The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?.

The nonempty set with no accumulation points and no isolated points cannot exist. An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). A nonempty set with no boundary points and no isolated points also cannot exist.

(a) A nonempty set with no accumulation points and no isolated points cannot exist. An accumulation point in a set is a value that every open interval contains a point from the set different than itself. An isolated point is a point that has an open interval containing only itself. Every point in a nonempty set must be either an accumulated point or an isolated point.

(b) An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). An interior point is a point where an open interval around the point lies completely within the set, which doesn't exist for this set. Also, this set does not contain any isolated points because between any two rational numbers, there always exists another rational number.

(c) A nonempty set with no boundary points and no isolated points cannot exist. A boundary point is a point that every neighborhood contains at least one point from the set and its complement. If a set does not have any boundary points, it means it cannot be separated from its complement, so it must be an empty set.

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Answer:

  There are 10 packets of​ sweet-pepper seeds and 6 packets of​ hot-pepper seeds.

Step-by-step explanation:

Let h represent the number of packets of hot pepper seeds. Then 16-h is the number of packets of sweet pepper seeds. The total cost of a 16-packet mix is ...

  4.56h + 2.32(16 -h) = 3.16·16

  2.24h + 37.12 = 50.56 . . . . . . . simplify

  2.24h = 13.44 . . . . . . . . . . . . . . subtract 37.12

  13.44/2.24 = h = 6 . . . . . . . . . . divide by 2.24

  16 -h = 16 -6 = 10 . . . . . . . . . . . number of sweet pepper seed packets

There are 10 packets of​ sweet-pepper seeds and 6 packets of​ hot-pepper seeds.

Answer:

95.44% of hotels are with rate between 144 and 176 euros

Step-by-step explanation:

Given

Mean = μ = 160 euros

SD = σ = 8 euros

We have to find the z-scores for both values

So,

z-score for 144 = z_1 = (x-μ)/σ = (144-160)/8 = -16/8 = -2

z-score for 176 = z_2 = (x-μ)/σ = (176-160)/8 = 16/8 = 2

Now the area to the left of z_1 = 0.0228

Area to the left of z_2 = 0.9772

Area between z_1 and z_2 = z_2-z_1

= 0.9772-0.0228

=0.9544

Converting into percentage

95.44%

Therefore, 95.44% of hotels are with rate between 144 and 176 euros..

Using the Empirical Rule for a bell-shaped distribution, we find that approximately 95% of the hotel rates are between 144 and 176 euros.

The question asks for the percentage of hotels with rates between 144 and 176 euros given a bell-shaped and symmetrical distribution of nightly rates for a three-star hotel in Paris, with a mean of 160 euros and a standard deviation of 8 euros. To solve this, we can apply the Empirical Rule which states that approximately 95% of data within a bell-shaped distribution lies within two standard deviations of the mean.

Calculating two standard deviations from the mean (160 ± (2 × 8)), we get the range from 144 to 176 euros. Therefore, using the Empirical Rule, we can conclude that approximately 95% of the hotel rates fall within the given range.

Answer:

a) decay factor is b = 0.9

b) y = 20,000(0.9)^x

c) y = $10,629

Step-by-step explanation:

a) What is the decay factor for the value of the car?

The formula used to find the decay factor is

y = a(b)^x

where y = future value

a = current value

b = decay factor

x = time

The decay factor is: b = 1-r

We are given rate r = 10% or 0.1

b = 1 - 0.1

b = 0.9

So, decay factor is b = 0.9

b) Write an equation to model the car’s value.

Using the formula:

y = a(1-r)^x

y = 20,000(1-0.1)^x

y = 20,000(0.9)^x

c) Use your equation to determine the value of the car six years after Kelly purchased it.

y = 20,000(0.9)^x

We need to find value after 6 years, so x=6

y = 20,000(0.9)^6

y = 10,628.82

y = $10,629

Answer:

9 represents the initial height from which the ball was dropped

Step-by-step explanation:

Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

[tex]f(n)=9(0.7)^{n}[/tex]

The general formula for the geometric progression modelling this scenario is:

[tex]f(n)=f_{0}(r)^{n}[/tex]

Here,

[tex]f_{0}[/tex] represents the initial height i.e. the height from which the object was dropped.

r represents the percentage the object covers with respect to the previous bounce.

