two boats leave a dock at the same time. boat a goes due north 500 feet and stops. boat b goes due east 400 feet and stops and turns directly towards boat a. what angle must b turn to face and proceed directly to boat a

The inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we know that:

The T-shirts cost $5.

The shorts cost $9.

The total budget is $35.

Then, the inequality can be:

5x + 9y ≤ 35

Where x and y are the number of t-shirts and shorts purchased.

5(3) + 9(2) ≤ 35

15 + 18 ≤ 35

33 < 35

Therefore, the inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.

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Correct question:
On a clearance rack, t-shirts cost $5 and shorts cost $9. You have $35 to spend. Write a correct inequality that models the possible combinations of t-shirts, t, and shorts, s, you can buy.

1100 children and 1900 adults attended the local zoo on that day.

A system of equations or an equation system is a finite set of equations for which common solutions are sought.

Given:

A local zoo's admission fee is $1.50 for children and $4.00 for adults.

On a certain day, 3000 people enter the zoo and $9250.00 is collected.

We have to determine how many children and how many adults attended?

Solution:

Let number of children enter the zoo = x

Then number of adults enter the zoo = 3000-x

Total collection =  $9250

Collection from children + Collection from adults = 9250

1.50 × x + 4(3000-x) = 9250

1.5x + 12000 – 4x = 9250

1.5x - 4x  = 9250 - 12000

-2.5x = -2750

2.5x = 2750

X =2750/2.5

X = 1100

Number of children enter the zoo = x = 1100

Number of adults enter the zoo = 3000 - x = 3000 - 1100 = 1900

Therefore 1100 children and 1900 adults attended the local zoo on that day.

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8 songs

number of songs = 32

time = 4minutes

let the number of song per minute = y

32 songs = 4 minute

y = 1 minute

Cross multiply:

32(1) = 4(y)

32 = 4y

32/4 = 4y/4

y = 8

This means the number of songs that can be downloaded per minute is 8yna

The number of large glasses that will be filled is 10 glasses.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers.

Given that the large glass holds 5/6 cup of water and you have 8 cups of water. The number of glasses filled will be:

= 8 ÷ 5/6

= 8 × 6/5

= 48/5

= 9.6

= 10 glasses approximately

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7)

The given function is

Recall that the degree of the polynomial is the highest power of the variable.

The degree of the given polynomial function is 3.

we know that a cubic function is a polynomial function with degree 3.

Hence the given function is a cubic function.

Option D is correct.

Answer:

[tex]y=-\frac{5}{4}x+6[/tex]

Step-by-step explanation:

[tex]m=\frac{-4-1}{8-4}=-\frac{5}{4} \\ \\ y-1=-\frac{5}{4}(x-4) \\ \\ y-1=-\frac{5}{4}x+5 \\ \\ y=-\frac{5}{4}x+6[/tex]

Answer:

y=-1.25x+6

Step-by-step explanation:

use slope formula to find slope

y2-y1/x2-x1

-4-1/8-4

-5/4

-1.25

y=-1.25x is the equation we can make with this slope and fill in the equation with one of the coordinates to find y intercept

1=-1.25(4)

1=-5

We need to add 6 for this to be true so y intercept is 6

The equation is

y=-1.25x+6

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After 5.94 sec it will reach at maximum height.

An algebraic equation of the second degree in x is a quadratic equation. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the standard quadratic equation.

y = -16a² + 190x + 72

for maximum y value we need to find y'(x)

y' = -32x + 190

put y' = 0

-32x + 190 = 0

x = 5.94 sec

so after 5.94 sec it will reach at maximum height.

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x = -0.6

The equation that represents this scenario is:

0.7x + 0.1*3 = 0.4(x + 3)

Solving for x, we have:

0.7x + 0.3 = 0.4x + 0.12

0.7x - 0.4x = 0.12 - 0.3

0.3x = -0.18

x = -0.18/0.3

= -0.6

37.5 is the answer for your question

Given:

The volume of the cubic prism is 45 cubic inches.

Let the side length = x

So,

Taking the cubic root of 45

So, the answer will be the side length = 3.557 inches

Could be the two

For example for less than we will obtain -12+8x<-44

For the greater than -12+8x>-44

Answer:

24 ft by 15 ft

Step-by-step explanation:

Let l be the length of the garden. Then

l - 9 is the width of the garden.

