(12 points) Let X = (1,2,3,4,5).
(a) Find the number of sequences of length 7 over X.
(b) A palindrome of length kis a sequence aja2 ... 0 such that alk-1...0,01 = 0102 ...k-101ka Find the number of palindromes of length 7 over X.
(c) How many three digit odd positive integers with distinct digits can you write using only the numbers in X?​

Amount used in 3 cups

Began milk=2L

Milk left

Answer:

1821 mL or 1.821 L

Step-by-step explanation:

Converting L to mL :

Unit rate : 1 L = 1000 mL

⇒ 2L = 2000 mL

Now three amounts of 57 mL, 69 mL, and 53 mL are used. They need to be subtracted from the total.

⇒ Remaining = 2000 - [57 + 69 + 53]

⇒ Remaining = 2000 - 179

⇒ Remaining = 1821 mL or 1.821 L

Answer:

92%

Step-by-step explanation:

From the two column proof below, we have been able to prove that line  CD bisects ∠ACB

We are given that;

Triangle ABC is isosceles

∠A ≅ ∠B

CD is perpendicular to AB (Thus, CD is the altitude to the base of the triangle)

We want to prove that: Line Segment CD bisects ∠ACB i.e angle ACD = angle BCD

In triangles ACD and BCD;

Statement 1; AC = BC

Reason 1; They are sides of an isosceles triangle ABC

Statement 2; CD = CD

Reason 2; They are common sides of the two triangles

Statement 3; ∠ADC = ∠BDC = 90°

Reason 3; Because CD is the altitude to the base

Statement 4; ΔACD ≅ ΔBCD

Reason 4; RHS theorem (right angle-hypotunese-side theorem)

Statement 5; AD = BD

Reason 5; RHS theorem (right angle-hypotunese-side theorem)

Statement 6; ∠ACD = ∠BCD

Reason 6; Angles opposite to the equal sides are also equal

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Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

Slightly greater than 1.

Step-by-step explanation:

Greater than 1

Convert each to fractions with common denominators

(2 + 7/8) - (1 + 7/9)

2 + 7/8 - 1 - 7/9

1 + 7/8 - 7/9

1 + 63/72 - 56/72

1 + 7/72

1  7/72 is slightly greater than 1.

By answering the presented question, we may conclude that The domain of the function shown on the graph is: -10 < x < 2

The domain of a function is the range of possible values that it can accept. These numbers represent the x-values of a function such as f. (x). The domain of a function is the range of possible values that can be used with it. This set includes the value returned by the method after adding the x value. A function with y as the dependant variable and x as the independent variable has the formula y = f. (x). When a single value of y can be created successfully from a value of x, that value of x is said to be in the function's domain.

The domain of the function shown on the graph is:

-10 < x < 2

Therefore, the correct answer is option C.

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Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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\(\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}\)

If x and y be  i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.

Yes, x y are x y independent studysoup.

Here  x and y be i.i.d. unif(0, 1)

The i.i.d stands for independent and identically distributed

unif means that the uniformly distributed

Here x and y are i.i.d unif (0,1)

The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable

Here we have to find the covariance of x + y and x - y

According to the properties of covariance

Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0

Because Cov(x, x) = Cov (y, y)

Cov(y, x) = Cov(x, y)

Therefore, the covariance of x+y and x - y is 0.

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Answer: This is the answer. please give me the brainliest. Thanks

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 500

p = 0.58

q = 1 - 0.58 = 0.42

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96

Therefore, the margin of error of the population proportion estimation for a 95% confidence interval is

1.96√(0.58)(0.42)/500 = 0.043

Answer:

520=20x+234

15 packages

Step-by-step explanation:

520-234

286

286/20

14.3, so she needs 15 packages

The criteria should be used to prove that the pair of triangles are congruent, as mentioned below.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

The angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

Hence, these above criteria should be used to prove that pair of triangle are congruent.

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The three solutions are (0,3), (1, 3/2) and (2,0)

Given the equation below expressed as;

y = -3/2x + 3

If the value of x is zero, then;

y = -3/2(0) + 3

y = 3

Hence one of the solution is  (0, 3)

If the value of x is 1 then;

y = -3/2(1) + 3

y = -3/2 + 3

y = 3/2

Hence another solution is  (1, 3/2)

If the value of x is 2, then;

y = -3/2(2) + 3

y = -3 + 3

y = 0

Hence another of the solution is  (2, 0)

The three solutions are (0,3), (1, 3/2) and (2,0)

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Answer:

%50 if will be on heads twice

Step-by-step explanation:

Answer:

X=15

Step-by-step explanation:

50−x=80−3x

Step 1: Simplify both sides of the equation.

50−x=80−3x

50+−x=80+−3x

−x+50=−3x+80

Step 2: Add 3x to both sides.

