What is the largest multiple of 30 which is less than 520?

Equation of parabola in vertex form is :

[tex](x-h)^{2} = 4a(y-k)[/tex]

[tex](x-0)^{2} = 4a(y-180)[/tex]

it passing through (1,164)

∴ [tex](1-0)^2=4a(164-180)[/tex]

[tex]1 = 4a(-16)[/tex]

⇒ [tex]-64a = 1[/tex]

⇒ [tex]a = -\frac{1}{64}[/tex]

∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]

[tex]x^2 = -\frac{1}{16}(y-180)[/tex]

[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]

Here, the equation of parabola in vertex form is:

[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]

What is Parabola?

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.

What is cone?

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.

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The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

What is the vertex form of quadratic equations?

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

The given parent function is f(x) = (x - 3)² - 4.

comparing with the standard vertex form of the parabola, we get

                  a = 1, h = 3 and k = -4.

Now to find 'b', we have to simplify the given function in the form of f(x) = ax² + bx + c

                  f(x) = (x - 3)² - 4

                  f(x) = (x² - 6x + 9) - 4

                  f(x) = x² - 6x + 5

Comparing with f(x) = ax² + bx + c we get, c = -6.

Hence, The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

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Answer:

a) 24 minutes

b) 20 mph

Step-by-step explanation:

  time= 12 min

         [tex]\sf = \dfrac{12}{60} \ hour[/tex]

 speed = 60 mph

[tex]\sf \boxed{distance =speed * time}[/tex]

                [tex]\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m[/tex]    

a) Speed = 30 mph

      [tex]\sf \boxed{time = \dfrac{distance}{speed}}[/tex]

               [tex]\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes[/tex]

It will take 24 minutes.

c) time = 36 minutes

           [tex]\sf = \dfrac{36}{60} \hour[/tex]

 [tex]\sf \boxed{speed= \dfrac{distance}{time}}[/tex]

            [tex]\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph[/tex]

Average speed = 20 mph

Answer:

(2x+6) = (x+9) ; x = 3

Step-by-step explanation:

-x both sides ; 2x-x = x and -6 both sides which is x = 3

Answer: (0.4k+0.6w)

Step-by-step explanation:

the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.

The total volume of the solution as an algebraic expression is

0.4k + 0.6w.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount of acid added to the solution = 40% of k  

Amount of water added to the solution= 60% of w

Now,

The total volume of the solution.

= 40% of k + 60% of w

= 40/100 x k + 60/100 x w

= 0.40k + 0.60w

Thus,

The volume is 0.4k + 0.6w.

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Answer:

Step-by-step explanation:

570.675

The remainder is the amount "leftover" after performing some computation.

Hence,

(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.

(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.

What is a remainder?

The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.

Here given that,

The strength of boys is [tex]121[/tex]

The strength of girls is [tex]116[/tex]

So, the total number of students are

[tex]121+116=337[/tex]

The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.

So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-

[tex]\frac{337}{9}=37[/tex]

and the remainder value is [tex]4[/tex].

Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.

So,

[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.

Hence,

(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.

(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.

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The decimal form of the number is :

9804.0

What is the decimal number?

Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.

If the question is,

4x1+8 x 100 + 9 × 1000, then simplify it first

4x1+8 x 100 + 9 × 1000=4+800+9000=9804

So, the decimal form is :

9804.0

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Answer:IT WOULD BE 60.00

Step-by-step explanation:

BC 40 = 60

Answer:

y=60°, x=60°

Step-by-step explanation:

X=60° Angles in a Equaliteral triangles are all 60°

Alternate angle to get the base angle close to y

Y=60° because of Isoceless angles

To maximize the $40,000 allocated to reach the most people, using linear programming, 10 TV ads and 175 radio ads should be used

The number of people reached is 595,000

Linear programming is a method of maximizing a straight-line or linear function that consists of two or more variables such as the cost and the number of people reached.

Let R represent the number of radio ads and let T represent the number of television ads.

The constraints are;

200·R + 500·T ≤ 40,000

R ≥ 10

T ≥ 10

The maximum value function is 7,000·T + 3,000·R

R ≥ T

R - T ≥ 0

R ≥ T

The equations are therefore;

200·R ≤ 40,000 - 500·T

R ≤ (40,000 - 500·T)/200 = 200 - 2.5·T

R ≤ 200 - 2.5·T

When R = T, we have;

T = 200 - 2.5·T

3.5·T = 200

T = 200 ÷ 3.5 ≈ 57.14

The value of the maximizing function, 7,000·T + 3,000·R, at the vertices of the feasible region are therefore;

(T, R)

At (10, 10); 7,000 × 10 + 3,000 × 10 = 100,000

At (10, 175); 7,000 × 10 + 3,000 × 175 = 595000

At (57.14, 57.14); 7,000 × 57.14 + 3,000 × 57.14 = 571400

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Answer:

36

Step-by-step explanation:

substitute m = - 3 into the expression

m² - 7m + 6

= (- 3)² - 7(- 3) + 6

= 9 + 21 + 6

= 36

The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

Given that,

For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

We have to find will she pay interest at all.

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $6490

r is 7.26%

t is 5 years

So,

i= 6490×0.0726×5

i= $2355.87

Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

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If Jolyn scores 48 points, and the z-score of this value is 3, then her mean points in this normally distributed game is equal to 27.

