Can someone help me please?

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}[/tex]

The probability that at most eight of ten independently selected specimens have a hardness less than 73.84 is 0.2639.

Probability:

The chance that a particular event (or set of events) will occur is expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.

Here we have to find the probability:

The probability that each specimen has a hardness less than 73.84 is:

p =Ф( Z< 973.84 - 70)/ 3)

= Ф(Z<1.28 ) = 0.899

P(X<=8) = 1 - P(X=9) - P (X=10)

= 0.2639

So out of 10 specimens, the probability that 8 or fewer have a hardness less than 73.84 is 0.2639

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The first statement is false and the second statement is true.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.

A random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.

Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.

⇒  The number of cars that go through the drive-in window at a local bank each hour.

The number of cars can be counted and can be an integer like 10, 20,100 etc.

∵ The number of cars is countable it is not an example of a continuous random variable        

⇒ The high daily temperature in Anchorage.

High daily temperature can be an integer or function like 60°, 120° etc

∵ The high daily temperature is an example of a continuous random variable.

Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.

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The complete question is

The exact values of the six trigonometric functions for the point (x, y) = (20, 21) are listed below:

sin θ = 21 / 29, cos θ = 20 / 29, tan θ = 21 / 20, cot θ = 20 / 21, sec θ = 29 / 20, csc θ = 29 / 21

Points in rectangular format are points of the form (x, y), where x and y represent the position of the point respect to the origin and along the respective orthogonal axis.

The line segment between the origin and that point represents the hypotenuse of a right triangle. Then, we can determine the six trigonometric functions by using the following formulae:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

If we know that x = 20 and y = 21, then the exact values of the trigonometric functions are:

sin θ = 21 / √(20² + 21²)

sin θ = 21 / 29

cos θ = 20 / √(20² + 21²)

cos θ = 20 / 29

tan θ = 21 / 20

cot θ = 20 / 21

sec θ = √(20² + 21²) / 20

sec θ = 29 / 20

csc θ = √(20² + 21²) / 21

csc θ = 29 / 21

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Answer:

64/125 > 150/512

Step-by-step explanation:

4/5 *4/5 *4/5 = 64/125 (also equals 0.512)

5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)

Therefore: 0.512 > 0.293

Answer:

Step-by-step explanation:

Answer 10.5

Answer: -64

Step-by-step explanation:

(8−2 • 35)−2

8-70-2

8-72

-64

Answer:

(8 - 2 • 35) - 2 = -64

Step-by-step explanation:

Given problem,

→ (8 - 2 • 35) - 2

Let's solve the problem,

→ (8 - 2 • 35) - 2

→ (8 - (2 × 35)) - 2

→ (8 - 70) - 2

→ -62 - 2

→ -64

Hence, the answer is -64.

Answer:

 3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16 

Step-by-step explanation:

Hope it helps you buddy(:

Answer: 16

You already got the answer- But whatever.

The values of [x], [y] and [z] are 2, 0 and 7.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have the following system of equation -

3x+y-4z=-22

2x+3y+4z=32

x-y+2z=16

We can write -

x - y + 2z = 16

x = 16 + y - 2z

So, we can write 3x + y - 4z = -22 as -

3(16 + y - 2z) + y - 4z = -22      ...eq[1]

and we can write 2x + 3y + 4z = 32 as -

2(16 + y - 2z) + 3y + 4z = 32      ...eq[2]

Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.

We get y = 0 and z = 7

So -

x = 16 + 0 - 14

x = 2

Therefore, the values of [x], [y] and [z] are 2, 0 and 7.

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The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.

To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.

Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.

Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.

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The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

From the table

The investment in 1 year = $20000

The investment in 2 year = $21750

The investment in 3 year = $23500

The investment in 4 year = $25250

The investment in 5 year = $27000

Then the equation will be

y = 20000 + 1750x

Where y is the investment in dollars

x is the number of years

Draw the graph as number of years in x axis and the amount of investment in y axis

Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

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The probability that we will see at least two meteors in the first minute is 1251.5.