Comparing the given scenario with general equation, we can write:

[tex]f_{0}[/tex] = 9

r = 0.7 = 70%

i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.

The correct answer would be: C. 5.02 x 10^18

Here's how you solve it!

Since the earthquake registered is 7.4 on the scale let it represent RS=7.4

The reference intensity is 2.0 x 10^11 so let it represent RI= 2.0 x 10^11

Now you need to use the formula.

[tex]RS=log(\frac{I}{I_{r} } )[/tex]

Then we need to plug in the values for the formula

[tex]7.4=log(\frac{I}{2.0 x 10^{11} } )[/tex]

[tex]I=10^{7.4}[/tex] x [tex]2.0[/tex] x [tex]10^{11}[/tex]

[tex]I= 5.02[/tex] x [tex]10^{18}[/tex]

Hope this helps! :3

Answer:

5.02×10^18

I got it right.

Answer:

Δ ABC was dilated by a scale factor of 1/3, reflected across the y-axis

and moved through the translation (1 , -2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The similar triangles have equal ratios between their

  corresponding side

- So lets find from the graph the corresponding sides and calculate the

  ratio, which is the scale factor of the dilation

- In Δ ABC :

∵ The length of the vertical line is y2 - y1

- Let A is (x1 , y1) and B is (x2 , y2)

∵ A = (-6 , 0) and B = (-6 , 3)

∴ AB = 3 - 0 = 3

- The corresponding side to AB is FE

∵ The length of the vertical line is y2 - y1

- Let F is (x1 , y1) , E is (x2 , y2)

∵ F = (3 , -2) and E = (3 , -1)

∵ FE = -1 - -2 = -1 + 2 = 1

∵ Δ ABC similar to Δ FED

∵ FE/AB = 1/3

∴ The scale factor of dilation is 1/3

* Δ ABC was dilated by a scale factor of 1/3

- From the graph Δ ABC in the second quadrant in which x-coordinates

 of any point are negative and Δ FED in the fourth quadrant in which

 x-coordinates of any point are positive

∵ The reflection of point (x , y) across the y-axis give image (-x , y)

* Δ ABC is reflected after dilation across the y-axis

- Lets find the images of the vertices of Δ ABC after dilation and

 reflection  and compare it with the vertices of Δ FED to find the

 translation

∵ A = (-6 , 0) , B = (-6 , 3) , C (-3 , 0)

∵ Their images after dilation are A' = (-2 , 0) , B' = (-2 , 1) , C' = (-1 , 0)

∴ Their image after reflection are A" = (2 , 0) , B" = (2 , 1) , C" = (1 , 0)

∵ The vertices of ΔFED are F = (3 , -2) , E = (3 , -1) , D = (2 , -2)

- Lets find the difference between the x-coordinates and the

 y- coordinates of the corresponding vertices

∵ 3 - 2 = 1 and -2 - 0 = -2

∴ The x-coordinates add by 1 and the y-coordinates add by -2

∴ Their moved 1 unit to the right and 2 units down

* The Δ ABC after dilation and reflection moved through the

  translation (1 , -2)

Answer:

y = 3x

Step-by-step explanation:

y = mx + b

(x,y) = (1,3)

m = 3

3 = 3(1) + b

3 = 3 + b

3 - 3 = b

0 = b

y = 3x

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data we have to:

[tex]m = 3\\(x, y) :( 1,3)[/tex]

So, the equation is of the form:

[tex]y = 3x + b[/tex]

We substitute the point and find b:

[tex]3 = 3 (1) + b\\3 = 3 + b\\b = 3-3\\b = 0[/tex]

Finally, the equation is of the form:

[tex]y = 3x[/tex]

Answer:

[tex]y = 3x[/tex]

Answer:

[tex]\frac{\pi}{2}[/tex] radians

Step-by-step explanation:

We can use the concept of proportion to answer this question.

