A certain four​-cylinder combination lock has 55 numbers on it. to open​ it, you turn to a number on the first​ cylinder, then to a second number on the second​ cylinder, and then to a third number on the third cylinder and so on until a four​-number lock combination has been affected. repetitions are​ allowed, and any of the 55 numbers can be used at each step to form the combination.​ (a) how many different lock combinations are​ there

This should help

3 * a - 2 = a + 10

Answer:

parabola

Step-by-step explanation:

That would be a parabola.  The "single point" is the "focus" of the parabola, and the "given line" is the "directrix."

Answer:

It is the answer C

Step-by-step explanation:

The homogeneous ODE

[tex]36y''-y=0[/tex]

has characteristic equation

[tex]36r^2-1=0[/tex]

with roots at [tex]r=\pm\dfrac16[/tex], and admits two linearly independent solutions,

[tex]y_1=e^{x/6}[/tex]

[tex]y_2=e^{-x/6}[/tex]

as the Wronskian is

[tex]W(y_1,y_2)=\begin{vmatrix}e^{x/6}&e^{-x/6}\\\\\dfrac16e^{x/6}&-\dfrac16e^{-x/6}\end{vmatrix}=-\dfrac13\neq0[/tex]

Variation of parameters has us looking for solutions of the form

[tex]y_p=u_1y_1+u_2y_2[/tex]

such that

[tex]u_1=-\displaystyle\int\frac{y_2xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]

[tex]u_2=\displaystyle\int\frac{y_1xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]

We have

[tex]u_1=\displaystyle3\int x\,\mathrm dx=\dfrac{3x^2}2[/tex]

[tex]u_2=\displaystyle-3\int xe^{x/3}\,\mathrm dx=-9e^{x/3}(x-3)[/tex]

and we get

[tex]y_p=\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]

The general solution is

[tex]y=y_c+y_p[/tex]

[tex]y=C_1e^{x/6}+C_2e^{-x/6}+\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]

The initial conditions tell us

[tex]\begin{cases}1=C_1+C_2+27\\\\0=\dfrac{C_1}6-\dfrac{C_2}6-\dfrac92\end{cases}\implies C_1=\dfrac12,C_2=-\dfrac{53}2[/tex]

so that the particular solution is

[tex]y=\dfrac12e^{x/6}-\dfrac{53}2e^{-x/6}+\dfrac32x^2e^{x/6}-9e^{x/6}(x-3)[/tex]

Answer:

Step-by-step explanation:

If MN is tangent of a circle then the angle M is a right angle.

We have a dimeter of acircle d = 8 cm.

Therefore the radius CM = 8 cm : 2 = 4cm.

In a right triangle CMN use the Pythagorean theorem:

[tex]CM^2+MN^2=CN^2[/tex]

Substitute CM = 4cm and CN = 9.9 cm:

[tex]4^2+MN^2=9.9^2[/tex]

[tex]16+MN^2=98.01[/tex]          subtract 16 from both sides

[tex]MN^2=82.01\to MN=\sqrt{82.1}\\\\MN\approx9.1[/tex]

Answer:

92

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

140 = x+2 + 2x

Combine like terms

140 = 3x +2

Subtract 2 from each side

140-2 = 3x+2-2

138 = 3x

Divide by 3

138/3 = 3x/3

46=x

We want to find angle B

B = 2x

B = 2(46)

B = 92

Answer:

y = -3x + 20

Step-by-step explanation:

See attached photo for explanation

Angles are usually  given in degrees or in radians.

A circle is 360 degrees.

To convert degrees to radians, multiply the known degree by π/180.

Example 45 degrees = 45 x π/180 = 0.7854 radians.

To convert radians to degrees, multiply the known radian by 180/π.

5 radian = 5 x 180/π = 286.48 degrees.

The correlation between the measurements is written below.

An angle is a combination of two rays with a common endpoint.

The endpoint is called as the vertex of the angle,the rays are called the sides.

The various units in which angle is measure are Degree, radians and revolutions

A revolution is the measure of an angle formed when the initial side rotates all the way around its vertex until it reaches its initial position

One radian (1 rad) is the measure of the central angle (an angle whose vertex is the center of a circle) that intercepts an arc whose length is equal to the radius of the circle.

A degree is equal to 360 revolutions.

