The table below represents the relationship of the amount of snowfall ( in inches) in 5 cities to the amount of time
(in hours) of a recent winter storm.

344 180 274 358 64 121 32 96 151 275 93 49

Out of the 12 numbers above, 5 (in bold type) are 100 or less.

5/12 = 0.41666...

Answer: 0.417

The probability that an employee selected randomly has a birthday in the first 100 days is 0.417

Recall :

Probability = required outcome / Total possible outcomes

Total possible outcomes :

Required outcomes :

Therefore,

Therefore, the selection probability is 0.417

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we are given

[tex]f(x)=2x^4-x^3+x-2[/tex]

we can check each options

option-A:

-1,1

we can plug x=-1 and x=1 and check whethet f(x)=0

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

At x=1:

[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]

[tex]f(1)=0[/tex]

so, this is TRUE

option-B:

0,1

we can plug x=0 and x=1 and check whethet f(x)=0

At x=0:

[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]

[tex]f(0)=-2[/tex]

At x=1:

[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]

[tex]f(1)=0[/tex]

so, this is FALSE

option-C:

-2,-1

we can plug x=-2 and x=-1 and check whethet f(x)=0

At x=-2:

[tex]f(-2)=2(-2)^4-(-2)^3+(-2)-2[/tex]

[tex]f(-2)=36[/tex]

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

so, this is FALSE

option-D:

-1,0

we can plug x=-1 and x=0 and check whethet f(x)=0

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

At x=0:

[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]

[tex]f(0)=-2[/tex]

so, this is FALSE

Answer:

y=8x/9

Step-by-step explanation:

Given that 8 euros were worth $9 and

24 euros were worth $27.

Let y represent the number of Euros and x no of dollars.

Given that the relation is of the form y = kx+C

When x=0 y =0,

i.e. C =0

Hence equation is of the form y = kx

Substitute x=8 and y =9

We get 9 = 8k

Or k =8/9

Hence relation is y=8x/9 is the relation between x and y.

WE can verify this for 27 dollars worth 24 euros.

24 =8/9(27) is true.

Thus equation is verified.

Initial salary =  $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

[tex]a_n = ar^{n-1}[/tex]

1) [tex]a_n = 50000(1.05)^{n-1}[/tex]

2) In order to find salary in 5 years we need to plug n=5, we get

[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]

= 50000(1.21550625)

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]

Plugging n=10, a = 50000 and r= 1.05.

[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]

[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]

= 628894.62678.

(3x^2 + 2x + 7X^3) + (10x^2 + 6x + 9)

Combine all the like terms.

There is only one term with X^3 so that stays the same.

Add 3X^2 and 10x^2 to get 13x^2.

Add 2x and 6x to get 8x.

There is only one term with a variable, so that also stays the same.

Now place them in order from highest exponent to lowest:

7x^3 + 13x^2 + 8x + 9

The answer is A.

The value of x is option C. 13.

The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.

Given is a triangle ABC.

A line PQ is drawn which is parallel to the line BC.

We have to find the value of x, which is the length of AQ.

Using the triangle Proportionality theorem,

AP / PB = AQ / QC

Substituting the values,

6 / 12 = x / 26

Cross multiplying,

12x = 6 × 26

x = 156 / 12

x = 13

Hence the value of x is 13.

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Answer:

The correct answers are 40, 120, 240, and 320

Step-by-step explanation:

.

Answer:

1 ,3 , 4, 6

Step-by-step explanation:

Answer : A

Example: 5 × 8 = 40

A.  8 × 5 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here applies commutative property of multiplication.

B.  10 × 4 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not applies commutative property of multiplication.

C.  20 × 2 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not  applies commutative property of multiplication.

(2, 0) would be the new x - intercept.

The equation of a parabola can be written in vertex form as:

y = a(x - h)² + k

Here, h represents the x-coordinate of the vertex. The x-intercepts of the parabola are the points where the parabola crosses the x-axis (i.e., where y = 0).

Given that one x-intercept is at (-4, 0), we know that x-intercepts are symmetrically located around the vertex. If the vertex's x-coordinate h is increased by 6, the entire parabola shifts horizontally to the right by 6 units.

Since the x-intercept is affected by the shift in the vertex:

Before the shift: one of the x-intercepts is at -4.

After the shift by h, the new x-intercept will be located 6 units to the right of the original intercept.

Therefore, the new x-intercept will be at:

-4 + 6 = 2

I think your answer is B.

Answer:

Quadratic, because the height increases and then decreases.

Step-by-step explanation:

In an exponential function, the graph will either increase or decrease over the entire domain.  It does not change direction.

We can see from the table that the heights increase and then decrease; this means it cannot be an exponential function.

A quadratic function has a graph that is u-shaped.  It will start out either increasing or decreasing, and then after the maximum or minimum is reached, it changes direction.

We can see from the table that this is what the heights do; this means it is a quadratic function.

Answer:

Deposit each quarter = $342.68

Step-by-step explanation:

Formula use in this problem:

[tex] FV=C\times \left [ \frac{(1+i)^n-1}{i} \right ]\times (1+i) [/tex]

Where,  

          FV is future value, FV=$3000

C is cash flow quarterly( need to find),C=?

