X
18. MODELING WITH MATHEMATICS The inequality
3x + 2y 2 93 represents the numbers x of multiple-
choice questions and the numbers y of matching
questions you can answer correctly to receive an A on
a test. You answer 20 multiple-choice questions and
18 matching questions correctly. Do you receive an A
on the test? Explain.

Answer:

B.) The interquartile range of the data is 2

Step-by-step explanation:

Answer:

a = \(\frac{11}{7}\) ; b = \(\frac{6}{7}\)

Step-by-step explanation:

\(\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = a + b\sqrt{2} \\\\\)

Rationalising \(\frac{3 + \sqrt{2}}{3 - \sqrt{2} }\) gives :-

\(\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = \frac{(3 + \sqrt{2})(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2}) } = \frac{(3 + \sqrt{2})^2}{3^2 - (\sqrt{2})^2 } = \frac{11 +6\sqrt{2} }{7}\)

Comparing \(\frac{11 + 6\sqrt{2} }{7}\) with \(a + b\sqrt{2}\) gives

a = \(\frac{11}{7}\) & b = \(\frac{6}{7}\)

Answer:

\(\frac{11}{7}\) + \(\frac{6}{7}\) \(\sqrt{2}\)

Step-by-step explanation:

Given

\(\frac{3+\sqrt{2} }{3-\sqrt{2} }\)

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of 3 - \(\sqrt{2}\) is 3 + \(\sqrt{2}\) , thus

= \(\frac{(3+\sqrt{2})(3+\sqrt{2}) }{(3-\sqrt{2})(3+\sqrt{2}) }\) ← expand numerator/ denominator using FOIL

= \(\frac{9+6\sqrt{2}+2 }{9-2}\)

= \(\frac{11+6\sqrt{2} }{7}\)

= \(\frac{11}{7}\) + \(\frac{6}{7}\) \(\sqrt{2}\) ← in the form a + b\(\sqrt{2}\)

with a = \(\frac{11}{7}\) and b = \(\frac{6}{7}\)

Answer:

b 16.4 ft

Step-by-step explanation:

To solve this problem using a graphing calculator, we need to plug in the value of q (which is given as 7) into the equation y = 2 csc e, and then graph the resulting equation.

First, we need to convert the angle e from degrees to radians, because the csc function takes its input in radians. We can use the conversion formula:

radians = degrees x (π/180)

So for e = 2, we have:

e (in radians) = 2 x (π/180) = 0.0349 radians

Now we can plug this value into the equation y = 2 csc e:

y = 2 csc(0.0349) ≈ 103.8 feet

This tells us that the length of the rafters needed to make the roof is approximately 103.8 feet. However, the question asks us to round to the nearest tenth of a foot, so the answer is:

y ≈ 103.8 feet ≈ 103.8 rounded to the nearest tenth of a foot

Therefore, the length of the rafters needed to make the roof for q 7" is approximately 103.8 feet, rounded to the nearest tenth of a foot.

So the correct answer is (b) 16.4 feet.

Using the graphing calculator, we find that the length of the rafters needed is approximately 16.4 feet, Therefore, the correct answer is option B, 16.4 feet.

To find the length of the rafters needed for the roof with an angle of 7 degrees, we'll use the given function y = 2 * csc(e), where e is the angle formed by the rafters and the top of the wall. Here's a step-by-step explanation:

1. Convert the angle from degrees to radians: e (in radians) = (7 degrees * π) / 180 ≈ 0.1222 radians.

2. Calculate the cosecant  (csc) of the angle e: csc(0.1222) ≈ 8.185.

3. Plug the value of csc(e) into the function: y = 2 * 8.185 ≈ 16.37.
Using a graphing calculator, we can input the function y = 2 csc e and graph it. Then, we can use the given angle of 2 to find the length of the rafters needed for a roof with a peak of 7 feet.

4. Round the length to the nearest tenth of a foot: 16.37 ≈ 16.4 feet.
When we graph the function, we can see that the length of the rafters is the distance between the x-axis and the point on the graph where y = 7.
So, the length of the rafters needed to make the roof for an angle of 7 degrees is approximately 16.4 feet (Option b).

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The calculated value of the area of the shaded region is 3.4 square inches

Given that

Side lengths = 8

Vertex angle = 50

So, we have

Area = 1/2 * 8² * sin(50)

Evaluate

Area = 24.5

Given that

Radius, r = 8

Vertex angle = 50

So, we have

Area = Angle/360 * πr²

Evaluate

Area = 50/360 * 22/7 * 8²

Evaluate

Area = 27.9

This is calculated as

Shaded region = 27.9 - 24.5

So, we have

Shaded region = 3.4

Hence, the area of the shaded region is 3.4 square inches

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Complete question

An isosceles triangle ABC is shown below with legs that measure 8 inches and a vertex angle of 50'.

(a) Determine the area of AABC.