So, the probability that we will see at least 2 meteors in the first minute:

Then, in 1 minute:

Now, at least 2 meteors in 1 minute:

Solve as follows:

Therefore, there is a 1251.5 percent probability that we will observe two meteors or more in the first minute.

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the population would be 7,518,400

469,900 • 2^20/5

* 20/5 is part of the exponent

Answer:

7518400

Step-by-step explanation:

Doubling time model:

         [tex]P= P_o 2^{\frac{t}{D}}[/tex]

Here, P is the initial value, D is the time taken to double the quantity, t is the given period of time.

 [tex]P_o = 469,900\\\\\\D = 5 \ years\\t = 20 \ years[/tex]

                    [tex]P = 469,900 * 2^\frac{20}{5}\\\\P = 469,900 * 2^4[/tex]

                         = 469,900 * 2 * 2 * 2 * 2

                         = 7518400

The value of x is 15

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .

Thus

∠1 + ∠2 = 90°

x° + (3x+30)° = 90°

x + 3x + 30 = 90

4x = 90-30

4x = 60

x = 15

Therefore the value of x is 15.

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Step-by-step explanation:

remember, the circumference of a circle is

2×pi×r

and that is for the full 360° of a circle.

how long will the arc length of 1° be ?

well,

2×pi×r / 360

and how long will the arc length of 78° be ?

well,

78 × 1° = 2×pi×r × 78/360

you see ? that is the whole trick ...

now we only need to enter the value for r (radius).

and that is GH = 9 units.

so, the length of the arc GJ is

2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =

= 12.25221135... ≈ 12.25 units

Answer:

OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!

Love from Ella

The graph of the linear equation:

y - 4 = (2/3)*(x + 2)

Can be seen on the image at the end.

Here we have the following linear equation:

y - 4 = (2/3)*(x + 2)

Isolating y, we get:

y = (2/3)*(x + 2) + 4

To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.

If we use x = 1 we get:

y = (2/3)*(1 + 2) + 4

y = (2/3)*3 + 4

y = 2 + 4 = 6

y = 6

Then we have the point (1, 6)

if x = 4 then:

y = (2/3)*(4 + 2) + 4

y = (2/3)*6 + 4

y = 4 + 4 = 8

So we have the point (4, 8)

Then the graph of the linear equation is the one you can see below:

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The equation of the relation x and y is y = 4x  - 4

The relation follows a linear pattern. Therefore, the relationship is linear.

A linear relationship can be represented in different form such as slope intercept form and point slope form.

Let's represent the equation in slope intercept form.

y = mx + b

where

Therefore,

m = 4 - 0 / 2 - 1

m = 4 / 1

m = 4

Therefore, let's find the y-intercept using (1, 0)

y = 4x + b

0 = 4(1) + b

b = -4

Therefore, the equation is y = 4x - 4

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Answer: 31

Step-by-step explanation:

the prime factorization of 961 is 31×31  the value of the square root of 961 is 31.

Hope this helps! Have a good day! :)

The selling price of the the purse in a department store is cents.

For the given question-

A purse in such a department store costs $12.50 at wholesale.

The purse will be 140% more expensive at the store.

Then,

140% of 12.50 = 140 x 12.50 / 100

140% of 12.50 = 17.5

Selling price  = percent increase + cost price

Selling price  = 17.5 + 12.5

Selling price  = $30.0

Selling price  = 3000 cents

Thus, the selling price of the the purse in a department store is cents.

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The Maximum and Minimum values of x is  = (3,30)

The maximum of a quadratic function occurs at

x = − b/2a

If  a is negative, the maximum value of the function is

f ( − b/2a).

f max x  =ax^2+bx+c occurs at

x = −b/2a

Finding the value of

x = −b/2a

Substitute in the values of a and b.

x = − 18/2(3)

Simplify

x = -3

Replace the variable x with -3 in the expression

f (-3) = -3(-3)^2+18(-3)+3

f(-3) = - 27 +54 +3

f(-3) = -30

f(3) = 30

The maximum   of -3x^2+18x+3 = (3,30)

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Answer:

x=35

Step-by-step explanation:

29+6=35

btw are you sure that you are in highschool???

