7 less than 5 times a number

Answer: 1.616 of adding and subtracting will be 1.476

Step-by-step explanation:

Answer:

1.616

Step-by-step explanation:

Too easy to explain. Sorry.

Answer:

(x - 1)^2 =1/2 ( y - 5) or 2x^2 - 4x - y + 7 = 0

Step-by-step explanation:

(x - 1)^2 =1/2 ( y - 5)

or

x^2 - 2x + 1 = y/2 - 5/2

2x^2 - 4x + 2 - y + 5 = 0

2x^2 - 4x - y + 7 = 0

Summit (1,5) = (h,k)

4p = 2

p = 1/2

(x - h)^2 = 1/2(y - k)

The 95% confidence interval is larger because it provides a higher level of confidence and captures a wider range of values.

The best point estimate of the mean is indeed 28 pounds, as provided in the information.

To find the 90% confidence interval of the mean, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / √sample size)

Using a confidence level of 90%, we find the critical value associated with a two-tailed test to be approximately 1.645 (from a standard normal distribution table).

Calculating the confidence interval:

Lower bound = 28 - (1.645 * (44 / √60)) ≈ 27.1

Upper bound = 28 + (1.645 * (44 / √60)) ≈ 28.9

Therefore, the 90% confidence interval of the mean weight for the overweight men is approximately 27.1 pounds to 28.9 pounds.

To find the 95% confidence interval of the mean, we follow the same process as in part (b) but with a different critical value. For a 95% confidence level, the critical value is approximately 1.96 (from a standard normal distribution table).

Calculating the confidence interval:

Lower bound = 28 - (1.96 * (44 / √60)) ≈ 26.9

Upper bound = 28 + (1.96 * (44 / √60)) ≈ 29.1

Therefore, the 95% confidence interval of the mean weight for the overweight men is approximately 26.9 pounds to 29.1 pounds.

The 95% confidence interval is larger than the 90% confidence interval. This is because a higher confidence level requires a wider interval to capture a larger range of possible values and provide a higher level of certainty. The 95% confidence interval is associated with a greater range of values and is more likely to contain the true population mean.

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Answer:

522.1

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

Side b = 204

Angle ∠A = 90°

Angle ∠B = 23°

Angle ∠C = 180-90-23 = 67°

a = b·sin(A)/sin(B) = 522.09815

Considering the hypotheses tested, it is found that the p-value for Nicolas's test is of 0.101.

At the null hypotheses, it is tested if the mean is of 24, that is:

\(H_0: \mu = 24\)

At the alternative hypotheses, it is tested if it is different, hence:

\(H_1: \mu \neq 24\)

As we are testing if the mean is different of a value, we have a two-tailed test, with t = -1.79 and 12 - 1 = 11 df. Hence, using a t-distribution calculator, the p-value is of 0.101.

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Answer:

x=\frac{94}{\sin 10}=541.3244\approx 541.3\text{ feet}

x=

sin10

94

​

=541.3244≈541.3 feet

Step-by-step explanation:

According to the question, the best approximation of the area of the cross-section is 38.484 square centimeters.

To find the area of the cross-section, we can use the formula for the area of a circle.

The cross-section is perpendicular to a radius of the sphere and intersects the radius one-fourth of the way from the center of the sphere to its surface. This means that the length of the segment from the center of the sphere to the cross-section is one-fourth of the radius.

Given that the radius of the sphere, r, is 14 centimeters, the length of the segment from the center to the cross-section is \((\frac{1}{4})\) * 14 = 3.5 centimeters.

The cross-section is a circle with a radius of 3.5 centimeters. Therefore, the area of the cross-section is given by the formula: A = π * \(r^2.\)

Substituting the value of the radius, we have A = π * \((3.5)^2\).

Calculating the approximate value, we get A ≈ 38.484 square centimeters.

Therefore, the best approximation of the area of the cross-section is 38.484 square centimeters.

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Answer:

x = ±3 sqrt(2)

Step-by-step explanation:

x^2 = 18

Take the square root of each side

sqrt(x^2) = sqrt(18)

x = ± sqrt(18)

x =±sqrt(9*2)

x = ±sqrt(9) sqrt(2)

x = ±3 sqrt(2)

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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The correct answer is option D which is the expression is, 11 over 24 times r plus negative 8.

In mathematics, creating equations from word descriptions is referred to as a "word problem."

For example, in the question, equations are expressed in words and then rewritten in figures, which is the preferred way to write equations.

The equation is rewritten in words and solved as below.

How to write and solve the equation

Given expression is,

\((\frac{-1}{8}*r-5-\frac{1}{6} *r)-(\frac{-6}{8} *r+3)\)

solving the equation:

= \((\frac{-1}{8} *r-5-\frac{1}{6} *r)-(\frac{-6}{8} *r+3)\)

= \((\frac{-r}{8} -5-\frac{r}{6} )-(\frac{-6r}{8} +3)\)

opening the parenthesis leads to change of signs as follows

= \(\frac{-r}{8} -5-\frac{r}{6} +\frac{6r}{8} -3\)

= \(\frac{-r}{8} -\frac{r}{6} +\frac{6r}{8} -5-3\)

= \(\frac{-3r-4r}{24}+\frac{6r}{8} -8\)

= \(\frac{-7r}{24} +\frac{6r}{8} -8\\\)

= \(\frac{-7r+18r}{24} -8\)

= \(\frac{11r}{24} -8\)

= \(\frac{11}{24} *r+(-8)\)

Therefore the correct answer is option D which is 11 over 24 times r plus negative 8.

