ITEM 14 - from the lesson Modeling with Linear Inequalities

Catherine is practicing math and science questions to prepare for her upcoming exams. It takes her 12 minutes to do a math question and 5 minutes to answer a science question.

Among the following options, which one should she choose if she wants to spend less than an hour practicing?

Hint: Set up an equation to represent the scenario. Here is how you should set your equation up.


A. 3 math questions and 5 science questions

B. 2 math questions and 7 science questions

C.5 math questions and 1 science question

D.4 math questions and 3 science questions

(56.42155, 63.57845) is the 95% confidence interval  of the population mean number of days it takes to find a job.

In frequency statistics, a confidence interval is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used.

Given a=0.05, Z(0.025)=1.96

SO 95% confidence interval is

xbar+/-Z*s/vn

--> 60+/- 1.96*10/sqrt(30)

-> (56.42155, 63.57845)

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The percent change in the number of pounds that Jake can lift is 80%.

From the information illustrated, Jake could lift 25lbs and one month later he could lift 45lbs.

The percentage change will be:

= Change in pounds / Original pounds × 100

= (45 - 25) / 25 × 100

= 20 / 25 × 100

= 4 / 5 × 100

= 80%

The percentage change is 80%.

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Answer:

Slope = 1

Step-by-step explanation:

To find the slope you must do this equation: [tex]m=\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]. [tex]y_{2}[/tex]=4 [tex]y_{1}[/tex]=1 [tex]x_{2}[/tex]=4 [tex]x_{1}[/tex]=1. Then do the math, 4-1=3 divided by 4-1=3. You will then get 3/3=1. 1 is your slope.

Answer:

x = 16, y = -1

Step-by-step explanation:

