Records at an insurance company showed that the first 30 customers made an average of 5 claims each through their lifetime. After the records of a further 75 customers had been assessed, the average claim rose to 6 per customer. What is the average number of claims by the last 75 customers only?

Answer:

a. ∛(x+4)/3

Step-by-step explanation:

y = 3x³ -4

step 1: x = 3y³ - 4   (swap x and y)

step 2: 3y³ = x + 4

            y³ = (x + 4) / 3

            y = ∛(x+4)/3    (solve y)

f⁻¹(x) = ∛(x+4)/3    (inverse notation)

Answer:

45.90

Step-by-step explanation:

$60.00 15% off = $51.00

$51.00 10% off = 45.90

Answer:

hello

Step-by-step explanation:

\(137 = - 151 + t \\ 137 + 151 = t \\ t = 288\)

hope this is correct.

Answer:

The two right sided polygons.

Step-by-step explanation:

the first polygon can be split by only x-axis, while last polygon can be split by all aces

\(.\)

The polygons B and D are having reflection symmetry. Therefore, options B and D are correct answers.

We need to select all the polygons that have reflection symmetry.

Reflection symmetry is a type of symmetry about reflections. Even if there exists at least one line that divides a figure into two halves such that one half is the mirror image of the other half, it is known as reflection symmetry. It is also known as line symmetry.

When you divide the figures B and D in the middle you will get the symmetrical halves.

The polygons B and D are having reflection symmetry. Therefore, options B and D are correct answers.

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Answer:

  D.  x is all real numbers

Step-by-step explanation:

The graph only goes from -11 to +11 in the horizontal direction, but that domain is not a choice. Apparently, we're to assume the graph extends to infinity both to the left and the right.

The domain is the horizontal extent of the function, so is ...

  x is all real numbers

Answer:

c Describe the constraints of the domain .

Step-by-step explanation:

I know I'm correct

The given expression can be simplified to obtain as 5a² + 4a + 5.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is (8a²+ 6a+ 5) + (-3a² - 2a).

It can be simplified as,

(8a²+ 6a+ 5) + (-3a² - 2a)

Arrange the like terms as,

⇒ 8a² - 3a² + 6a - 2a + 5

⇒ 5a² + 4a + 5

Hence, the simplification is obtained as 5a² + 4a + 5.

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The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Tables are used to show the relationship between variables in a visual form. The equation of the situation is: \(y = 7x\)

The complete table is as follows:

\(\left[\begin{array}{cccccc}{Pages}&1&2&4&6&8\\{Photos}&7&14&28&42&56\end{array}\right]\)

Given that:

\(2\ page = 14\ photos\)

Let:

\(y \to pages\)

\(x \to photos\)

So, we have:

\(2y = 14x\)

Divide by 2

\(y = 7x\)

To fill the table, we simply multiply both sides by the same constant.

Multiply by 0.5

\(2\ page \times 0.5= 14\ photos \times 0.5\)

\(1\ page = 7\ photos\)

Multiply by 2

\(2\ page \times 2 = 14\ photos \times 2\)

\(4\ page = 28\ photos\)

Multiply by 3

\(2\ page \times 3 = 14\ photos \times 3\)

\(6\ page = 42\ photos\)

So, the table is as follows:

\(\left[\begin{array}{cccccc}{Pages}&1&2&4&6&8\\{Photos}&7&14&28&42&56\end{array}\right]\)

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Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Answer: a ratio of 4:9, I apologize if incorrect.

x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

Given, the zeros of a polynomial be,

-3 , 3 and -2

As, the polynomial has 3 zeros then the degree of the polynomial is also be , 3.

