Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 95 miles per hour. The eastbound train travels at 75 miles per hour. How long will it take for the two trains to be 442 miles apart?

Answer:

1

Step-by-step explanation:

The value of z-score will be –0.4. Then the correct option is B. The probability will be 0.34458. Then the correct option is C.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The annual salary of teachers in a certain state X has a mean of $54,000 and standard deviation of σ = $5,000.

The probability that the mean annual salary of a random sample of 64 teachers from this state is less than $52,000 will be

The mean of the sampling distribution of sample of means is $54,000 and the standard deviation is select an answer $5000.

Then the z-score will be

z = (52000 – 54000) / 5000

z = –2000 / 5000

z = –0.4

Then the correct option is B.

Then the probability will be

P(x < 52000) = P(z < 0.-4)

P(x < 52000) = 0.34458

Then the correct option is C.

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The expression equivalent to (8 x 10⁻⁵)+(6 x 10⁻⁵) / 5.6 x 10⁻³ on solving is  2.5 x 10⁻², so option B is correct.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The example of expression can be taken as x + y, where x and y are expressed as the sum.

Given:

(8 x 10⁻⁵)+(6 x 10⁻⁵) / 5.6 x 10⁻³

Take  10⁻⁵ common

10⁻⁵ (8 + 6) / 5.6 x 10⁻³

14 x 10⁻⁵ / 5.6 x 10⁻³

2.5 x 10⁻²

Thus, the (8 x 10⁻⁵)+(6 x 10⁻⁵) / 5.6 x 10⁻³ = 2.5 x 10⁻²

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Answer:

\(5x + 1 + 90 + 7x - 7 \\ 12x + 84 \\ 12x = - 84 \\ x = 7\)

No. We cannot always use synthetic divison to divide polynomials.

Synthetic division can only be used to divide polynomials if the degree of the denominator is  equal to one.

Synthetic division is only used for a linear factor of the denominator.

When the degree of the denominator is greater than one, we can use long division.

So, we cannot always use synthetic division for dividing polynomials

Therefore, no. We cannot always use synthetic divison to divide polynomials.

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Answer:

18 feet

Step-by-step explanation:

Equilateral triangles have 3 equal sides.

If one side is 6 feet, the other two are also 6 feet.

Perimeter is all the sides added.

6 + 6 + 6

= 18

Answer:

The length of YZ is 14 inches.

Step-by-step explanation:

Given, Raidius of the circle is 7 inches.

The Centre is X.

To Find: The length of YZ is _____ inches.

Solve:

radius is 7 inches

diameter = raidius + raidius

diameter = 7 + 7

diameter = 14 inches.

The Solution is 14.

The proportional relationship used to determine the total number of chairs in x rows is given as follows:

y = 38x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

There are 304 chairs in 8 rows, hence the constant is given as follows:

k = 304/8

k = 38.

Meaning that the equation is given as follows:

y = 38x.

And that the fourth option is correct.

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Answer:

45

Step-by-step explanation:

Number of Latvian footballers(n¹) = 36

Numer of footballers of other nationalities(n²)=36/4=9

Now total number of footballers= n¹+n²= 36+9 =45

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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Answer:

ind f(x) and g(x) so that the function can be described as y = f(g(x)). (1 point) y = Four divided by x squared. + 9

=

Answer:

integrates by parts:

             U = x   dV = f''

            dU  = dx   V = f'

The integral becomes:

     x f'  - integral f' dx

 =   x  f'  -  f

limit as x->4 :   4 * f'(4) - f(4) = 4 * -3 -  7

                                  = -12-7 = -19

limit as x->1 : 1 * f'(1) - f(1) = 1 * 9 - 8 = 1

subtracting: -19-1 = -20

Step-by-step explanation:

Answer:

x = 19°

Step-by-step explanation:

.........................

Forgive me if wrong

Answer:

Sammy: 20 Cheng: 30

Step-by-step explanation:

We can say that Sammy can do the job in \(x\) hours. So Cheng would take \(x + 10\) hours. So we can say the the velocity or speed of both of them combined is \(\frac{1}{x} + \frac{1}{x + 10} = 12\). Multiplying , we get \(1 = 12(\frac{1}{x} + \frac{1}{x + 10})\). Simplifying, we get (x-20)(x+6)=0 and this means Sammy takes 20 hours and Cheng takes 20+10=30 hours to do the job.