3x - 12y = 60------> x - 4y = 20

x + 2y = 14--------> x + 2y = 14

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

-6y = 6

y = -1

x + 2(-1) = 14

x - 2 = 14

x = 16

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

d = [tex]\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]

~~~~~~~~~~~~~~~

A ( 3 , 6 )

B ( 0 , 1 )

C ( 4 , 0 )

AB = [tex]\sqrt{(0-3)^2 + (1-6)^2}[/tex] = 3√5 ≈ 6.71

AC = [tex]\sqrt{(4-3)^2 + (0-6)^2 }[/tex] = √37 ≈ 6.08

BC = [tex]\sqrt{(4-0)^2 + (0-1)^2 }[/tex] = √17 ≈ 4.12

AB ≠ AC ≠ BC ⇒ Δ ABC is a scalene triangle

Answer: The quotient is x²- 1

Answer: 2

Step-by-step explanation:

Equation: 3a + 4 = 5a

-5a+3a+4 = 5a-5a

-2a+4 = 0

-2a+4-4 = 0-4

-2a = -4

a = 2

Done!

The length of the segment BD is 2.4 units and that of AB is 4 units.

According to the question,

We have the following information:

We have a figure of triangle in which there are two right-angled triangles.

Now, we can find the length of the segment BD and AB using the Pythagoras theorem.

Using it in triangle BDC:

[tex]BC^{2} = CD^{2} + BD^{2}[/tex]

Putting the values of BC and CD:

3*3 = 1.8*1.8+[tex]BD^{2}[/tex]

9 = 3.24+[tex]BD^{2}[/tex]

Subtracting 3.24 from both sides:

9-3.24 = [tex]BD^{2}[/tex]

[tex]BD^{2}[/tex] = 5.76

BD = 2.4 units

Now, using the same theorem in triangle BDA:

[tex]AB^{2} = BD^{2}+ AD^{2}[/tex]

[tex]AB^{2}[/tex] = 5.76+3.2*3.2

[tex]AB^{2}[/tex] = 5.76+10.24

[tex]AB^{2}[/tex] = 16

AB = 4 units

Hence, the length of the segment BD is 2.4 units and that of AB is 4 units.

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Answer:

milk

Step-by-step explanation:

The measure of angle 1 is 48°.

The measure of angle 2 is 132°.

The measure of angle 3 is 132°.

What are the measure of angles?

Angle 1 and angle 48 are vertically opposite angles. Verticly  opposite angle have the same values. Thus, angle 1 would be 48.

Angle 1 and 2 are interior opposite angles. Thus, both angles should add up to 180 degrees.

180 - 48 = 132

Angle 2 and 3 are alternate external angles. Thus, they are equal.

Angle 3 would be 132.

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The acceleration produced by a car will decrease as its mass rises. Less acceleration will be recorded by the computer system, which will cause a drop in the acceleration value on the graph.

Graph:

An organized visual representation of any data in mathematics is called a graph. The graph shows the correlation between the variable values. In graph theory, a graph is used to represent the collection of objects that are somehow connected to one another. In essence, the objects' vertices or nodes are mathematical concepts, and the connections between the nodes are represented by the edges. Different types of graphs are used in mathematics and statistics to visually display data. The discipline of graph theory is the study of points and lines. It is a field of mathematics that specializes in the study of graphs. This image visually illustrates the mathematical truth. The graph theory is used to study relationships.

Complete question:

Use the image to answer the question. Students are using the experimental setup shown in the image in which the two ends of a string are attached to a car and to a hanger. The students conduct three trials in which they place metal discs on the hanger to manipulate the force applied to the car. As a result, the car accelerates along the table while two photogate probes collect motion data. On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.

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The equation of parabola with vertex at (2, 4) and directrix y = 7 is (x - 2)^2 = -12(y - 4)

We know that the equation of standard parabola is (x - h)^2 = 4p(y - k), where p≠ 0.

here, the vertex =  (h, k)

and the directrix is the line y = k - p.

We have been given  vertex at (2, 4) and directrix y = 7

so, h = 2, k = 4

k - p = 7

4 - p = 7

- p = 7 - 4

p = -3

so, equation of parabola would be, (x - 2)^2 = 4(-3)(y - 4)

(x - 2)^2 = -12(y - 4)

Therefore, the equation of parabola with vertex at (2, 4) and directrix y = 7 is (x - 2)^2 = -12(y - 4)

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2 half dollars just mean a dollar. In that case, that's 10 dimes. (10*10=100)

Answer:

10 dimes

Step-by-step explanation:

So in order to get this answer we first must know that...

1 half dollar = 50 cents

1 dime = 10 cents

So...

5 dimes = 50 cents

2 half dollars = 100 cents aka $1

10 dime = 100 cents aka $1

Therefore we can use our common sense to figure out that 2 half dollars is 10 dimes.

Answer:

3 hours

Step-by-step explanation:

3 hours will cost 2.50*3 which is 7.50 + the base price of 5.

So that would be $12.5 leaving you with $1.5

Answer:

Step-by-step explanation:

1

Answer:3

Step-by-step explanation: 3x3=9

Answer:

3

Step-by-step explanation:

√9

=√3²

=√(3²)

=3

{as square root =1/2, 2*1/2 = 1}

The height of the kite is approximately 112.763 meters above the ground.

The situation is represented by the following geometric diagram, a right triangle with a known hypotenuse (r), in meters, and a known acute angle (θ), in degrees. The height of the kite (h), in meters, is represented by the leg opposite to the acute angle and can be found by trigonometric functions:

sin θ = h / r

h = r · sin θ

h = 120 · sin 70°

h ≈ 112.763 m

