Expand using Pascal's triangle: (x + 1)4.

0.10 > 0.05 is value of p - value of the data .

What does P stand for?

If we use 10% p - value cutoff = 0.10

then as 0.10 > 0.05

reject the null / data is consistent with the alternative hypothesis .

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The required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]

Separate the solutions as:

[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

Therefore, the required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

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The profit made from the business that receives an initial $100 investment are as follows;

1. The amount received from the investment is $15

2. The number of lawns that should be mowed to buy the switch is 23 lawns

3. The profit made from the business considering the cost and the initial investment of the parents is $170

An investment is the money directed towards an asset purchase to increase the valuation of the business and products within a time period.

The amount invested = $100

The amount desired as return = 10% of the amount made from the business

1. The amount charged per lawn = $15

The number of lawn mowed = 10

The revenue of the business = 10 × $15 = $150

The amount paid as return on investment = 10% × $150 = $15

2. The amount required to buy the switch = $300

The number of lawns to be mowed, n, is therefore;

300 = 15 × n - 10% × 15 × n = 15·n - 1.5·n = 13.5·n

300 = 13.5·n

n = 300/13.5 ≈ 23 ( rounding up to the nearest whole number)

The number of lawns to be mowed is 23 lawns

3. The revenue from mowing 20 lawns is 20 × $15 = $300

The amount received by the investing parents = 10% × $300 = $30

The amount received from the parents investment = $100

The profit made after 20 lawns = $300 - $30 - $100 = $170

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If shipments increased by 7% (which is the same as 0.07) per year, then the shipment in a year can be found by multiplying the shipments in the previous year by 1.07.

Therefore, if [tex]x[/tex] represents the number of years since 2000 and [tex]f(x)[/tex] represents the number of shipments, then [tex]f(x)=3173000(1.07)^x[/tex].

The equivalent monthly rate of the number of security breaches is of 5.31%, using an exponential function.

An increasing exponential function is modeled according to the rule presented by the equation as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the parameters of the exponential function are listed as follows:

In the context of this problem, considering the increase at an yearly rate of 86%, the parameter rate r is given as follows:

r = 0.86.

Hence the function is defined as follows:

[tex]A(t) = A(0)(1.86)^t[/tex]

One year is composed by 12 months, hence the monthly increase is calculated as follows:

[tex]r_m = (1.86)^{\frac{1}{12}} - 1 = 0.0531[/tex]

The monthly increase rate is of 5.31%.

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Answer:

The answer is 5.3

The value of x is 25

What is congruent polygons ?

A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.

Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.

1. Pairs of congruent corresponding parts

 ∠A = ∠C     AB = CD

 ∠B = ∠D    AH = CF

 ∠H = ∠F    HG = FE

 ∠G = ∠E    GB = ED

To find the value of x

4x + 5 = 105

4x = 105 - 5

4x = 100

 x = [tex]\frac{100}{4}[/tex]

    = 25

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The proportional of price of the drink to the number of ounces is 0.2.

In the given question we have to find the proportional of price of the drink  to the number of ounces.

As given from the table that;

Drink Size (oz)     12                16                20

Price (dollars)       2.40            3.20            4.00

If we find the proportional of price of the drink to the number of ounces. Then;

Price of the drink/Number of drink = 2.40/12 = 3.20/16 = 4.00/20

Price of the drink/Number of drink =  0.2       = 0.2        = 0.2

So we can see that the proportional of price of the drink to the number of ounces is 0.2.

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Answer:

Yes it is proportional.

Answer:

The guy under me is correct

Step-by-step explanation:

Answer:

x - 5

Step-by-step explanation:

Factor the expressions that are not already factored

(x^2 - 9x + 20) / (x - 4)

Cancel out x - 4 in both numerator and denominator

[tex]\frac{(x-5)(x-4)}{x-4}[/tex]

x - 5

Broccoli and peppers occupy 11/12 of the gardenAs a result, 11/12 of the garden is filled with vegetables.

1,Let's add up those two fractions to determine how much of the entire garden contains broccoli and peppers since we know that 1/4 of the garden has broccoli and 2/3 of the garden contains peppers.