Let the polynomial be,

p(x) = (x - (-3))(x - 3)(x - (-2))

p(x) = (x + 3)(x - 3)(x + 2)

On multiplying the factors, we get

p(x) = (x² - 3²)(x + 2)

p(x) = (x² - 9)(x + 2)

p(x) = (x³ - 9x + 2x² - 18)

p(x) = x³ + 2x² - 9x - 18

So, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

Hence, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

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Answer:

Image A could be a Cylinder

Image B is a Tetrahedron

Step-by-step explanation:

Hope this helps : )

Answer:  60

Step-by-step explanation:

Formula to calculate sample size (n):

\(n=(\dfrac{\sigma\times z^*}{E})^2\)

, where \(\sigma\) = population standard deviation, E Margin of error , z* = critical value for the confidence interval.

As per given , we have

E =5

\(\sigma=15\)

Critical value for 99% confidence = 2.576

Then,

\(n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60\)

So, Required sample size = 60 .

The cost of the manicure (b) is,

⇒ b = $4.275

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Delaney gave her nail technician a $4.50 tip.

And, The tip was 5% of the cost of the manicure.

Now, Let the cost of the manicure = b

Hence, We get;

⇒ b = $4.50 - 5% of 4.50

⇒ b = 4.50 - 5/100 × 4.50

⇒ b = 4.50 - 5 × 0.045

⇒ b = 4.50 - 0.225

⇒ b = $4.275

Thus, The cost of the manicure (b) is,

⇒ b = $4.275

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Answer:

2.9 over 1

Step-by-step explanation:

Answer:

Given - angles measures X°

To find - measure of X

Solution -

X + X + X + X + X + X = 360 °

6x = 360°

x = 360/6

x = 60°

Answer:

You can run 5 miles in 30 minutes.

Step-by-step explanation:

y = \(\frac{1}{6}\) x

y = \(\frac{1}{6}\) (30)

y = 5 miles

You can run 5 miles in 30 minutes.

Answer:

Ok I might misunderstand this but this is what I got ( in order )

Step-by-step explanation:

Find the factors of x that makes it zero.. Equate the equation to y and use it to find the value of y. Then get your values for x and y and plot the graph

Answer:

78

Step-by-step explanation:

plug in -3 as x

6(2(-3)^2-5)

6(2(9)-5)

6(18-5)

6(13)

78

Answer:

I think its 0.02

Step-by-step explanation:

I might be wrong

Answer:

0.72 mile

Step-by-step explanation:

Each block is 0.12, it asks what 6 blocks would be.

0.12 x 6 = 0.72 therefore the answer is D

Answer:

19) x=4

20) x=7

21) x=15.5

22) x= -7

23) x=9

24) x=5

25) x=-6 (Im pretty sure)

26)x=4

27)x=10

28) x=-9

Step-by-step explanation:

Solution:

Given:

Hence,

Since 60minutes make 1 hour, then 81minutes is;

Adding this to the arrival time;

Therefore, the estimated arrival time is 10:21 pm

Answer: 10:21 PM

Step-by-step explanation:

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

d.  0.71 percentage points

Step-by-step explanation:

13.62 % is .1362 in decimal

  quarterly period compounding makes periodic (quarterly) interes rate

         = .1362/4 = .03405 per period

  FOUR periods in a year

    (1+ .03405)^4 = 1.1433  

            which means effective interest is .1433  or 14.33 %

14.33 - 13.62 = .7115 percentage points difference

The given equation is

If we subtract 0.6 on each side, we get

Therefore, the given expression is equivalent to B.

If we multiply the given equation with 3, we get

Therefore, the given expression is equivalent to C.

At last, if we subtract 0.6 and 4 on each side, we get

Therefore, the given expression is equivalent to E.

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

Triangle Proportionality Theorem:

To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.

We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are  ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:

BA/DE = CA/CE and CB/DE = AB/BD

We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:

BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)

Cross-multiplying both equations, we obtain:

BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)

Adding the two equations, we get:

BA * CE + CB * DE = (DE + CE) * CA

Dividing both sides by CB * DE, we obtain:

BA/CB = (DE + CE)/CE * CA/DE = DE/CD

Thus, we have proven the Triangle Proportionality Theorem.

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