Answer:

35

Step-by-step explanation:

29+6 is 35 u sure in high school?

There are no values within the interval that satisfies the condition stated by Rolle's theorem.

In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:

f'(c) = [f(b) - f(a)] / (b - a), where a < c < b

Where:

First, evaluate the function f(x) at x = - 4:

x = - 4

f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8

f(- 4) = - 64 - 64 + 64 + 8

f(- 4) = - 56

Second, evaluate the function f(x) at x = 4:

x = 4

f(4) = 4³ - 4 · 4² - 16 · 4 + 8

f(4) = 64 - 64 - 64 + 8

f(4) = - 56

Third, determine the first derivative of the function f(x) and evaluate it at x = c:

f(x) = x³ - 4 · x² - 16 · x + 8

f'(x) = 3 · x² - 8 · x - 16

x = c:

f'(c) = 3 · c² - 8 · c + 16

Fourth, find the roots of the quadratic function found in the previous step.

3 · c² - 8 · c + 16 = 0

In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.

Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.

Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.

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Dimensions 5in x 10in x 10in will yield a box with a max. volume of  500 cubic inches.

Volume =  height x length x width

Considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

Square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

Therefore,

V = x  (30-2x) (30-2x)                --------------------------------- (1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative with respect to x:

dV /dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

    dV/dx = 0

⇒  4 (3x² - 60x +225)=0

⇒ 3x² - 60x+225=0   (taking 3 common)

⇒ x² - 20x + 75 =0

Solving this quadratic equation, we get,

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

    x=15

Or,  x-5=0

   x = 5

If we substitute x = 15 in equation (1), volume becomes zero.

Therefore, x cannot be 15

When x= 5, putting in the equation (1)

V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yield a box with a max. volume of  500 cubic inches

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Answer:

( y + 3 ) = - ( x + 6 )

Step-by-step explanation:

The Equation of Line in Point-Slope Form is

[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]

So by Substitution by the Givens

( y - (-3) ) = -1( x - (-6) )

( y + 3 ) = - ( x + 6 )

Glad to Help

The salary of Kayden after 4 years will be $ 221,952.00

The annual salary is $48000

Salary rise is $4500

The rate of the this salary can be found out by [tex]\frac{48,000- 4500}{48000}[/tex]

= [tex]\frac{43,500}{48,000}[/tex] × 100

= 90.6 %

The time interval is 4 years

thus the prinicipal amount is given as $48000.

thus simple interest is P × R × T/ 100

which when calculated will give us

simple interest = $221,952.00

$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.

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Lamp that can be bought with $12 is 21

What is an example of a unitary method?

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

How is the unitary method divided?

This can be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees. In order to determine the value of one unit, we essentially divide the total value of a set of items by the number of units. The unitary approach is this.

Given that

Kwai bought 15 lamp for $8.25

$8.25 = 15 lamp

$1 = 15/8.25

$12 = (15/8.25)*12 = 21 approx.

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The height of the trees in the year 2010, given their average rate of growth will be 21 foot

The trees are said to grow at a rate of 3/4 foot per year. In decimals this is:

= 3 / 4

= 0.75

The number of years between 1990 and 2010 is:

= 2010 - 1990

= 20 years

The height of the trees in 2010 would be:

= Current height x ( Rate of growth x number of years)

= 6 x (0.75 x 20)

= 21 foot

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Answer:

59/15

Step-by-step explanation:

8/5 + 7/3                       Multiply the numerator and denominator by the LCF of the denominator

(3/3) 8/5 + 7/3 (5/5)      Multiply

24/15 + 35/15                Add the numerators

59/15