[tex]l(l - 9) = 360[/tex]

[tex] {l}^{2} - 9l = 360[/tex]

[tex] {l}^{2} - 9l - 360 = 0[/tex]

[tex](l - 24)(l + 15) = 0[/tex]

[tex]l = 24[/tex]

[tex]l - 9 = 15[/tex]

(since l + 15 = 0 will give a negative value for l).

So the dimensions of this garden are 24 ft and 15 ft.

Given,

The initial balance in the checkbook is $463.18.

The deposite money is $265.

The amount of check is $198.73.

The charge paid for bank is $2.50.

The ending balance at the month end is,

Hence, option b ($526.95) is correct.

EXPLANATION

Let's see the facts:

Ipad pen cost = -$105

Best friend ----> +$12

---------------

-$93

Babysitting Saves +$20/week

We are still needing $93 dollars to buy the pen, so, if she earns $20 peer week, then she should work:

$93 = 20 $/week * number of weeks

Calling x to the number of weeks and turning this into an inequality:

12 + 20x ≥ 105

Subtracting -12 to both sides:

20x ≥ 105-12

Simplifying:

20x ≥ 93

Dividing both sides by 20:

x ≥ 93/20

Simplifying:

x ≥ 4.65

Answer: Amelia should at least work 5 weeks in order to save the money to buy the Ipad pen.

Answer:

attached at point A; forms a right angle; attached at point B; forms a right angle; same; yes

Step-by-step explanation:

Answer:

Step-by-step explanation: you can rewrite 2/3 plus 1/6 as: 2 3 + 1 6 To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator.

Answer:

he sample standard deviation for Car 1 is 8.2 miles and the sample standard deviation for Car 2 is 9.3 miles.

Step-by-step explanation:

If we have the triangle ABC and we want to obtain the triangle DEF, we need to multiply every side of the triangle ABC by 3 as:

5 * 3 = 15

4 * 3 = 12

3 * 3 = 9

So, the scale factor of triangle ABC to triangle DEF is 3

Answer: 3

Answer: -2

Step-by-step explanation:

To find the slope of a line, we use the formula [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

{x(2),y(2)} coordinates of second points in line

{x(1),y(1)} coordinates of first points in line

So to solve, you take any set of your coordinates given and you chose one to be your second set and your first set. Then you take the y from your 1st set, and you subtract it from the y from your 2nd set. Then you take that and you put it over from what you get when you take the x from the 1st set, and you subtract that from the x in your 2nd set.

So when I solve using this the coordinates given, I get -12-8/17-7

This equals to -20/10, and that equals to -2.
So you find the slope of the line as -2

3/4 cups of water would need for only one cup of Pancake mix.

From the question, we have

1-1/2 cups water would he need for every 2 cups of pancake mix.

3/2 cups water would he need for every 2 cups of pancake mix.

Required cups water for only one cup of Pancake mix = 3/(2*2)

=3/4

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

3/4 cups of water would need for only one cup of Pancake mix.

From the question, we have

1-1/2 cups water would he need for every 2 cups of pancake mix.

3/2 cups water would he need for every 2 cups of pancake mix.

Required cups water for only one cup of Pancake mix = 3/(2*2)

=3/4

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}+ \frac{\sqrt{3} }{4}[/tex]

Step-by-step explanation:

Refer to the triangle diagrams I attached. Use SOH CAH TOA

[tex]sin(45)*cos(45)+sin (30)* sin (60)[/tex]

The exact value of sin(45) is [tex]\frac{\sqrt{2} }{2}[/tex]

[tex]\frac{\sqrt{2} }{2}*cos(45)+sin (30)* sin (60)[/tex]

The exact value of cos(45) is [tex]\frac{\sqrt{2} }{2}[/tex]

[tex]\frac{\sqrt{2} }{2}*\frac{\sqrt{2} }{2}+sin (30)* sin (60)[/tex]

Multiply [tex]\frac{\sqrt{2} }{2}*\frac{\sqrt{2} }{2}[/tex].

[tex]\frac{\sqrt{2}^{2} }{4}+sin (30)* sin (60)[/tex]

Rewrite [tex]{\sqrt{2}^{2}[/tex] as 2.