Sammy can pave a driveway in 15 hours while it takes Cheng 25 hours to do the same work alone. We find these numbers by setting up and solving equations based on their combined work rate.

Let's denote the time it takes for Sammy to pave a driveway as x hours. Because Cheng takes 10 hours longer to do the same job, we'll represent Cheng's paving time as x + 10 hours. The question gives us that together, Sammy and Cheng can pave a driveway in 12 hours.

The work rate for any worker is defined as 'one job' divided by the 'time to complete that job', which gives us 1/x jobs/hour for Sammy and 1/x + 10 jobs/hour for Cheng. The combined rate is 1/12 jobs/hour. Therefore, set the equation for Samy and Cheng's combined work rate: 1/x + 1/x + 10 = 1/12.

Solving this equation will give you:

x = 15 hours for Sammy and x + 10 hours = 25 hours for Cheng.

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Answer:

Remember length times width times height when finding volume.

In non-terms of pi, the answer would be \(2\) \(ft^2\)

Answer:

Volume is 2ft

Step-by-step explanation:

Multiply the length x width once you find the answer for lengthxwidth.

Multiply the answer you got by height

Answer:

Choice C. \(3,\! 780\).

Step-by-step explanation:

The word "\(\verb!TENNESSEE!\)" contains nine letters:

If all these nine letters are unique, the number of possible arrangements would be:

\(P(9, 9) = 9! = 362,\! 880\).

However, because some of these letters were not unique, a large number of that \(362,\!880\) arrangements would be duplicates. What would be the exact number of duplicates? Start by considering giving each of the duplicate letters an index number. For example, consider the duplicates due to the letter "\(\verb!E!\)". There are four \(\verb!E!\)'s in \(\verb!TENNESSEE!\). Label them as \(\verb!E!_1\), \(\verb!E!_2\), \(\verb!E!_3\), and \(\verb!E!_4\):

\(\begin{array}{ccccccccc}\verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ & \uparrow & & & \uparrow & & & \uparrow & \uparrow \\ & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\end{array}\).

These four \(\verb!E!\) can be shuffled and rearranged to give a large number of duplicates:

\(\begin{array}{r|ccccccccc}& \verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ &&\uparrow&&&\uparrow&&&\uparrow &\uparrow\\ 1 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\\ 2 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_4 & \verb!E!_3 \\ 3 & & \verb!E!_1 & & & \verb!E!_4 & & & \verb!E!_3 & \verb!E!_2 \\\ \vdots & & \vdots & & & \vdots & & & \vdots&\vdots \\4! = 24&&\verb!E!_4 & & & \verb!E!_3 & & & \verb!E!_2 & \verb!E!_1 \end{array}\).

Each of these duplicate corresponds to a unique way for arranging four unique item in a row. There are \(4! = 24\) ways to arrange four unique items in a row. Therefore, for each arrangement that is truly unique, the letter "\(\verb!E!\)" alone would have caused the arrangement to be counted \(4! = 24\) times if the nine letters were assumed to be unique.

At the same time, letters "\(\verb!N!\)" and "\(\verb!S!\)" would further exaggerate the count by a factor of \(2\) each. On the other hand, the letter \(\verb!T!\) appeared only once and would not create duplicates.

Overall, if the nine letters were assumed to be unique, each arrangement that is truly unique would have been counted:

\(4! \times 2! \times 2! \times 1! = 96\; \text{times}\).

The count based on the incorrect assumption (that the nine letters are all distinct) is \(362,\!880\). Divide that count by the factor of exaggeration (\(4! \times 2! \times 2! \times 1! = 96\)) to find the number of arrangements that are truly unique:

\(\begin{aligned} & 362,\!880 \times \frac{1}{4! \times 2! \times 2! \times 1!} = 3,\!780\end{aligned}\).