The height of the kite is approximately 112.763 meters.

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Answer:

y = 3/5 x

Step-by-step explanation:

Direct variation:

y = kx

We need to find k.

x = 15; y = 9

9 = k × 15

k = 9/15 = 3/5

Answer: y = 3/5 x

Answer: x=-16

Step-by-step explanation:

g^-1 is the inverse of the g(x) graph meaning that the x and g(x) values of the g(x) graph switch places. So in the table when  x=-2 g(x)=-16

Answer:

W= P/2 - L

By doing the algebraic work you get W=P/2 - L

The value of this simplification is - 20. 72.

What is simplification?

The act of simplifying something that is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.

Here, we have

Given the equation, we solve this through simplification

We get,

= {(1.88 + 2.12) × 0.1875}/{(0.625 - 0.722)÷2.888} + {(1.44 + 0.56)÷0.5}/{(7.7÷24.75 + 0.133)× 4.5}

= 0.75/(-0.033) + 4/1.988

= -22.72 + 2.00

= - 20.72

Hence, the value of this simplification is - 20. 72.

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Using the given information, the scale of the map is 1 : 1250000

From the question, we are to determine the scale of the map.

From the given information,

An actual distance of 50km corresponds to 4cm on the map

To determine the scale of the map,

First, we will convert 50 km to cm

50 km = 50000 m

50000m = 5000000 cm

∴ 50 km = 5000000 cm

Thus,

An actual distance of 5000000 cm corresponds to 4cm on the map

That is,

4 cm represents 5000000 cm

Dividing by 4

Then,

1 cm represents 1250000 cm

Hence,

The scale is 1 : 1250000

Here is the complete question:

What is the scale if: an actual distance of 50km corresponds to 4cm on the map.

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Answer:

Side YZ

Step-by-step explanation:

think of the triangles as mirrors of each other

and pay attention to the symbols that correspond from side to side, and angle to angle

Answer:

Step-by-step explanation:

Find the slope of PQ

[tex]\frac{9 - (-1)}{5-0}=\frac{10}{5}[/tex] or just [tex]2[/tex]

The perpendicular slope is the negative reciprocal

Use a slope of [tex]-\frac{1}{2}[/tex]

Use the point-slope form of a equation and point P to find a new equation in slope-intercept form

[tex](y- (-1))=-\frac{1}{2}(x-0)[/tex]

[tex]y+1=-\frac{1}{2} x[/tex]

Subtract the 1 from both sides of the equation

[tex]y=-\frac{1}{2}x-1[/tex]

Step-by-step explanation:

elementary school has 651 students and 31 teachers.

the teacher/student ratio is therefore 31/651 or simplified 1/21.

elementary and middle school together have 1197 students. that means the middle school has

1197 - 651 = 546 students

their teacher student ratio is then

x/546

and that must be the same as for the elementary school.

so,

x/546 = 1/21

x = 546/21 = 26

so, the middle school has 26 teachers.

Answer:10,600 to 16,400

Step-by-step explanation:

First you subtract the margin of error to find  the least amount of hours.

6.75 - 1.45 = 5.3 x 2,000(people) = 10,600 (least amount of hours)

Then you add the margin of error to find the most amount of hours.
6.75 + 1.45 = 8.2 x 2,000(people) = 16,400 (most amount of hours)

The margin of error just shows that people spent at least 5.3 and at most 8.2 hours at the park.

You multiply those numbers with how many people went to the park. 2,000

That means the answer is C: 10,600 TO 16,400.

Plus.....I took the test and got it right!

Answer:

Anny consumed 25% time in stretching

Total time taken by anny in gym = 1 hour.

Time spent by anny on the treadmill= 25 minutes.

Time spent by anny in lifting weights= 20 minutes.

And remaining time anny spent on streching,

we have to find what percent did anny spend on streching.

Therefore anny consumed 25% time in streching.

Answer is 25%.

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All apply values to the equation are:

0 ⇒ A

π/3 ⇒ B

5π/3 ⇒ E

What is an equation?

A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.

Main Body:

∵ 0 ≤ x ≤ 2π is the domain for angle x

∴ 0 ≤x/2  ≤ π is the domain of angle

∵ sin(x/2) + cos(x) - 1 = 0

→ To solve the equation we should use the rule of cosine double angle

∵ cos(x) = 1 - 2 sin²(x/2)

→ Substitute it in the equation above

∴ sin(x/2) + (1 - 2 sin²(x/2) = 0

∴ sin(x/2) + 1 - 2 sin²(x/2) = 0

→ Add the like terms

∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0

∴ sin(x/2) - 2 sin²(x/2) = 0

→ Take sin(x/2) as a common factor

∴ sin(x/2) [1 - 2sin(x/2)] = 0

→ Equate each factor by 0

∵ sin(x/2) = 0

→ The value of sine equal zero on the x-axis

∴ x/2 = 0, π, 2π

∵ The domain of x/2  is 0 ≤ (x/2) ≤ π

∴  x/2 = 0 and π ⇒ 2π refused because ∉ the domain

→ Multiply both sides by 2 to find x

∴ x = 0 and 2π

∵ 1 - 2sin(x/2) = 0

→ Subtract 1 from both sides

∴ - 2sin(x/2) = -1

→ Divide both sides by -2

∴ sin(x/2) = 1/2

→ The sine is positive in the 1st and 2nd quadrants

∴ (x/2) lies on the 1st OR 2nd quadrants

∵ (x/2) = sin⁻¹(1/2)

∴ (x/2) =  π/6 =  ⇒ 1st quadrant

→ Multiply both sides by 2

∴ x = π/3

∵ (x/2) = π -π/6  = 5π/6 ⇒ 2nd quadrant

→ Multiply both sides by 2

∴ x = 5π/3

∴ The values of x are 0,π/3 , 5π/3 , 2π

Hence  apply values are:

0 ⇒ A

π/3⇒ B

5π/3⇒ E

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Answer:

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Step-by-step explanation:

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