The arc CD is given to be 1/4 in measure of the circumference of the circle. A complete circle is 360 degrees in measure which in radian measure is 2π

So, the arc which 1/4 in measure of the circumference will make an angle which is 1/4 of the angle of the entire circle.

i.e.

Angle formed by the arc =[tex]\frac{1}{4} \times 2 \pi =\frac{\pi}{2}[/tex] radians

Therefore, the radian measure of the central angle of arc CD is [tex]\frac{\pi}{2}[/tex] radians

Answer:

To remove 5x and create and linear equation

Step-by-step explanation:

5x+(-4)=6x+4

The equation can be solved by arranging terms so that numbers can be on one side and other constants will be on the other side.

This is given by the associative rule that states:

(-5x) + 5x + (-4) = 6x +4 - 5x

giving:

-4 = x + 4

this gives, x= -8

Hence a linear equation with a solution.

Answer:

65.4

Step-by-step explanation:

Use the Law of Sines here.  The Law is as follows:

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

We only have need for 2 of those 3 proportions.  Since we can have only 1 unknown in a single equation, we have to use angle C as that unknown.  That means that other angle and side have to be given in the problem.  Angle B is given as 45 and side b is given as 7, so we will use those.

[tex]\frac{sinC}{9}=\frac{sin45}{7}[/tex]

We solve for sinC:

[tex]sinC=\frac{9sin45}{7}[/tex]

Doing that on our calculator gives us

sinC = .9091372901

Taking the inverse sin in degree mode gives you that angle C = 65.4

Answer:

Step-by-step explanation:

In this problem, we will use ratios

60%------->120 guests

30%-------->60guests

10%---------->20guests

Multiply by 10 to both sides to get 200

100%--------> 200 guests

hope this helps!

Answer:

(1,4)

Step-by-step explanation:

Let's this of [tex]y=\sqrt{x}[/tex] which is it's parent function.

How do we get to [tex]y=-\sqrt{x-1}+4[/tex] from there?

It has been reflected about the a-axis because of the - in front of the square root.

It has been shifted right 1 unit because of the -(1) in the square root.

It has been moved up 4 units because of the +4 outside the square root.

In general:

[tex]y=a(x-h)^2+k[/tex] has the following transformations from the parent:

Moved right h units if h is positive.

Moved left h units if h is negative.

Moved up k units if k is positive.

Moved down k units if k is negative.

If [tex]a[/tex] is positive, it has not been reflected.

If [tex]a[/tex] is negative, it has been reflected about the x-axis.

[tex]a[/tex] also tells us about the stretching factor.

The parent function has a starting point at (0,0).  Where does this point move on the new graph?

It new graphed was the parent function but reflected over x-axis and shifted right 1 unit and moved up 4 units.

So the new starting point is (0+1,0+4)=(1,4).

Answer:

Step-by-step explanation:

You must specify the domain of the function.

We know: There is no square root of the negative number.

Therefore

x - 1 ≥ 0        add 1 to both sides

x ≥ 1

The first argument for which the function exists is the number 1.

We will calculate the function value for x = 1.

Put x = 1 to the equation of the function:

[tex]y=-\sqrt{1-1}+4=-\sqrt0+4=0+4=4[/tex]

Therefore the starting point of the graph of given function is (1, 4).

Answer:

n=48

Step-by-step explanation:

n  

_ = 1 6

3

Multiply each side by 3

n/3 * 3 = 16*3

n = 48

Step-by-step explanation:

u.v=|u||v|cos60°

u.v=(2.5)(3.2)(1/2)

u.v=(8)(1/2)

u.v=4

Answer:

  $0.65

Step-by-step explanation:

When d increases by 1, A(d) increases by 0.65 dollars.

Thomas gets paid $0.65 for every mile of travel.

Answer:

50% is the answer.

Step-by-step explanation:

All three persons have different blood groups.

Mary has O blood type.

Her husband has B blood type.

Her father in law has A blood type.

As everyone has different blood groups and the child's group depends on parents blood groups so we have 2 options left.

Hence, the probability that the child will have type O blood is = [tex]\frac{1}{2}[/tex] =50%

Answer:

50/ 50

Step-by-step explanation:

The father's father blood doesn't really matter since the husband has type B. It's just a 50/50 chance between B and O.

