Opal is buying chocolates and flowers for valentine's day. She pays $15 for each bouquet and $5.80 for each box of chocolates. Her total bill comes out to $218.20 and she bought a total of 17 items. How bouquets and how many boxes of chocolates did she buy?

Step-by-step explanation:

remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the associated angles are always opposite of each other.

and ... the sum of all angles in a triangle is always 180°.

sin(90) = 1.

1.

another right-angled triangle.

500/sin(90) = depth/sin(37)

depth = 500×sin(37)/1 = 300.9075116... m

2.

another right-angled triangle.

the ladder is the Hypotenuse (baseline).

the height of the wall and the ground distance are the 2 legs.

the angle we are looking for is opposite of the wall height.

so, we get

14/sin(90) = 13/sin(elevation) = 14

sin(elevation) = 13/14 = 0.928571429...

angle of elevation = 68.2132107...°

3.

both lines are tangents to the circle. so, both distances (from the starting point J to the touching points K and M) must be equal.

so,

5x - 4 = 2x + 2

3x = 6

x = 2

Diameter=6units

Area:-

Amy's average speed during her whole journey from London to Newcastle (300 miles) was 51.422 miles per hour.

This is calculated by taking the total distance and dividing it into the total time.

First part of ther journey: 165 miles at 60mph, which is equal to 2.75 hours

Second part of her journey: 135 miles in 3.083 hours (3 hours and 5 minutes)

Average speed: 300 miles / 5.834 = 51.422 miles per hour

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Answer: B. The volume of the cylinder is smaller than the volume of the prism.

Step-by-step explanation

Did the test!

The volume of the cylinder is smaller than the volume of the prism.

We have given that,

a. The volume of the cylinder is greater than the volume of the prism

b. The volume of the cylinder is smaller than the volume of the prism.

C. The volume of the cylinder is the same as the volume of the prism

d.You cannot compare the volumes of different shapes

We have to determine the,

the volume of a cylinder with a radius of 3 units and a height of 12 units compared to the volume of a rectangular prism with dimensions 16 units x 16 units x 9 units.

[tex]v=\pi r^2h[/tex]

The volume of the cylinder is smaller than the volume of the prism.

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Answer:

x≥42

Step-by-step explanation:

[tex]x\geq 42[/tex]

That would be the inequality, since it is equal to 42 and greater than 42, it is going to organize these numbers from least to greatest.

11% of $150 =

10% = $15

1% = $1.50

$15+$1.50= $16.50

$150-$16.50= $133.50

Clementine has $133.50 left

Answer: Taxes: 11 & 16.50 Earnings after: 133.50

Step-by-step explanation: ok

Answer:

X = 1

Step-by-step explanation:

1) Move the 3x to the left hand side and change its sign:

4x-19+3x=-12

2) Move 19 to the right hand side and change its sign:

4x+3x=-12+19

3) collect the like terms:

4x+3x= 7x

-12+19= 7

4) Divide both sides by 7

X = 1

Answer:

4x − 19 = −3x − 12

Let's first get rid of any constants, either from the left or right side.

I'll start with the left, by using the inverse operations.

The inverse operation of subtraction (since 19 is negative) is addition.

So, we add 19 to both sides.

Remember that whenever we use inverse operations we need to do the same for the other side, consequently both sides.

+19             +19

Now, we'll end up with:

4x = -3x + 7

Let's get rid of other terms(grouping them), such as -3x.

We do this by adding 3x to both sides because the inverse operation of subtraction (since 3 is negative) is addition.

Add 3x to both sides,

+3x     +3x

7x = 7

Get rid of the co-efficient of x, which is 7.

We do this by dividing by 7 from both sides since the inverse operation of multiplication (because 7 is being multiplied by x) is division.

Divide by 7 from both sides:

÷7 ÷7

x = 1, the value of x is 1.