Answer:

Quadratic regression: y=A+Bx+Cx2

The value of c does not affect the covariance of Y and Z.

The covariance of Y and Z can be calculated as Cov(Y, Z) = E[YZ] - E[Y]E[Z]. Since X is Bernoulli with parameter p and E[X] = p, we have E[Z] = pE[Y]. Hence,

Cov(Y, Z) = E[YZ] - E[Y]E[Z]

= E[YXY] - pE[Y]^2

= pE[Y^2 X] - pE[Y]^2

= p(E[Y^2]E[X] + Var[Y]p) - pE[Y]^2

= p(1 * p + 1 * p^2) - p^2

= p - p^2

It can be seen that the value of c does not affect the covariance of Y and Z.

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Given:

Sides of rectangle

x+14

x-20

Required:

To tell which does equation show

Explanation:

Represent (area) is a quantity used to indicate the extent of a surface or plane figure

Required answer:

(area)

Answer:

Step-by-step explanation:

HCF of 45 and 60

= 15

45/3

=15

3/3

=1

1 mile= 15 min

x by 4

4 mile = 60 min

4 mile= 1 hour

Answer:

3/45

Step-by-step explanation:

you need to use distance divided by time to find his rate of speed.

Your ability to borrow money at lower rates improves as your credit score increases. Option D.

Your ability to borrow money at lower rates improves as your credit score increases.

A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.

Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.

While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.

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Answer:

The side length is \(\frac{6}{\sqrt{2} }\).

Step-by-step explanation:

We are given the diagonal of the square: 6 meters.

Using the formula with given side length:

\(a=q\div\sqrt{2}\)

We can see that the diagonal length of the square divided by the square root of 2 can find the missing side length.

Hence the answer is 6√2.

The two unit rates that represent the given recipe are:

A unit rate is a rate in which the denominator is 1. In the given recipe, we can express two unit rates as follows:

Milk per egg:

The recipe uses 2 tablespoons of milk for every 3 eggs. To express this as a unit rate, we can divide both sides by 3 to get the amount of milk used per egg, hence, the unit is 2/3 tablespoons of milk per egg

Eggs per milk:

We can express the recipe in terms of eggs per tablespoon of milk. To do this, we can divide both sides by 2 to get the number of eggs per tablespoon of milk, hence, the unit is 3/2 eggs per tablespoon of milk

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Answer:

24 square units

Step-by-step explanation:

The formula for computing the area of a trapezoid is shown below:

As we know that

Area of a trapezium is

\(= \frac{1}{2} \times h(a+b)\)

where

h = perpendicular height

The a and b =  length of the parallel sides.

Now,

h = 2 - -2 = 4 units

a = 5 - -3 = 8 units

b = 3 - -1 = 4 units

Now placing these values to the above formula

So, the area of a trapezoid is

\(= \dfrac{1}{2} \times 4(8+4)\)

\(= 2 \times 12\)

= 24 square units.

Hence we applied the above formula so that the area of trapezoid could come

Answer: The answer would be 1

Step-by-step explanation:

Rise over run or fall over run so the fall is 10 and run is 10 and 10/10 is 1.

To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

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♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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Answer:

Step-by-step explanation:

To prove that 2 lines are parallel find the pair of corresponding angles equal in measure

From the given figure

Then the statement 3 is

Since we prove that Then VX // SU

Then the statement 6 is

VX // SU ---------- Converse of Corresponding Angles Theorem

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=3\\ k=-10\\ \end{cases}\implies y=a(~~x-3~~)^2 + (-10)\hspace{4em}\textit{we also know that} \begin{cases} x=0\\ y=8 \end{cases} \\\\\\ 8=a(~~0-3~~)^2 + (-10)\implies 8=9a-10\implies 18=9a\implies \cfrac{18}{9}=a \\\\\\ 2=a\hspace{7em}y=2(~~x-3~~)^2 + (-10)\implies \boxed{y=2(x-3)^2-10}\)

Answer:

2

Step-by-step explanation:

g(x) = 2x-1

g(-3)+5

2(-3)-1 +5

-6-1+5

-7+5

-2