For babysitting, Zou Jing charges a flat fee of $10, plus $15 per hour. Write an equation for the cost, C, after h hours of babysitting. How much money will she make if she baby-sits 5 hours? How many hours does Zou Jing need to babysit to afford a PS5 ($500)?

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

y=0.002x² +0.15x + 2 and y=x set best models the point of intersection of the arrow and the target because it accounts for the fact that the arrow is travelling in a parabolic arc, while the target is located on a straight line.

A parabolic arc is defined by its vertex, focus, and directrix. The arc can be used to describe the trajectory of a projectile, the shape of a satellite dish, or the shape of some suspension bridges.

The equation y=0.002x² +0.15x + 2 models the parabolic arc of the arrow's trajectory and the equation y=x models the straight line of the target.

This equation set is the only one that correctly models both the parabolic arc of the arrow and the straight line of the target.

To better understand why this equation set is the correct answer, let's look at the other equation sets.

The equation set y=-0.002x²+0.15x+2 and y=-x does not work because the equations do not model a parabolic arc and a straight line, respectively.

The equation set y=0.002x²+0.15x + 2 and y=0,2x does not work because the second equation, y=0.2x, does not model a straight line, but rather a line with a slope of 0.2.

Finally, the equation set y=-0.002x² +0.15x+2 and y = 0.2x does not work because the first equation, y=-0.002x² +0.15x+2, does not model a parabolic arc.

Therefore, the equation set y=0.002x² +0.15x + 2 and y=x is the correct answer because it is the only equation set that accurately models both the parabolic arc of the arrow and the straight line of the target.

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The True statements are:

Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

For D (x) = 2 x:

- x is the independent variable,

- D ( 6 ) = 2 · 6 = 12.

10 = 2 · 5,     12 = 2 · 9,     - 4 = 2 · ( - 2 ).

True statements are:

A ) D ( x ) is a function.

D ) D ( x ) is a direct variation.

E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).

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The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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The circumference of the walkway is 26 x + 16 when two words are added together.

A walkway around a rectangular garden.

The garden's size is 4(4.5 x + 1.5) square meters.

The garden's and the walkway's combined area is 5.5(8 x + 4)

We must locate the location of the walkway.

By deducting the size of the pathway from the area of the

from the combined area, a rectangle

Simplify it to provide the combined area as 5.5(8 x + 4)

The total area is equal to 5.5(8 x) Plus 5.5. (4)

∴Area added together: 44 x + 22

Simplify: The garden's area is 4(4.5 x + 1.5).

The garden's size is equal to 4(4.5 x) Plus 4. (1.5)

The garden's size is equal to 18 x + 6.

Subtract the garden's area from the total area now.

The walkway's area is equal to (44 x + 22) minus (18 x + 6)

Area of the walkway is equal to 44x + 22 - 18 x - 6

- Add similar phrases.

The walkway's size is equal to (44 x - 18 x) +. (22 - 6)

Walkway area equals 26 x plus 16

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The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

y = 5 sin (2x) + 4

Step-by-step explanation:

this is sines function,

the amplitude is [9 - (-1)]/2 = 10/2 = 5

the period is 2πx/π = 2x

the x-axis of actual function is at y = 4

so, the function is :

y = 5 sin (2x) + 4

Answer:

25km/h

Step-by-step explanation:

It would be helpful to understand the 24 hour clock in this case so you don't get confused by the AM and PM. For reference, 5 AM is technically 17AM, since 5 + 12 = 17.

The ship departed at 9pm, subtract that from 17 and you'll get 8 hours.

17 - 9 = 8

We know that there are 8 hours total, and since the ship traveled 200km, we set up a fraction, which is 8hr/200km. Since we want the average speed, we'll go by km/hr. To do this, we need to set the hrs to 1.