Answer:

B

Step-by-step explanation:

angles on the circumference of a circle subtended on the same arc are congruent , then

x = 52°

Answer:

D. 20°

Step-by-step explanation:

just do an elimination, since 52° is big then X it obviously can't be 96°. And that leaves us with 32° and 20°. As you can see 32° is bigger than X then it's 20° ♡

Answer:

5 cm height

Step-by-step explanation:

V = L * W * H

V / (L* W) = H      =  5cm height

Answer:

? = 85°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum of the angles around a point = 360° , so

interior angle on right = 360° - 250° = 110°

sum the interior angles and equate to 540°

110° + 115° + 120° + 110° + ? = 540° , that is

455° + ? = 540° ( subtract 455° from both sides )

? = 85°

Answer:

45 in 6 hours

Step-by-step explanation:

3 inches in 2 minutes

So every hour, it can do 90 inches (since we multiply 2 times 30, we have to multiply 3 times 30)

So next we need to find out how much it goes in 6 hours, so we take 6 x 90.  That gives us 540.  

Lastly, we take 540 and divide it by 12 (since there are 12 inches in a foot) and that gives us 45 feet in 6 hours.

Answer:

540 feet

Step-by-step explanation:

Convert hours to minutes - 6 * 60 = 360 minutes

3 inches in 2 minutes = 1.5 inches in 1 minute (I did this just to make the next steps easier)

Figure out the number of feet moved in 6 hours - 1.5 * 360 = 540 feet

:)

Answer:

Step-by-step explanation:

The average rate of change of a function on an interval is the ratio of the change in function value to the length of the interval.

__

The average rate of change of f(x) on the interval [5, 10] is ...

  (f(10) -f(5))/(10 -5) = (-0.1(10²) -(-0.1(5²)))/(10 -5) = (-0.1(10 -5)(10 +5))/(10 -5)

  = -0.1(10 +5) = -1.5 . . . . average rate of change of f(x)

The average rate of change of g(x) is calculated the same way, and the simplification of the calculation is the same. The average rate of change of g(x) is ...

  -0.4(10 +5) = -6 . . . . average rate of change of g(x)

The ratio of the average rates of change is ...

  g'(x)/f'(x) = -6/-1.5 = 4

The rate of change of g(x) is 4 times that of f(x).

_____

Additional comment

In the above, we made use of the factoring of the difference of squares in order to simplify the expression: a² -b² = (a +b)(a -b). This let us cancel the denominator factor to show us an interesting fact about the rate of change of a quadratic function.

If we generalize the result we found above, we see that the average rate of change of h(x) = kx² on the interval [a, b] is ....

  h'(x) = k(b +a) . . . . . squared term coefficient times the sum of the ends of the interval

You will notice that (b+a)/2 is the midpoint of the interval, so the average rate of change can also be expressed as ...

  h'(x) = 2k × (midpoint of interval [a, b])

Answer:

x + y = 9

Step-by-step explanation:

Line is passing through the points (9, 0) and (0, 9)

-> y - intercept (b) = 9

& slope (m) = (9 - 0)/(0 - 9) = 9/(-9) = -1

Equation of line in slope-intercept form is given as:

y = mx + b

Plugging in the values of m and b in the above equation, we find:

y = (-1)x + 9

-> y = -x + 9

-> x + y = 9

This is the required equation of the line

[Note: there are several other points through which line is passing and those points can also be selected for finding the required equation]

Answer:

third one is the correct answer

Using an exponential function, it is found that the value of the function when x = 4 is of f(4) = 15.95.

It is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, we have that f(-1)=5, hence:

[tex]5 = ab^{-1}[/tex]

[tex]\frac{a}{b} = 5[/tex]

a = 5b

We also have that f(7)=32, hence:

[tex]32 = ab^7[/tex]

Since a = 5b:

[tex]5b^8 = 32[/tex]

[tex]b = \sqrt[8]{\frac{32}{5}}[/tex]

b = 1.2612.

a = 5b = 5 x 1.2612 = 6.306.

Hence the function is given by:

[tex]y = 6.306(1.2612)^x[/tex]

Then, when x = 4, we have that:

[tex]y = 6.306(1.2612)^4 = 15.95[/tex]

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Answer:

1.2

Step-by-step explanation:

9.2 + 8d = 73.2

d = 8

then first term is   9.2 - d = 1.2

The first term of an arithmetic sequence is 1.2 with a common difference of 8.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

Tenth term of an arithmetic sequence = 73.2  or

a+(10-1)d = 73.2 ....(1)

Second term of an arithmetic sequence = 9.2 or

a+(2-1)d = 9.2 .....(2)

Where a is the first term and d is a common difference.

Solving equations (1) and (2)

From the equation (2) put the value of d in the equation (1), we get:

a+9(9.2-a) = 73.2

a+82.8 - 9a = 73.2

-8a = -9.6

a = 1.2

Thus, the first term of an arithmetic sequence is 1.2 with a common difference 8.

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Answer:

90 is the answer

Step-by-step explanation:

360° / 4= 90°

A mean is an arithmetic average of a set of observations. The amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.

A mean is an arithmetic average of a set of observations. it is given by the formula,

[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]

As it is given that Jack makes $12 on Monday, $14 on Tuesday, $18 on Wednesday, $16 on Thursday, $26 on Friday and $22 on Saturday. And we need to know how much he should earn on Sunday, so the average is $19. Therefore, we can write,

[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]

[tex]19 = \dfrac{12+14+18+16+26+22+x}{7}\\\\133 = 108 + x\\\\133-108=x\\\\x = 25[/tex]

Hence, the amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.

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Answer:

Reasons will be definitions, postulates, properties and previously proven theorems. “Given” is only used as a reason if the information in the statement column was given in the problem. Use symbols and abbreviations for words within proofs.

Step-by-step explanation:

Reasons will be definitions, postulates, properties and previously proven theorems. “Given” is only used as a reason if the information in the statement column was given in the problem. Use symbols and abbreviations for words within proofs.

It is equivalent to 7(6) + 14

Step-by-step explanation:

⇒ 7 (6 + 2) = 7 × 8 = 56

7(6) + 14 = 42 + 14 = 56

Answer:

267.95 cm³ (nearest hundredth)

Step-by-step explanation:

Formulae

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Diameter of a circle}=\sf 2r\quad\textsf{(where r is the radius)}[/tex]

Given:

⇒ radius = 8 ÷ 2 = 4cm

[tex]\begin{aligned}\implies \textsf{Volume} &=\sf \dfrac43 \cdot 3.14 \cdot 4^3\\ & = \sf 267.95\:cm^3\:(nearest\:hundredth)\end{aligned}[/tex]

Answer:

267.95 cm³

Step-by-step explanation:

Volume of a sphere

Here, diameter = 8 cm.

But, diameter = 2 x radius

Therefore, radius = 4 cm.

Solving

The linear function that can be used to find the amount in dollars Luis can spend on entertainment is given by:

f(x) = (x - 35)/6.

A linear function is modeled by:

y = mx + b

In which:

In this problem:

Hence, the function is given by:

f(x) = (x - 35)/6.

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The approximate angle that the wire meet the ground is 56.4 degrees

The given set up result in a right triangle. A right triangle has one of its angles as 90degrees.

From the given diagram, we are to caculate the measure of beta. Using the SOH CAH TOA identity

sinβ = opposite/hypotenuse

sinβ = 10/12

sinβ = 0.8333

β = arcsin(0.8333)

β = 56.4 degrees

Hence the approximate angle that the wire meet the ground is 56.4 degrees

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Answer:

$3h

Step-by-step explanation:

w=$44+$12h

w=$35+$15h

$44+$12h=$35+$15h

         -12              -12

$44=$35+$3h

-35    -35

$9=3h

/3   /3

$3=h