The correlation between the measurements can be written as

[tex]\rm 1 \;radian =(\dfrac{180}{\pi })^o = \dfrac{1}{2\pi } revolution[/tex]

For example 30° = π/6 radian = 1/12 revolutions

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the distance from the origin is 5, so

sqrt(x²+y²)=5

x²+y²=25

substitue y=x²

y+y²=25

y²+y-25=0

solve using calculator or the formula

to get

y =( -1+sqrt(1+4*25))/2

or y = (-1-sqrt(1+4*25))/2

the second solution is rejected because a square cannot be negative

the value of x is the positive or negative (sqrt... or -sqrt...) or y

Answer:

D : One Real Root

Step-by-step explanation:

Isolate "4x" by subtracting 7 from both sides.

So we get

4x = -7

Then we divide each side by 4 to get -7/4

x = -7/4 so there is only one real root.

Final answer:

The equation 4x+7=0 is a linear equation with only one real root, which is -1.75. Therefore, the correct option is d. 1 real root.

Explanation:

The given equation 4x+7=0 is a linear equation, not a quadratic equation. To find the roots, we only have one variable raised to the first power, which means this equation will only have one solution. We can solve this by isolating the variable x:

4x = -7

x = -7 / 4

x = -1.75

Therefore, the correct answer is d. 1 real root, as the equation has exactly one real solution and no imaginary roots.

Answer:

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Step-by-step explanation:

If the line is 3x - 4y = 1 then the line which is parallel will have the same coefficients of x and y. Parallel lines never cross and to ensure this have the same slope. The slope is a ratio which can be solved for in an equation using the coefficients of x and y. Here the slope is:

3x - 4y = 1

-4y = -3x + 1

y = 3/4x - 1/4.

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Answer: y= 3/4x +5

Step-by-step explanation: just did it

If the graph of any function is an unbroken curve, then the function is continuous. Let's study the function at the the point [/tex]x=5[/tex]:

At this point the function has the following value:

[tex]f(5)=-\frac{3}{4}[/tex], so the function in fact exists here, but let's find the limit here using:

[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]

So:

[tex]\underset{x\rightarrow5}{lim}\frac{x^2-7x+10}{x^2-14x+45}[/tex]

By factoring out this function we have:

[tex]\underset{x\rightarrow5}{lim}\frac{(x-2)(x-5)}{(x-5)(x-9)} \\ \\ \therefore \underset{x\rightarrow5}{lim}\frac{(x-2)}{(x-9)} \\ \\ \therefore \frac{(5-2)}{(5-9)}=-\frac{3}{4}[/tex]

Since [tex]\underset{x\rightarrow5}{lim}f(x)=f(5)[/tex] then the function is continuous here.

Let's come back to our function:

[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]

If we factor out this function we get:

[tex]f(x)=\frac{(x-2)}{(x-9)}[/tex]

Notice that at x = 9 the denominator becomes 0 implying that at this x-value there is a vertical asymptote. The graph of this function is shown below and you can see that at x = 9 the function is not continous

Therefore, the answer is:

b. continous at every point exept [tex]x=9[/tex]

Answer:

B: continuous at every real number except x = 9

Step-by-step explanation: EDGE 2020

Answer:

Option c. Reflection across the x-axis and vertical stretch by a factor of 7

Step-by-step explanation:

If the graph of the function [tex]y = cf(x)[/tex] represents the transformations made to the graph of [tex]y = f(x)[/tex] then, by definition:

If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor a.

If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor a.

If [tex]c <0[/tex] then the graph is reflected on the x axis.

In this problem we have the function [tex]y = -7secx[/tex] and our paretn function is [tex]y = secx[/tex]

therefore it is true that

[tex]c = -7\\\\|-7|> 1\\\\-7 <0[/tex].

Therefore the graph of [tex]y = secx[/tex] is stretched vertically by a factor of 7 and is reflected on the x-axis

Finally the answer is Option c

Answer:

Yes

Step-by-step explanation:

This is a function since it is one to one. The writing is unclear here though since the function could be f(x) = x + (12/5) or f(x) = (x+12)/5. Either way the function passes the vertical line test when graphed. Both functions show a linear function. See the two attached graphs. Both are functions since the vertical line does not cross more than once through the function when drawn.

Answer:

e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.

Step-by-step explanation:

The central limit theorem states that

"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."

This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean.  This does not state that the sample mean will always be the same as the population mean.

correct answer is option (c)

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.

What is Standard deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

How Standard deviation is calculated?

Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. The formula is:

[tex]\begin{aligned} &\text{Standard Deviation} = \sqrt{ \frac{\sum_{i=1}^{n}\left(x_i - \overline{x}\right)^2} {n-1} }\\ &\textbf{where:}\\ &x_i = \text{Value of the } i^{th} \text{ point in the data set}\\ &\overline{x}= \text{The mean value of the data set}\\ &n = \text{The number of data points in the data set} \end{aligned}[/tex]

So, In the given options,

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken is False, because according Central limit theorem,

regardless of the shape of the population(X): If the sample size is greater than 30. The Sample distribution will be Normal Distribution.