8/x = 1

x = 8

200/8 = 25

Your answer is 25km/hr

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

Answer:

k = \(\frac{1}{9}\)

Step-by-step explanation:

Using the discriminant

Δ = b² - 4ac

For a repeated real solution then

b² - 4ac = 0

Given

16x² - \(\frac{8}{3}\) x + k = 0

with a = 16, b = - \(\frac{8}{3}\) , c = k

(- \(\frac{8}{3}\) )² - ( 4 × 16 × k) = 0

\(\frac{64}{9}\) - 64k = 0 ( subtract \(\frac{64}{9}\) from both sides )

- 64k = - \(\frac{64}{9}\) ( divide both sides by - 64 )

k = \(\frac{1}{9}\)

Answer:

t = 108

Step-by-step explanation:

\(\frac{5}{9}\) t - 27 = \(\frac{1}{9}\) t + 21 ( subtract \(\frac{1}{9}\) t from both sides )

\(\frac{4}{9}\) t - 27 = 21 ( add 27 to both sides )

\(\frac{4}{9}\) t = 48 ( multiply both sides by 9 )

4t = 432 ( divide both sides by 4 )

t = 108

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Answer:

The balance of the account is $64,190.

Step-by-step explanation:

The amount of money after t years of continous compounding is given by the following equation:

\(P(t) = P(0)e^{rt}\)

In which P(0) is the initial deposit and r is the interest rate, as a decimal.

$60,000 deposited for 6 years at 1.125% interest compounded continuously.

This means that \(P = 60000, r = 0.01125, t = 6\)

So

\(P(6) = 60000e^{0.01125*6} = 64190\)

The balance of the account is $64,190.

The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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Answer:

19,958,400

Step-by-step explanation:

There are 12 ways the photographer could go in picking the first card.

After picking the first one, there will be 11 ways left for the second.

After picking the first one, there will be 10 ways left for the third, and so on...

So our answer = (12)(11)(10)(9)(8)(7)(6)(5) = 19,958,400

Answer:

15 m E. B. C. D. that's why I will be there

Answer:

Yes, my favorite personally is the last jedi

Step-by-step explanation:

Answer:

I love star wars!

My personal favorites are The Clone Wars, The Phantom Menace, Revenge of the Sith, A New Hope, The Empire Strikes back, Return of the Jedi, and The Mandalorian. Just to name a few :P

Step-by-step explanation:

Answer:

No solutions.

Step-by-step explanation:

9|x-1|=-45

Divide 9 into both sides.

|x-1| = -45/9

|x-1| = -5

Absolute value cannot be less than 0.

Answer:

No solution

Step-by-step explanation:

=> 9|x-1| = -45

Dividing both sides by 9

=> |x-1| = -5

Since, this is less than zero, hence the equation has no solutions

Answer:

43 inches deeper and it will be 6 feet deep

Answer:

3feet 7inches

Step-by-step explanation:

2feet + 3feet=5feet  5inches+7inches =1 feet

5feet + 1 feet=6feet

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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Answer:

120 and 40

Step-by-step explanation:

Given

\(\angle 1 = 160\)

\(\angle 2 = 80\)

Rotation = 180 degrees

Translation = 40 units down

Required

A measure of the resulting angles

180 degrees rotation

Rotation only affects the positioning of angles and does not change the measure of the angles.

So, the measure of both angles remain unchanged.

40 units down translation

This will reduce the measure of both angles by 40 degrees.

So:

\(\angle 1 = 160 - 40 = 120\)

\(\angle 2 = 80 - 40 = 40\)

Answer:

a)  zero triangles.

b)  one triangle.

Step-by-step explanation:

In triangle ABC:

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 51^{\circ}}{10}=\dfrac{\sin B}{28}\)

\(\implies \sf \sin B=\dfrac{28\sin 51^{\circ}}{10}\)

\(\implies \sf \sin B=2.176008...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, zero triangles are possible.

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

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle A:

\(\implies \sf \dfrac{\sin A}{24}=\dfrac{\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=\dfrac{24\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=1\)

\(\implies \sf A=\sin^{-1}(1)\)

\(\implies \sf A=90^{\circ}\)

Therefore, one triangle is possible (see attachment).

Answer:

5

Step-by-step explanation:

Answer:

its A

Step-by-step explanation: i passed the test