[tex]25mn^2 +5mn =5mn(5n+1)[/tex]

The complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).

The given polynomial is 25mn^2 + 5mn. To find the complete factored form, we can factor out the GCF (Greatest Common Factor) from each term, which in this case is mn:

So, the complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).

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Answer:

Answer choice C

Step-by-step explanation:

When the values of x are greater than 2, the solution works. When the values oclf x are less than 3, the solution also works. :)

Answer:

C

Step-by-step explanation:

Inequalities of the form | x | > a have solutions of the form

x < - a OR x > a, thus

2x + 1 < - 5 OR 2x + 1 > 5 ( subtract 1 from both sides of both )

2x < - 6 OR 2x > 4 ( divide both sides of both by 2)

x < - 3 OR x > 2

Solution set is

{ x | x > 2 or x < - 3 } → C

a. If c is a constant then the sum of such constants is the same as multiplication of constants. Therefore [tex]\Sigma_{k=1}^{n}c=nc[/tex]

b. [tex]\Sigma_{k=1}^{n}k=1+2+3+\dots+\infty=\infty[/tex]

c. [tex]\Sigma_{k=1}^{n}k^2=1+4+9+\dots+\infty=\infty[/tex]

d. [tex]\Sigma_{k=1}^{n}k^3=1+8+27+\dots+\infty=\infty[/tex]

Hope this helps.

r3t40

Answer:1866

Step-by-step explanation:

Given

n=200

x=118

Population proportion P=[tex]\frac{118}{200}[/tex]=0.59

[tex]\alpha [/tex]=0.005

Realiability =99%

[tex]Z_{\frac{\alpha }{2}}=2.576[/tex]

Margin of erroe is given by [tex]\sqrt{\frac{p\left ( 1-p \right )}{N}}[/tex]

0.03= [tex]\sqrt{\frac{0.59\left ( 1-0.59 \right )}{N}}[/tex]

85.667=[tex]\sqrt{\frac{N}{0.6519}}[tex]

N=1865.88[tex]\approx 1866 Students[/tex]

To estimate the proportion of students receiving financial aid within 3% with 99% reliability, the dean needs to sample about 1846 students. This is calculated using the formula for the sample size in a proportion estimation with a 99% confidence level and a 3% margin of error.

The subject matter of your question involves using statistics to estimate a population proportion with a specified confidence level and margin of error. This can be calculated using the formula for the sample size in a proportion estimation: n = (Z² * p * (1-p)) / E², where Z is the Z-score, p is the preliminary estimate of the proportion, and E is the desired margin of error.

In this case, the Z-score for a 99% confidence level is approximately 2.58 (you can find this value in a standard normal distribution table). The preliminary estimate of the proportion (p) can be obtained from the initial sample: 118 in 200. So, p = 118/200 = 0.59. The desired margin of error (E) is 3%, or 0.03.

Putting these values into the formula, we get n = (2.58²* 0.59 * (1 - 0.59)) / 0.03² = approximately 1846. This means the dean would need to randomly sample about 1846 students to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability.

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Answer:

  (1/2)(sin(105°) +sin(345°))

Step-by-step explanation:

The relevant identity is ...

  sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))

This falls out directly from the sum and difference formulas for sine.

Here, you have α = 45° and β = 60°, so the relevant expression is ...

  sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))

Recognizing that -15° has the same trig function values that 345° has, this can be written ...

  sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))

Given that angle A is 45 degrees and angle B is 60 degrees, we use the product-to-sum identity in Trigonometry to find sin(A)cos(B). The correct answer after simplifying the formula sin(A)cos(B) = ½ [sin(A + B) + sin(A - B)] is ½ [sin(105) + sin(345)].

In Mathematics, especially Trigonometry, there is a formula known as product-to-sum identities. One of the identities is Sin(A)Cos(B) = ½ [sin(A + B) + sin(A - B)].

Given that angle A is 45 degrees and angle B is 60 degrees, we will find sin(A)cos(B) by substituting A and B in the formula.