Hence,

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.

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Answer:

Step-by-step explanation:

We know that the sum of the measures of angles on one side of the parallelogram is 180°.

We have the equation:

(6x - 12) + (132 - x) = 180

6x - 12 + 132 - x = 180               combine like terms

(6x - x) + (-12 + 132) = 180

5x + 120 = 180              subtract 120 from both sides

5x = 60          divide both sides by 5

x = 12

Opposite angles in the parallelogram are congruent.

Therefore:

6y + 18 = 6x - 12

Put the value of x to the equation and solve it for y:

6y + 18 = 6(12) - 12

6y + 18 = 72 - 12

6y + 18 = 60           subtract 18 from both sides

6y = 42          divide both sides by 6

y = 7

Answer:

(F-G)(x) = -1

Step-by-step explanation:

The notation (F - G)(x) means to subtract each function when x = 6. According to the sets when x = 6 then F is (6,8) and G is (6,9). To subtract the functions, subtract their output values. (F-G)(x) = 8 - 9 = -1.

Answer:31.56

Step-by-step explanation:

take 37.50 and divide it by 100

then multiply that by 80

you should get 30,

30 is 80% of 37.50 which is 20% off of the original price

then you divide 30 by 100 and multiply it by 5.2

this will get you 1.56

add that to 30 and you get 31.56

1/4 = 1/8

times by 4 to find the whole song as 1/4 × 4 is 1

1 = 4/8

4/8 = 1/2 of a minute

No, it is not the same because in option 1, the interest is calculated based on two different principal amounts and then added together. The principal amounts will be different every year because of the varying interest rates. Since one of the interest rates in option 1 is 7%, the principal will grow at a faster rate because the interest rate is applied to a greater and greater principal amount over time. In option 2, the interest is being calculated only on one principal  

Answer:

Step-by-step explanation:

No, they are not always the same - the only time that they will be the same is after the first year:

$4000*1.05 + $4000*1.07 = $8480 = $8000*1.06

From there on, they will diverge. For example after the second year:

$4000*1.05^2 + $4000*1.07^2 = $8989.6

$8000*1.06^2 = $8988.8

After the third year:

$4000*1.05^3 + $4000*1.07^3 = $9530.672

$8000*1.06^3 = $9528.128

After the nth year:

The first option gives $4000*(1.05^n + 1.07^n)

The second option gives $8000*(1.06^n)

= $4000*(2)*(1.06^n)

= $4000*(1.06^n + 1.06^n)

Because 1.07^n - 1.06^n > 1.06^n - 1.05^n for n>1, the first option will be a better investment.

Answer:

X= 5

EF= 58 degrees

GH= 55 degrees

Step-by-step explanation:

Answers on edg.

Answer:

14

Step-by-step explanation:

each bag weighs 0.625 ounces

The cost of each bag of popcorn will be 0.625 ounces.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

As per the given,

Weight of empty bag  = 5 ounce

Weight of full bag = 35 ounce

Weight of popcorns bag = 3 5 - 5 = 30 ounce

Number of bags = 48

Per bag weight = 30/48 = 0.625 ounce

Hence "The cost of each bag of popcorn will be 0.625 ounces".

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[tex]\boxed{A=43.54cm^2}[/tex]

To find this area we will use the law of cosine and the Heron's formula. First of all, let't find the unknown side using the law of cosine:

[tex]x^2=12^2+8^2-2(12)(8)cos(65^{\circ}) \\ \\ x^2=144+64-192(0.42) \\ \\ x^2=208-80.64 \\ \\ x^2=127.36 \\ \\ x=\sqrt{127.36} \\ \\ \therefore \boxed{x=11.28cm}[/tex]

Heron's formula (also called hero's formula) is used to find the area of a triangle using the triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] being [tex]a,\:b\:and\:c[/tex] the corresponding sides of the triangle.

So the semiperimeter is:

[tex]s=\frac{12+8+11.28}{2} \\ \\ s=15.64cm[/tex]

So the area is:

[tex]A=\sqrt{15.64(15.64-12)(15.64-8)(15.64-11.28)} \\ \\ \therefore \boxed{A=43.54cm^2}[/tex]

Answer: [tex]0.0003136\ J[/tex] or [tex]3.136*10^{-4}J[/tex]

Step-by-step explanation:

By definiition, when you multiply 1 Newton (N) by 1 meter (m), the unit obtained is an unit called "Joule", whose symbol is J.