I is rate of interest ( divide by 4), i=[tex] \frac{0.08}{4}=0.02 [/tex]

N number of cash flow, n=8

Substitute all these values into formula to solve for C

[tex] 3000=C\times \left [ \frac{(1+0.02)^8-1}{0.02} \right ]\times (1+0.02) [/tex]

[tex] C=\frac{3000\times 0.02}{[(1+0.02)^8-1]\times (1+0.02)}[/tex]

So, C=$342.68

Final answer:

To achieve $3000 in 2 years in an account with 8% interest compounded quarterly, you should deposit $364.11 each quarter.

Explanation:

To find out how much you need to deposit each quarter to have $3000 in 2 years in an account that pays 8% interest compounded quarterly, you would use the future value of a series formula given by:

S = R [((1 + i)^n - 1) / i]

Where:

S = the future value of the series (in this case, $3000)

R = the regular deposit amount per period (what we're solving for)

i = the interest rate per period (8% per year or 0.08 divided by 4 for quarterly = 0.02)

n = the total number of compounds over the period (2 years * 4 quarters/year = 8 compounds)

Plugging in our values:

$3000 = R [((1 + 0.02)^8 - 1) / 0.02]

$3000 = R * [((1.02)^8 - 1) / 0.02]

$3000 = R * 8.2432

So, solving for R, we get:

R = $3000 / 8.2432 = $364.11

Therefore, to have $3000 in 2 years with an account that pays 8% interest compounded quarterly, you need to deposit $364.11 at the start of each quarter.

The expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

Which expression could be Amina's result?

From the question, we have the following parameters that can be used in our computation:

The list of options

Also, we have that

Her result shows two solutions that are complex numbers with imaginary parts

This can be expressed as

[tex]x = \dfrac{a \pm i\sqrt{b}}{c}[/tex]

From the list of options, the expresion that are of the above form are

[tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

hence, the expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

Question

Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?

It is the transformation shown in (B)

(look at one point of the letter P and how it moves precisely 3 units. Also there is only the move, no flipping of the figure)

Answer is B.

B shows a translation of 3 units to the right

In a right triangle, the sum of the squares of the legs is the square of the hypotenuse.

So, you would have

[tex] a^2+b^2=c^2 [/tex]

If you plug the values, you have

[tex] (2\sqrt{3})^2+b^2=(2b)^2 [/tex]

So, you end up with a quadric equation in b:

[tex] 12+b^2=4b^2 \iff 3b^2=12 \iff b^2=4 \iff b=2 [/tex]

So, the three sides are

[tex] a=2\sqrt{3},\ b=2,\ c=4 [/tex]

Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.

First, we need to convert the weight of the pears from pounds and thirds to decimal form.

To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):

3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds

Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:

.6666 pounds * 16 = 10 ounces

So, each friend received 10 ounces of pears.

Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.

First, we need to convert the weight of the pears from pounds and thirds to decimal form.

To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):

3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds

Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:

.6666 pounds * 16 = 10 ounces

So, each friend received 10 ounces of pears.

Answer:

Option A : the interest for the shoe charge is $2.45.

Step-by-step explanation:

As given, Bank card is charging 1.4% monthly interest on credit card charges.

This amount is charged on $175.

We have the interest value as :

[tex]0.014\times175=2.45[/tex] dollars

Hence, the interest for the shoe charge is $2.45.

The digit in the hundred millions place is 9.

Final answer:

The digit in the hundred-millions place of the number 875,932,461,160 is 7.

Explanation:

The digit in the hundred-millions place of the number 875,932,461,160 is 7. Let's break down the places of the number:

So in the number 875,932,461,160, 7 is the digit in the hundred-millions place.

Solution :

Given that in the right triangle , ∠A=30° and AB = 12√3 .

As the figure is missing and its not clearly mentioned that AB is the base or hypotenuse of the right triangle. So two cases arises-

Case 1: AB is the base for ∠A of  the right triangle (as shown in figure 1).

As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]

Here , AB is the base and AC is the hypotenuse , and ∠A=30°

[tex]\Rightarrow cos(30)=\frac{AB}{AC} \\\\\Rightarrow AC=\frac{AB}{cos(30)}[/tex]

The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]

[tex]\Rightarrow AC=12\sqrt{3}\times\frac{2 }{\sqrt{3} }\\\\\Rightarrow AC=24[/tex]

Hence, AC is 24 unit long.

Case 2: AB is the hypotenuse for ∠A of  the right triangle (as shown in figure 2).

As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]

Here , AB is the hypotenuse and AC is the base, and ∠A=30°

[tex]\Rightarrow cos(30)=\frac{AC}{AB} \\\\\Rightarrow AC=AB\timescos(30)[/tex]

The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]

[tex]\Rightarrow AC=12\sqrt{3}\times\frac{\sqrt{3}}{2}\\\\\Rightarrow AC=18[/tex]

Hence, AC is 18 unit long.

Larry is 2365 feet above sea level. Hope this helps :o

Answer: the answer is b 2,741 sorry im late

its (a.) thats  it try it

Simplify as much as possible

1,750,932 x 2,355,435 = 4,124,206,515,420

4,124,206,515,420 x Y cannot be simplified anymore, therefore,

4,124,206,515,420 x Y is your answer

~Rise Above the Ordinary, Senpai

All we need to do here is simplify, since there is no given answer to y. The numbers you've provided are quite large, so I'd suggest just using a calculator, unless they're supposed to be decimals. The simplified answer to this is 412,320,615,420y.