−x+50+3x=−3x+80+3x

2x+50=80

Step 3: Subtract 50 from both sides.

2x+50−50=80−50

2x=30

Step 4: Divide both sides by 2.

2x \2 = 30 \2

Answer:

x=15

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Answer:

81%

Step-by-step explanation:

Because it is hard to compare percentage to fractions, we will first conevert 4/5 into a percentage. We get:

4/5 = 8/10 = 0.8 = 80%.

Comparing 81% to 80%, we can find out that 81% is greater than 4/5 or 81%.

Answer:

Where is the paper?

Step-by-step explanation:

The earth is 3.91×10^8 miles closer to the sun than jupiter

Distance is the space or gap between two points or bodies. It is a scalar quantity and measured in cm, m, km, miles e.t.c

The distance between the earth and the is 9.3×10^7 miles and the distance of Jupiter from the sun is 4.84×10^8 . This shows that the earth is closer to sun than Jupiter.

The dimension of how closer the earth is to the sun than Jupiter is therefore

( 4.84×10^8)-(9.3×10^7)= 3.91×10^8 miles

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Answer:

\(x=7+\sqrt{3},\:x=7-\sqrt{3}\)

Step-by-step explanation:

\(\mathrm{Switch\:sides}\)

\(x^2-14x+46=0\)

\(\mathrm{Solve\;wit\;Quadratic\;formula}\)

\(x_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:46}}{2\cdot \:1}\)

\(\sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:46}}{2\cdot \:1}=2\sqrt{3}\)

\(x_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{3}}{2\cdot \:1}\)

\(\mathrm{Separate\:the\:solutions}\)

\(x_1=\frac{-\left(-14\right)+2\sqrt{3}}{2\cdot \:1},\:x_2=\frac{-\left(-14\right)-2\sqrt{3}}{2\cdot \:1}\)

\(\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\)

\(x=7+\sqrt{3},\:x=7-\sqrt{3}\)

~Lenvy~

Answer:

29

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

166.8 in (4,237 mm) (2-door) 188.4 in (4,785 mm) (4-door)

The value of x is 70°. The correct option is A. 70

From the question, we are to determine the value of the measure of arc x

From one of the circle theorems, we have that

The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.

First, we will determine the value of the third angle in the triangle formed.

Let the angle be y

y + 15° + 20° = 180°

∴ y = 180° - 15° - 20°

y = 145°

Now, the angle supplementary to this is the angle the arc subtends at the circumference.

Thus,

The angle at the circumference = 180° - 145°

The angle at the circumference = 35°

From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°

∴ The measure of the arc is 70°

This is the value of x

Hence, the value of x is 70°. The correct option is A. 70

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Answer:

450 cubic inches

Step-by-step explanation:

the formula to get volume is l×w×h. 12.5×4.5×8=450

Step-by-step explanation:

Given the entry fee of $35, the additional hourly rate of $5, and the total cost of $60:

The independent variable in this given problem is the number of hours, while the dependent variable is the total cost.  

An easier way to understand these concepts is to realize that the total cost depends on the number of hours you spend at the Snow Play Ski Park. The total cost changes by $5 for every hour you spend at the park.

The $35 entry fee is the constant, or the y-intercept. It is the initial cost that you have to pay given the 0 number of hours spent at the park.

The function that represents the given situation is:

C(x) = 5x + 35

In order to determine how long can you be at the Snow Play Ski Park, substitute $60 as C(x) into the function:

C(x) = 5x + 35

60 = 5x + 35

Subtract 35 from both sides:

60 - 35 = 5x + 35 - 35

25 = 5x

Divide both sides by 5 to solve for x:

\(\frac{25}{5} = \frac{5x}{5}\)

x = 5

Therefore, if you have $60, then you can be at the Snow Play Ski Park for up to 5 hours.  

Note:

Please feel free to change the letter that represents the function to f ( x ) for Part B, if needed.

The probability that exactly one box remains empty = 9/16

Let us assume that b₁, b₂, b₃ and b₄ be four distinct balls and M₁, M₂, M₃ and M₄ are four boxes.

The total number of ways in which 4 different balls b₁, b₂, b₃ and b₄ can be placed in 4 distinct boxes would be,

n = 4⁴

And the number of ways to choose an empty box = ⁴C₁

The four balls must be distributed to the remaining 3 boxes so that no box is left empty. This means means one of those three boxes will receive two balls and the others will each receive one. There are ³C₁ ways to choose the box that will receive two balls and ⁴C₂  ways to choose which two balls will be placed in that box. The remaining balls can be placed in the remaining two boxes in 2! ways.

So, the number of ways that exactly one box remains empty

= ⁴C₁ × ³C₁ × ⁴C₂ × 2!

= 144

so, the required probability would be,

P = 144/ 4⁴

P = 9/16

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