In a normal distribution, the relative score or z-score can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Making mean (μ) the subject of formula, we have:

μ = x - zσ  x

Substituting the given parameters into the formula, we have;

Mean point, μ = 48 - (3 × 7)

Mean point, μ = 48 - 21

Mean point, μ = 27.

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The probability of selecting two cards that are not orange, is 0.483 and the probability of selecting two cards that are not red and green, is 0.393.

In the given question we have to find the probability.

From the question it is given that,

10 yellow, 6 green, 9 orange, and 5 red cards facedown.

Total number of cards = 10+6+9+5

Total number of cards = 30

Once a card selected, NOT replaced.

a.) Now finding the probability of selecting two cards that are not orange.

There are total orange cards = 9

The number of cards except orange card = 21

Then the probability of selecting one card except orange = 21/30

Then the probability of selecting other card except orange = 20/29

Then the probability of selecting two cards that are not orange is

P(O) = 21/30 * 20/29

P(O) = 420/870

P(O) = 0.483

Then the probability of selecting two cards that are not orange, is 0.483.

(b) Now finding the probability of selecting two cards that are neither red nor green.

The total number of cards except red and green card = 19

Then the probability of selecting one card except red and green card = 19/30

Then the probability of selecting other card except red and green card = 18/29

Then the probability of selecting two cards that are not red and green card is

P(RG) = 19/30 * 18/29

P(RG) = 342/870

P(RG) = 0.393

Then the probability of selecting two cards that are not red and green, is 0.393.

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The statement that is not true about body mass index is B. measures the percentage of one's body fat directly

The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.

The majority of the time, total body fat and BMI are correlated.

The Body mass index (BMI) formula

= weight in kilograms / square of height in meters

BMI Categories values are classified below

Underweight  ≤ 18.5

Normal weight = 18.5–24.9

Overweight = 25–29.9

Obesity = BMI of 30 or greater

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Answer:B

Step-by-step explanation:

For the linear function built from the scatter plot, it is found that:

The slope-intercept representation of a linear function is the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:

b = 500.

When the input increases by 200, the output increases by 1000, hence the slope is:

m = 1000/2 = 5.

Thus the equation is:

y = 5x + 500.

The graph is given by the image at the end of the answer.

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Answer:

18

Step-by-step explanation:

x = 4

4x

= 4 * 4

= 16

y = 2

4x + y

= 16 + 2

= 18

The cost of each ticket of the amusement park is $15.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two student groups went to an amusement park on the same day.

Group 1 bought 9 tickets and received a $120 discount.

Group 2 bought 3 tickets and received a $30 discount.

Let x be the amount of one ticket and y be the total amount.

According to the question:

We have system of equation,

y = 9x - 120    equation1

y = 3x - 30    equation 2

Subtract the equation 2 to equation 1.

So, 6x = 90

x = 15

Therefore,  $15 is the cost of each ticket.

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The rate of gaining altitude for the hiker is 530 feet per hour.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).

Its geometric aspect is the slope of the function at a given point.

The given equation for hiker's altitude is as below,

a = 12850 + 530h

Here a is the altitude in feet and h is time in hours.

In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,

a = 12850 + 530h

Differentiate the above equation w.r.t h as,

da/dh = 0 + 530

          = 530

Hence, the rate of gaining altitude is 530 feet per hour.

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The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).

In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:

y = a · x² + b · x + c

Where:

We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:

9 · a + 3 · b + c = 0

25 · a - 5 · b + c = 0

36 · a - 6 · b + c = - 36

Then, the solution to the system is found by numerical methods:

(a, b, c) = (- 4, - 8, 60)

The equation that contains the three points is y = - 4 · x² - 8 · x + 60.

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12 and 30 are the two numbers are greater than 6 with HCF  6 and LCM  60.

What is Highest common factor and Least Common Multiple?

Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.

Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.

HCF x LCM = Product of the numbers.

6 x 60 = 6a x 6b

10 = a x b

10 can be written as, 1 x 10 and 2 x 5.

But a and b > 1.

So, 10 = 2 x 5

a = 2, b = 5

Therefore, the two numbers are,

6a = 6(2) = 12 and

6b = 6(5) = 30

Hence, the two numbers with HCF  6 and LCM  60 are 12 and 30.

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The constant of proportionality in the equation y = 11x is  11 , the correct option is (a) .

in the question ,

it is given that

the equation is y = 11x

also given that the equation is proportional relationship ,

we need to find constant of proportionality .

we know that the proportional equation is written as y = k*x

where k is the constant of proportionality , on comparing it with the equation y = 11x

, we get k = 11 ,

So , the constant of proportionality is = 11 .

Therefore , The constant of proportionality in the equation y = 11x is  11 .

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To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected

The statistical measurement that would be used is the ANOVA.

A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."

ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.

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Answer:

give me the question dude......

Step-by-step explanation:

The angles that are congruent are as follows:

Vertical angles are angles that are opposite of each other when two lines cross. In other words, vertical angles are formed when two lines meet each other at a point.

Vertically opposite angles are congruent.

Therefore, let's find the angles that are congruent in the diagram.

When lines intersect angle relationship such as vertically opposite angles are formed.

Therefore, the following angles are congruent because they are vertically opposite angles.

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