constant.

In the given scenario, the particle is moving uniformly around a circle of radius 7 units, with an angular speed of 2 radians per second. In circular motion, the displacement can be represented by the arc length along the circumference of the circle.

Since the angular speed is 2 radians per second, the angular frequency (ω) is also 2 radians per second.

Since the particle is moving uniformly, the amplitude of the motion (A) is equal to the radius of the circle, which is 7 units.

The phase constant (φ) determines the initial position of the particle at t = 0.

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Answer:

pay me first

Step-by-step explanation: