Translate the sentence into an equation. Nine less than the product of 6 and a number equals 2.

Answer:

Step-by-step explanation:

Let the speed of the plane in sill air is p and the speed of the wind is w.

We have the following equations:

Add up the equations and solve for p:

Find the value of w:

\(\bold{\huge{\underline{ Solution }}}\)

Let assume that the speed of plane is x

whereas, The speed of the wind is y

According to the first condition

That is,

Speed of plane + Speed of wind = 259 km/h

Subsitute the required variables,

\(\bold{ x + y = 259 }\)

\(\sf{ x = 259 - y...eq(1) }\)

That is,

Speed of plane - Speed of wind = 211 km/h

\(\bold{ x - y = 211 ...eq(2) }\)

Subsitute eq(1) in eq( 2 ) :-

\(\sf{ 259 - y - y = 211 }\)

\(\sf{ 259 - 2y = 211 }\)

\(\sf{ - 2y = 211 - 259 }\)

\(\sf{ - 2y = -48 }\)

\(\sf{ y = }{\sf{\dfrac{-48}{-2}}}\)

\(\sf{ y = }{\sf{\cancel{\dfrac{-48}{-2}}}}\)

\(\bold{ y = 24 }\)

Thus, The speed of wind that is y is 24 km/h

Subsitute the value of y in eq(1) :-

\(\sf{ x = 259 - 24 }\)

\(\bold{ x = 235 }\)

Hence, The speed of the wind and the plane in still is air are 24km/h and 235km/h .

7-(-4) is 4 units from 7 in the negative direction.

The number line keeps going both ways. You can include 6, 7, and so on, all the way up to the hundreds, thousands, and beyond, because the set of natural numbers only extends to the right.

A number line is a diagram that shows numerical values along a straight line that can be drawn either horizontally or vertically. It's simple for us to compare and compute basic arithmetic operations on numbers when they are written down on a number line. A number line's origin is typically thought to be zero (zero). There are only positive numbers to the right of zero and only negative numbers to the left of zero.

therefore,

7 - (-4)

= 7 + 4

= 11

when we simplify the expression we get the answer as 11 units

the result is that 11 units is 4 units away from 7 in a negative direction.

Hence we get the complete sentence.

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The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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Answer:

A. $107.20

Step-by-step explanation:

dont know sorry

In this problem, we are given a population growth model for Riverside County, California, and we need to use the model to make predictions about the population. The model is given as P(t) = \(A(1.04)^t\), where A is the population at time t = 0 and t is the time in years. We are asked to write a specific model for the population in terms of years after 2007, predict the population in 2027, and determine when the population will reach 3,000,000.

1. To write a specific model for the population of Riverside County in terms of years after 2007, we need to determine the value of A, which represents the population at time t = 0. Since the population in 2007 reached 2,000,000, we can substitute this value into the model. Therefore, the specific model for the population in terms of years after 2007 is P(t) = \(2,000,000(1.04)^t\).

2. To predict the population in 2027, we need to substitute t = 2027 - 2007 = 20 into the model. Therefore, the population in 2027 is P(20) = \(2,000,000(1.04)^{20\).

3. To predict when the population will reach 3,000,000, we need to solve the equation P(t) = 3,000,000. Substituting the model equation, we get \(2,000,000(1.04)^t\) = 3,000,000. Solving this equation will give us the value of t when the population reaches 3,000,000.

By following these steps, we can utilize the given population growth model to make predictions about the population of Riverside County in the future.

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Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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Answer:

\(x=\sqrt{13}\)

Step-by-step explanation:

Base of the isosceles triangle = 4

Perpendicular of the triangle = 3

In an isosceles triangle , a perpendicular bisects a base equally. So, here the isosceles triangle consist of 2 right angled triangles.

In that right angled triangles,

Base = 4/2 = 2 (∵ A perpendicular divides a base into 2 equal parts. )

Perpendicular = 3

Hypotenuse = x

So , according to Pythagorean Theorem ,

\(Hypotenuse = \sqrt{Base^2 + Perpendicular^2}\)

Using all the values above into the formula gives :-

\(x =\sqrt{2^2 + 3^2} = \sqrt{4+9} =\sqrt{13}\)

The probability that all 4 will fire is 1/6 and at most 2 will not fire is 39/49.

From a lot of 10 missiles, 4 are selected at ran- dom and fired.

Sample space = 10

the lot contains 3 defective missiles that will not fire

Non - defective missiles = 7

probability that all 4 will fire

P(all four will fire) = \(\frac{7}{10}.\frac{6}{9} .\frac{5}{8}.\frac{4}{7}\)

P(all four will fire) = 840/5040

P(all four will fire) = 1/6

Atmost two will not fire = P(all fire) + P(1 will not fire) + P(two will not fire)

= \(\frac{4}{7} + \frac{3}{7}.\frac{1}{3} + \frac{2}{7}.\frac{2}{7}\)

= 4/7 + 3/21 + 4/49

= 39/49

Therefore, the probability that all 4 will fire is 1/6 and at most 2 will not fire is 39/49.

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Using the concepts of the hypothesis test, it is found that the p-value is of 0.0007 corresponding to  ten students who  were surveyed and asked how many hours they spent playing video games.

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

H\(_o\) = μ=10.2

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

H₁=μ> 10.2

Ten students were surveyed, so there are 9 df. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.

Thus, using a t-distribution calculator, the p-value of the test is of 0.0007.

Hence, when the ten students were surveyed and asked how many hours they spent playing video games and the test statistics is equal to 0.45,then the p-value is 0.0007

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The correct answer is C. 2.821. This critical t-value is used in hypothesis testing and confidence interval calculations to determine the boundaries for accepting or rejecting a null hypothesis or to estimate the range within which a population parameter is likely to fall.

To find the critical t-value that corresponds to 99% confidence and n = 10, we can use the t-distribution. With a 99% confidence level, we want to find the t-value that leaves 1% of the area in the tail of the distribution.

Since n = 10, the degrees of freedom for this calculation will be n - 1 = 10 - 1 = 9. Using a t-distribution table or a statistical calculator, we can find that the critical t-value for a 99% confidence level and 9 degrees of freedom is approximately 2.821 when rounded to three decimal places.

Therefore, the correct answer is C. 2.821. This critical t-value is used in hypothesis testing and confidence interval calculations to determine the boundaries for accepting or rejecting a null hypothesis or to estimate the range within which a population parameter is likely to fall.

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The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 \(m/s^2\)

To find average angular velocity during dive use formula,

\(\omega=\frac{\theta}{t}\)

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula \(s=ut+\frac{1}{2}gt^2\)

here u=initial velocity=0

s=displacement of diver=10.4m

\(10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s\)

angular velocity, \(\omega=\frac{15.7}{1.456}=10.78\ rad/sec\)

Thus, the average angular velocity during the dive is 10.78 rad/sec.

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Answer:

y = 1sin(3x)

Step-by-step explanation:

y = A sin( (2π/ω)x )

A is amplitude = 1

ω is period = 2π/3

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

y = 1sin( 2π / (2π/3) x)

y = 1sin(3x)

The equation for the graph with a sinusoidal wave, given an amplitude of 1, a period of 2π/3, and a phase shift of 0, is y = sin((2π/3)x).

The equation for a sinusoidal wave can be written as:

y = A * sin(ωx + φ)

In this case, we are given the values of amplitude (A = 1), period (ω = 2π/3), and phase shift (φ = 0).

The amplitude (A) represents the maximum displacement or height of the wave from the center line. In this case, it is 1.

The period (ω) represents the length of one complete cycle of the wave. The period is the reciprocal of the frequency, and in this case, it is 2π/3.

The phase shift (φ) represents any horizontal displacement of the wave. In this case, the phase shift is 0, indicating that the wave starts at its equilibrium position.

Using these values, the equation for the given graph would be:

y = 1 * sin((2π/3)x + 0)

Simplifying it further:

y = sin((2π/3)x)

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Answer:12,16

Step-by-step explanation:

Answer:

16,28. 4,16. I'm not sure though

Answer:

Opps i am really sorry i donot know it

Answer:

Step-by-step explanation:

It's 5 units

It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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Answer:

28.3 units^2

Explanation:

The area A of the circle is given by the formula

where

π = 3.1415..

d = diameter of the circle.

Now, in our case d = 6; therefore,

Rounded to the nearest tenth this is

Answer:

Step-by-step explanation:

You can set the equation up like this

80=2x

Divide both sides by 2

x=40

Answer:

$336

Step-by-step explanation:

The slope is (277-100)/(3-0) = 59.

So, since the cost is $100 when t=0, C=59t+100.

After 4 months, the cost is 59(4)+100 = $336.

6/11

Step-by-step explanation:

hope it helps also what's the dot?

The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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Answer:

x = - 92

Step-by-step explanation:

-1/4x + 3 = 23

Step One:

Subtract 3 from both sides

- 1/4x = 20

Step Two:

Multiply both sides by - 4

x = - 92

Answer:

-80

Step-by-step explanation:

-1/4x + 3 = 23

-1/4x = 23 - 3

-1/4x = 20

x = 20 : -1/4

x = 20 . 4/-1

x = 20 . -4

x = -80

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

Brainliest

Step-by-step explanation:

The one you chose is correct

The equation 5(x + 1) - x = 3(x - 1) + 7 has one solution which is x = -1.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given equation is,

5(x + 1) - x = 3(x - 1) + 7

Using the distributive property,

5(x + 1) = 5x + 5 and 3(x - 1) = 3x - 3

Substituting,

5x + 5 - x = 3x - 3 + 7

(5x - x) + 5 = 3x + (-3 + 7)

4x + 5 = 3x + 4

4x - 3x = 4 - 5

x = -1

Hence the solution of the given equation is -1.

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Answer: 30 mph

Step-by-step explanation: Divide 158,400 by 5280(the amount of feet in a mile) to get your answer.

Answer: B: b=1/2

Step-by-step explanation: 1/4+2/4=3/4

2/4=1/2 so B or b=1/2

plz mark me brainliest

How to Mark Brainliest:

look at the bottom right of an answer there should be a crown if not look if there are 2 players if yes reload the page if no wait for someone else to answer then reload. tap the crown to mark brainliest.

Answer:

D

Step-by-step explanation:

Probability that the die will show an even number

in one rolling is 3/6=0,5 = p

We have formula for repeating rolling

n!/(r!(n-r)!) p^r (1-p)^(n-r)

n = how many times we repeat rolling = 6

r = how many times we want something to happen

(show an even number exactly two times) = 2

15 *(0,5)^2 *(0,5)^4 = 0,234375