Joule (J) is an unit of energy, work or heat.

Then to solve the exercise, you must multiply 0.0196 N by 0.016 m. Therefore, you obtain that the product is:

[tex](0.0196N)(0.016m)=0.0003136J[/tex] or [tex]3.136*10^{-4}J[/tex]

Answer:   0.000314mn

Step-by-step explanation:

(0.0196N)*(0.016M)

     0.000314mn

What sentence below

Buckets of Soil : Buckets of Peat Moss = 5 : 4

Since Mr Carver needs to use 324 buckets in all,

He needs to use 324 * 5/9 = 180 buckets of Soil and 324 * 4/9 = 144 buckets of Peat Moss.

Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed, based on the given ratio of 5 buckets of soil to 4 buckets of peat moss.

The problem at hand revolves around ratios and proportions where Mr. Carver is using a mix of soil and peat moss in a specific ratio to fill a planting bed. Given the ratio of 5 buckets of soil to 4 buckets of peat moss, we need to find the total number of buckets for each that will sum up to 324 buckets. First, we'll find the total number of parts in the ratio by adding 5 (for soil) and 4 (for peat moss), which gives us 9 parts. Since we have the total amount of 324 buckets, we can find the value of one part by dividing 324 by 9, which gives us 36.

Once we have the value of one part, we multiply it by the number of parts for soil and peat moss to find their respective quantities:

Therefore, Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed.

Answer:

27 times

Step-by-step explanation:

Given that sphere A is  similar to sphere B

Let radius of sphere B be x. Then the radius of

sphere A be 3 times radius of sphere B = 3x

Volume of sphere A = [tex]V_A=\frac{4}{3} \pi (3x)^3\\V_A=36 \pi x^3[/tex]

Volume of sphere B = [tex]V_B = \frac{4}{3} \pi x^3[/tex]

Ratio would be

[tex]\frac{V_A}{V_B} =\frac{36 \pi x^3}{\frac{4}{3}\pi x^3 } \\=27[/tex]

i.e. volume of sphere is 27 times volume of sphere B.

Answer: 27

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

[tex]3 \times {( \frac{1}{8} )}^{2x} = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x} = 4 \\ \Leftrightarrow {( {2}^{ - 3}) }^{2x} = {2}^{2} \\ \Leftrightarrow {2}^{ - 6x} = {2}^{2} \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - \frac{1}{3} \\ \\ 2 {\sqrt[3]{5}}^{4x} = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^{4x} = 25 \\ \Leftrightarrow {5}^{ \frac{4x}{3} } = {5}^{2} \\ \Leftrightarrow \frac{4x}{3} = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = \frac{3}{2} [/tex]

Answer to Q1:

x= -1/3

Step-by-step explanation:

We have given the equations.

We have to solve these equations.

The first equation is :

[tex]3.(\frac{1}{8})^{2x}[/tex]

[tex](\frac{1}{8})^{2x}=4[/tex]

[tex](2^{-3x})^{2x}=4[/tex]

[tex]2^{-6x}=4[/tex]

[tex]2^{-6x}=2^{2}[/tex]

As we know that bases are same then exponents are equal.

-6x = 2

x = 2/-6

x=-1/3

Answer to Q2:

x = 3/2

Step-by-step explanation:

The given equation is :

[tex]2.\sqrt[3]{5}^{4x}=50[/tex]

We have to find the value of x.

First,we multiply both sides of equation by 1/2 we get,

[tex]5^{4x/3}=25[/tex]

[tex]5^{4x/3}=5^{2}[/tex]

4x/3=2

4x = 6

x = 3/2

Answer:

Step-by-step explanation:

If you are asking how many hours she spent on the batting lessons, we can use an equation to solve this type of problem.

Lets represent the hours she spent batting in august with h.

$35h+15=$155

Since each hour costs 35 dollars, its reasonable that $35 times the number of hours she spent practicing would be the correct way to represent that.

Now, lets solve.

Subtract 15 on both sides.

$35h=$140

Divide both sides by 35 to isolate h.

h=4

She spent four hours on batting lessons that month.

Hope this helps!

The number of hours will be 4 hours.

Let the number of hours used be represented by h.

Based on the question, the equation that will be used in solving the question will be:

15 + (35 × h) = 155

15 + 35h = 155

Collect like terms.

35h = 155 - 15

35h = 140

Divide both side by 35

35h/35 = 140/35.

h = 4.

The number of hours is 4 hours.

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