On substitution you get ½ [sin(45 + 60) + sin(45 - 60)], which simplifies to ½ [sin(105) + sin(-15)]. Note that sin(-15) is equivalent to sin(345) in the unit circle, therefore the expression further simplifies to ½ [sin(105) + sin(345)].

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Answer:

  x° = 78°

Step-by-step explanation:

x° is the measure of external angle BHC of triangle BHD. As such, its measure is the sum of the opposite interior angles at B and D:

  47° + 31° = x° = 78°

Answer:

Step-by-step explanation:

1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...

[tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]

is the matrix ...

[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]

The first row can be interpreted as the equation ...

  x -y = 3

  x -3 = y . . . . . add y-3

The second row can be interpreted as the equation ...

  z = 0

Then the solution set is ...

  (x, y, z) = (x, x -3, 0) . . . . matches selection B

__

2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.

Answer:

  6 lengths

Step-by-step explanation:

You essentially want the smallest integer solution to ...

  60x ≥ 350

  x ≥ 350/60

  x ≥ 5 5/6

The smallest integer solution to this is x = 6.

The minimum number of lengths of hose needed is 6.

_____

Informally, you know that dividing the required total length by the length of one hose will tell you the number of required hoses. You also know the ratio 350/60 is equivalent to 35/6 and that this will be between 5 and 6. (5·6 = 30; 6·6 = 36) The next higher integer value will be 6.

Answer:

50

Step-by-step explanation:

it is given that there is one variable with 1000 records

we have to find the records which is expected would be removed

it is given that one variable is missing with 5% that 0.05

we can find missing records by multiplying total number of records and the missing value with one variable

so the expected record removed will be =0.05×1000=50

Answer:

b) 4:3

Step-by-step explanation:

The point P is 4/7 of the distance from point M to point N. This means that moving from M to N, the total distance is divided into 7 equal parts and the point P lies after the 4 parts starting from M.

So, out of 7, 4 parts are present between M and P. and the remaining 3 parts are present between P and N. In other words we can say,when we move from M towards N, the line segment MP covers 4 out of 7 parts and the line segment PN covers the 3 parts.

So, we can conclude here that the point P partitions the directed line segment from M to N into a 4:3

Answer:

B. 4:3 is your answer

Answer:

81

Step-by-step explanation:

g(x) = x^4                     put f(x) in for x in g(x)

g(f(x)) = (f(x))^4             Substitute the value for f(x) which is (-2x - 5) put - 4 in for the x in f(x)

g(f(x) = (-2x - 5)^4

g(f(x)) = (- 2*(- 4) - 5)^4  Combine

g(f(x)) = (8 - 5)^4             Subtract

g(-4) = (3)^4                    Raise 3 to the 4th power

g(-4) = 81                        Answer.  

Answer:

D. 10.6

Step-by-step explanation:

Using Pythagoras' theorem

hyp² = side ² + side²

hyp² = 7² + 8²

hyp² = 49 + 64

hyp² = 113

hyp = sqrt of 113

hyp = 10.6

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)

The correct answer is option d. 10.6.

Given:

The hypotenuse is AC. Therefore, we use the formula:

AC² = AB² + BC²

Substituting the given values:

AC² = 7² + 8²
AC² = 49 + 64
AC² = 113

Now, take the square root of both sides to find AC:

AC = √113 ≈ 10.6

Thus, the missing length AC is approximately 10.6.

The correct answer is d. 10.6.

Complete question: Find the missing length on the triangle.  AB = 7, BC = 8 ∠B = 90°. Round your answer to the nearest tenth if necessary

a. 15

b. 113

c. 12

d. 10.6

Answer:

20

Step-by-step explanation:

Use the distance equation to find the length of each side:

d = √((x₂ − x₁)² + (y₂ − y₁)²)

where (x₁, y₁) and (x₂, y₂) are the points (the order doesn't matter).

AB:

d = √((-2 − (-2))² + (-2 − 4)²)

d = 6

BC:

d = √((4 − (-2))² + (-2 − (-2))²)

d = 6

AC:

d = √((-2 − 4)² + (4 − (-2))²)

d = 6√2

So the perimeter is:

AB + BC + AC

6 + 6 + 6√2

≈ 20