[tex]\frac{2}{4} +sin (30)* sin (60)[/tex]

Simplify

[tex]\frac{1}{2} +sin (30)* sin (60)[/tex]

The exact value of sin(30) is [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2} +\frac{1}{2} * sin (60)[/tex]

The exact value of sin(60) is [tex]\frac{\sqrt{3} }{2}[/tex]

[tex]\frac{1}{2} +\frac{1}{2} * \frac{\sqrt{3} }{2}[/tex]

Simplify

[tex]\frac{1}{2}+ \frac{\sqrt{3} }{4}[/tex]

a.

Function:

Factoring -3, we have:

Middle term facotizing the term inside parenthesis:

This is the factored form.

b.

h(t) is the height.

When it lands on the ground, the height (h(t)) is 0, so we have:

If we solve this equation for t, we get the line drone lands on the ground.

Let's do this:

Time can't be negative, so the solution is t = 8 seconds.

Answer:

h(t) = -3(t-8)(t+4) and 8 minutes

Step-by-step explanation:

Enjoy ur answer have a great day please mark as brainliest :D !!!

Answer:

no solution

Step-by-step explanation:

y = 2x + 6 → (1)

y = 2x - 1 → (2)

substitute y = 2x + 6 into (2)

2x + 6 = 2x - 1 ( subtract 6 from both sides )

2x = 2x - 7 ( subtract 2x from both sides )

0 = - 7 ← not possible

This indicates the system of equations has no solution

a=2

Explanation

Step 1

subtract 10 in both sides

Step 2

divide each side by 4

Answer

Explanation

Probability of an event is calculated as the number of elements in an event divided by the total number of elements in the sample space.

P(quarter)

Number of quarters = 4

Total number of coins in the jar = 6 + 14 + 16 + 4 =

We can solve the problem by using the probability binomial distribution model. The formula is:

Recall that:

Given:

number of samples(n) = 8

x = 3

8% of all major bridges in that city will have ratings of 4 or below implying that the probability of a bridge having a rating of 4 or below is 0.08.

Hence,

The probability that in a random sample of 8 major bridges in the city, at least 3 will have an inspection rating of 4 or below in 2020 would be:

Probability of at most 2 can be reduced to:

Evaluating the expression, we have:

The probability that at least 3 will have a rating of 4 and below:

Answer:

0.02110

The rate increases by a factor of 9 when the concentration is tripled.

It is given to us that the rate law is -

[tex]R=k(NO_{2} )^{2}[/tex] ----- (1)

We have to find out the change in the rate if the concentration is tripled.

When the concentration is tripled, we can rewrite the equation (1) as -

[tex]R_{new} =k(3*NO_{2} )^{2}\\= > R_{new} =9*k(NO_{2} )^{2}\\= > R_{new} =9R[/tex][From equation (1)]

Thus, we see that the rate increases by a factor of 9 when the concentration is tripled.

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The cost of 1 pound of orange will be $1.5. The total payment was $15. The total weight of orange was 10 pounds.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Here,

cost of 2 pound of orange=$3

cost of 5 pound of orange=$7.50

cost of 3 pound of orange=$4.50

Therefore,

The cost of 1 pound of orange is $1.5

The total payment made=$7.50+$4.50+$3

=$15

The total weight of oranges=2+3+5

=10 pounds

One pound of oranges will cost $1.5. $15 was paid in total. Orange weighed ten pounds in total.

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Given the measure:

202 grams

Let's convert the measure from grams to ounces.

Apply the standard metrics measure, where:

1 gram = 0.035274 ounce

Thus, we have:

202 grams = 202 x 0.03527 = 7.125 ounces.

Therefore, the converted measure in ounces is 7.125 oz

ANSWER:

7.125 oz

Applying the Pythagoras Theorem, the length of RS = 8 units.

According to the figure,

Diameter = 16 +4 = 20 units

So, the Radius = Diameter/2 = 20/2 = 10 units

Now,

Let the center be M, then

MT = 10 - 4 = 6 units

RT = x units

The radius is perpendicular to the chord,

So, MTR will be a right-angled triangle,

We will apply the Pythagoras theorem,

So, we have :

[tex]RT^{2} +TM^{2} =RM^{2}[/tex]

Here, RT = x units

TM = 6 units and RM = radius = 10 units

Putting these values in the Pythagoras theorem,

[tex]x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8[/tex]

Thus, the length of RS = 8 units.

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