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Answer:

y = -x + 2

Step-by-step explanation:

(-3,5) and (4,-2)

Slope: (-2-5)/(4 - - 3) = -7/7 = -1

y-intercept= -2 - (-1)(4) = -2 + 4 = 2

Answer:

Your answer is B

Step-by-step explanation:

The rule for angles is that 115 and the angles right next to it, the ones that form the x, will equal 180. That means all you have to do is 115-180=65.

Another rule is that the interior angles of a triangle will be 180, so you add the angles we know in each triangle, 80+65+angle 1 = 180. If you do this correctly you should get angle 1 to be 35. Then you repeat on the opposite side except this time the angles are 85+65+angle 2 = 180. If you do this one correct you should get 30. Which makes your answer B.

Sorry if this is confusing the book will have better explanations than I can give.

Answer:

$163.8 more.

Step-by-step explanation:

Let's use the formula Principle × Rate × Time, or PRT to find our simple interest. Let's fill in the blanks. Our principle is $630. Our rate is 6.5% and our time is 4 years. Next, we multiply all this. $630 × 13/200 × 4. Our answer would be 163.8. I hoped this helped.

=================================================

Explanation:

Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

If tan(theta) < 0, then this means cos(theta) > 0

So we have y < 0 and x > 0 which places the angle somewhere in Q4.

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

Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

a^2+b^2 = c^2

7^2+b^2 = 25^2

b^2+49 = 625

b^2 = 625-49

b^2 = 576

b = sqrt(576)

b = 24

So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

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

As an alternative, you could use the trig identity

sin^2(x) + cos^2(x) = 1

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

sin^2(x) + cos^2(x) = 1

(-7/25)^2 + cos^2(x) = 1

(49/625) + cos^2(x) = 1

cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

cos^2(x) = 576/625

cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)

f(×) =-1-21/4yn Thanks me later

Answer:

3.75

Step-by-step explanation:

1.25 times 3

Answer:

$3.33

Step-by-step explanation:

In order to find the unit rate, you divide the price of the product by the amount of it (oz, lbs, etc.) In this case, divide 1.25/12. You get 0.104. Then, multiply the single unit cost by 32. This results in 3.33. This means that your cost for a 32 ounce soda would be $3.33. Hope this helps :)

Answer:

-2.05

Step-by-step explanation:

You can just simply type this into your search bar, and when you do that, you get -2.05.

the coefficient of determination is 0.7, indicating that the independent variables explain 70% of the variation in the dependent variable.

The coefficient of determination, also known as R-squared, is a measure of how well the independent variables explain the variation in the dependent variable. It is calculated as the ratio of the explained variation to the total variation.

In this case, SST (total sum of squares) is 800 and SSE (error sum of squares) is 240. Therefore, the explained sum of squares (SSE) is 800 - 240 = 560.

The coefficient of determination is then calculated as:

R-squared = explained variation / total variation

R-squared = 560 / 800

R-squared = 0.7

Therefore, the coefficient of determination is 0.7, indicating that the independent variables explain 70% of the variation in the dependent variable.

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The coefficient of determination (R²) in this multiple regression analysis involving 15 independent variables and 200 observations is equal to 0.7.

To find the coefficient of determination, we'll use the following terms:

SST (total sum of squares), SSE (sum of squared errors), and

the formula R² = 1 - (SSE / SST).

the values for SST (800) and SSE (240).

Using the formula, we can calculate the coefficient of determination (R²) as follows:

R² = 1 - (SSE / SST)

R² = 1 - (240 / 800)

R² = 1 - 0.3

R² = 0.7

The coefficient of determination (R²) in this multiple regression analysis involving 15 independent variables and 200 observations is equal to 0.7.

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To provide a general real-valued solution to a linear system of differential equations, specific equations need to be provided. Without the specific equations, it is not possible to determine the exact solution.

In general, a linear system of differential equations can be written in matrix form as follows:

dY/dt = AY,

where Y is a vector of functions, t is the independent variable, and A is a constant matrix.

To solve this system, one can use methods such as matrix diagonalization, eigenvalues, and eigenvectors, or the method of variation of parameters. These methods allow you to find the general solution of the system, which represents a family of solutions that satisfy the given equations.

It is important to note that the specific form of matrix A and the initial or boundary conditions if provided, will determine the exact solution to the system of differential equations.