Consequently, 1/ 4 + 2/3 =?

It is necessary for the denominator to match.

Consequently, 1/4 x 3/ 3 = 3 / 12.

2/3 × 4 /4 = 8 / 12

Hence, 3 / 12 + 8 / 12 = 11 / 12

2  ,Amount of flour needed to complete both recipes =2+1/4+1

3,  Baked cake 1 /8 +3/4,

6  , Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes

= 54 / 12 x 5¹/₄

= 23 ⁵/₈ meters

7,   24 brownies = 9/2 cups of walnuts

    8 brownies =1 1/2 cups of walnuts

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Answer:

1300 and 750

Step-by-step explanation:

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The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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Answer:

Your answer is 17.5 hours

Step-by-step explanation:

Simply multiply 2.5 and 7 to get your answer.

You have to multiply the number of hours by the number of days to get the correct product or answer.

Answer:

Step-by-step explanation:

(12-5)x4=28

Answer:

6 months.

Step-by-step explanation:

Answer:

2xy(8x + 5)

Step-by-step explanation:

16x²y + 10xy ← factor out 2xy from each term

= 2xy(8x + 5)

Answer:

A

Step-by-step explanation:

Translation of 3 units is a plus 3 away from the x

Answer:

Peni will need a total of $17.90

Step-by-step explanation:

$1.20 x 7 = $8.40

$0.50 x 5 = $2.50

$1.00 x 7 = $7.00

$8.40 + $2.50 + $7.00 = $17.90

R square is the most appropriate compared to the adjusted r square value.

In mathematics, a coefficient is a multiplicative coefficient of some term in a polynomial,  series, or expression. Usually numeric, but can be any expression. If the coefficients themselves are  variables, they can also be called parameters.

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The equation in slope intercept form is x =4 .

Given:

x = -5

x + 5 = 0

here slope m = ∞.

line equation passes through (4,-3) with m = ∞

-3 = 1/0(4) + c

4 + c = 0

c = -4.

y = (1/0)x - 4

x - 4 = 0

x = 4.

Therefore the equation in slope intercept form is x =4 .

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Answer:

60°

Step-by-step explanation:

As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.

Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:

180 ÷ 3 = 60

Answer: 431 664.685 m2

Step-by-step explanation:

With the help of probability we can conclude our answer.

acc to our question-

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Answer:

bro u find it

Step-by-step explanation:

William will arrive home at 16:45, it will take 45 min to reach home.

Given, that William leaves work at 16:00

Distance from work to home is 36 kilometres

Also, he drives at an average speed of 48 km/hr

Now, using distance-speed relation to find the time

So, as we know Distance = Speed × Time

On putting the values of distance and speed, we get

36 km = 48 km/hr × Time

On dividing both the sides by 48, we get

36/48 = (48×Time)/48

36/48 = Time

Time = 0.75

Hence, he will take 0.75 hr to reach home.

0.75 hr ≈ 45 minutes

As, 1 hr = 60 minutes

0.75 hr = 0.75 × 60 = 45 minutes

So, William will arrive home at 16:45

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The length of the given isosceles triangle legs is 1.9 feet.

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

Given that,

The perimeter of an  isosceles triangle is 4.9 feet.

And, legs of the triangle are 0.3 foot less than twice the base.

Suppose the base of the triangle be x.

Then, its legs are 2x - 0.3.

As per the question the expression for the perimeter of the triangle is,

2x - 0.3 + 2x - 0.3 + x = 4.9

=> 5x - 0.6 = 4.9

=> 5x = 5.5

=> x = 1.1

Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,

2 × 1.1 - 0.3

= 1.9

Hence, the length of one of the triangle’s legs is 1.9 feet.

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The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:

40.01.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

Hence the quotient of the division is the numerator divided by the denominator.

In this problem, interpreting the blank variable as x, the fraction that represents the situation is:

x/40.01 = 1.

Applying cross multiplication, the numeric value of the variable x is obtained as follows:

x = 40.01 x 1

x = 40.01.

The complete problem asks for which number divided by 40.01 is close to 1.

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Answer: 9/2

Step-by-step explanation: Hope this helps.