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Answer:

The lengths of the diagonals are;

15.49 cm and 5.66 cm

Step-by-step explanation:

The given area of the parallelogram = 30 cm²

Also the length of 2 adjacent sides are 6 cm and 10 cm

Given that the formula for the area of a parallelogram = Base × Height, h where the base is either of the sides of the parallelogram we have;

When the base b = 10 m and the other side, a = 6 cm the diagonal, d is given by the relationship, d² = (a + √(b² - h²))² + h²

10 × h₁ = 30

h₁ = 30/10 = 3

d₁² = (b + √(a² - h₁²))² + h₁² = (10 + √(6² - 3²))² + 3² = 239.92 cm²

d₁ = √(239.92 cm²) = 15.49 cm

The other diagonal can be found from the following relationship;

d₂² = (b - √(a² - h₁²))² + h₁²

d₂² = (10 - √(6² - 3²))² + 3² = 32.08 cm²

d₂ = √(32.08 cm²) = 5.66 cm.

Answer: 76.8km/hr

Explanation:

PT1

sp1 - 30km/hr

d1 - 60km

60 divided by 30 = 2hrs

PT2

sp2 - 160km/hr

d2 - 180km

180 divided by 30 = 1hr, 7min, 30sec (1.125)

PT3

Total Time Taken - 2hrs + (1:07:30) 1.125 = 3.125hrs

Avg. Speed - (60km + 180km) divided by 3.125hrs

60km + 180km = 240

240km divided by 3.125 = 76.8km/hr

The system of equations has two solutions: (0,2) and (-4/5, -6/5).

The substitution method is a way to solve a system of two linear equations with two variables. The method involves solving one of the equations for one of the variables, and then substituting that expression into the other equation in place of the same variable. This process reduces the system of two equations and two variables to a single equation and a single variable, which can then be solved.

We have the system of equations:

4x² + y² = 4 ........(1)

y = x + 2 ........(2)

We can solve this system of equations by substitution.

Substitute (2) into (1) to eliminate y:

4x² + (x + 2)² = 4

Simplify and solve for x:

4x² + x² + 4x + 4 = 4

5x²+ 4x = 0

x(5x + 4) = 0

x = 0 or x = -4/5

If x = 0, then from equation (2), y = 2. So one solution is (x,y) = (0,2).

If x = -4/5, then from equation (2), y = -6/5. So the other solution is (x,y) = (-4/5, -6/5).

Therefore, the system of equations has two solutions: (0,2) and (-4/5, -6/5).

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Answer:

Let P be thd population of rabbit

P = 2 to the power of n

where n is the period of month

Answer: 0

Step-by-step explanation:

Slope (m) is defined by the formula change in y divided by the change in x. You could denote "change in" using Δ (delta).

The change in y is your final postion along the y-axis, subtracted by your initial position on the y axis.

The change in x is your final position among the x-axis, subtracted by your initial position.

Think of these two sets of coords like two positions. Your final y was 2, and your initial was also 2. Do 2 - 2 to get 0. We dont even need to solve for delta x because 0 divided by anything is zero. Therefore your slope will be 0. That basically means you have a critical point of the function. The tangent line will be completely horizontal along that interval of coords.

To find the slope of the line, I will be showing you the table method.

To find the slope of the line using the table method,

we start by making a table for our ordered pairs.

We will put the x values in the left column

and the y values in the right column.

Our first ordered pair is (-5, 2), so we put a

-5 in the x column and a 2 in the y column.

Our second ordered pair is (4, 2), so we put a

4 in the x column and a 2 in the y column.

Next, remember that the slope or m, is always equal to

the rate of change or the change in y over the change in x.

Using our table, we can see that the y values

go from 2 to 2 so the change in y is 0.

The x values go from -5 to 4 so the change in x is 9.

Therefore, the rate of change, or the change in y

over the change in x is 0/9 which simplifies 0.

This means that the slope is also equal to 0.

An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 19 - 6(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 19

Second term, a₂ = 13

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 13 - 19

Common difference, d = -6

Substituting the parameters into the mathematical expression, we have;

aₙ = 19 + (n - 1)(-6)

aₙ = 19 - 6(n - 1).

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The standard normal distribution is not uniform, but rather bell-shaped, symmetric about the mean, and unimodal. Therefore, the answer is b) It's uniform.

The standard normal distribution is a continuous probability distribution that has a mean of zero and a standard deviation of one.

It is characterized by being bell-shaped, symmetric about the mean, and unimodal, which means that it has a single peak in the center of the distribution.

The probability density function of the standard normal distribution is a bell-shaped curve that is determined by the mean and standard deviation.

The curve is highest at the mean, which is zero, and it decreases as we move away from the mean in either direction.

The curve approaches zero as we move to positive or negative infinity.

In a uniform distribution, the probability density function is a constant, which means that all values have an equal probability of occurring.

Therefore, the standard normal distribution is not uniform because the probability density function varies depending on the distance from the mean.

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Step-by-step explanation:

a1 = 27

r = -9/27 = -⅓

the formula :

an = a1. r^(n-1)

= 27. (-⅓)^(n-1)

= 3³(-3`¹)^(n-1)

= 3³(-3)^(1-n)

Answer:

$110.40

Step-by-step explanation:

8% of $120 is $9.06 so you take that away from 120 and you have 110.40