(b) Determine the area of the circular sector.

(c) Using your answers from (a) and (b), determine the area of the shaded region.

The points (4, -8) and (10,g) fall on a line with a slope of -1/6. Therefore the value of g is -9.

To find the price of g, we need to apply the concept of the slope of a line. The slope of a line is the degree of ways steep the line is, or how an awful lot it rises or falls because it moves from left to proper.

The slope may be calculated by the use of the system:

m= (y2-y1)/(x2-x1)

where m is the slope and (x1​,y1​) and (x2​,y2​) are any two factors on the road. The method essentially tells us that the slope is equal to the trade-in y divided by means of the alternate in x between the two points.

In this question, we are given two points on the line: (4,−8) and (10,g). We also are given the slope of the line: −1/6. We can plug these values into the formulation and get:

−1/6 = g-(-8) / 10-4

This equation may be simplified by way of multiplying both aspects by using 6 and including 8 on both sides:

−1=g+8

g=−9

So the price of g is −9. This way that the point (10,g) is actually (10,−9). We can take a look at our answer by plugging it lower back into the components and seeing if we get an equal slope:

−1/6=10−4−9−(−8)​

−1/6=6−1​

This is true, so our solution is accurate. To summarize, we used the formula for the slope of a line and substituted the given values to locate the price of g.

The cost of g is −nine, which makes the factor (10,g) equal to (10,−nine). This point lies at the equal line as (4,−8) with a slope of −1/6.

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The correct question is;

"The points (4, -8) and (10,g) fall on a line with a slope of -1/6. What is the value of g?"

The dependent variable in an experiment is the factor whose value is being measured or observed.

In an experiment, the dependent variable is the factor that is being observed or measured. It is the variable that responds to changes in the independent variable, which is the factor being manipulated or changed in the experiment. The dependent variable is often represented on the y-axis of a graph and is used to analyze and interpret the results of the experiment. For example, in an experiment testing the effect of fertilizer on plant growth, the dependent variable would be the plant growth, as it is being measured in response to the fertilizer treatment. The dependent variable is crucial in experimental design as it helps researchers determine the relationship between the independent variable and the observed outcome.

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Answer:

16 and 13

Step-by-step explanation:

Let the second no is x

First no = x+3

Twice the first is nine less than three times the second.

We can write in the form of equation as follows :

2(x+2) = 3x-9

Solving brackets first

2x+4=3x-9

Taking like terms together

9+4=3x-2x

13=x

First no = x+3 = 13 + 3 = 16

So, first and second numbers are 16 and 13 respectively.

The correct model to support the claim that more than 70% of students at De Anza College will transfer is the One sample Z test of proportion.

To determine whether more than 70% of students at De Anza College will transfer, we need to compare the proportion of students who transfer in a sample to the claimed proportion of 70%. Since we have a sample size of 450 students, the One sample Z test of proportion is appropriate.

The One sample Z test of proportion is used to compare a sample proportion to a known or hypothesized proportion. In this case, the known or hypothesized proportion is 70%, and we want to test if the proportion in the sample is significantly greater than 70%. The test involves calculating the test statistic, which follows a standard normal distribution under the null hypothesis.

By conducting the One sample Z test of proportion on the sample of 450 students, we can calculate the test statistic and determine whether the proportion of students who transfer is significantly different from 70%. If the test statistic falls in the critical region, we can reject the null hypothesis and support the claim that more than 70% of students at De Anza College will transfer.

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Answer:

35

Step-by-step explanation:

f(x)=5x^3-2x^2+3

f(2)=5x2^3-2x2^2+3

=5x8-2x4+3

=40-8+3

=40-5

=35

Answer:

35

Step-by-step explanation:

F(x) = 5x^3 -2x^2 + 3

Let x=2

F(2) = 5(2)^3 -2(2)^2 + 3

       = 5*8 -2(4) +3

       = 40 -8+3

       = 32+3

      = 35

Harry's speed on the freeway is 67 miles per hour

Time Harry drove on freeway = 3 hours

Time Harry drove on country road = 6 hours

Total distance covered by him = 483 miles

Let his speed be x miles per hour

Formula to be used:

Speed*Time = Distance

Therefore, the distance covered by him on the freeway  = 3x -----(1)

Distance covered by him on country road = 6(x - 20)------(2)

Formulating the equations using (1) and (2)

3x + 6(x-20) = 483

3x + 6x - 120 = 483

9x = 603

x = 67 miles per hour

So, his speed on the freeway is 67 miles per hour and on the country road it is 47 miles per hour

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Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;

f(x) = 3 - x²

f(x) = 3 - (-2)²

f(x) = 3 - 4

f(x) = -1

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Answer:

hope this helps

Step-by-step explanation:

2,995,384 - 89

==2,995,295

Answer:

the answer is 2,995,295

Answer:

\( \frac{7}{16} \)

Step-by-step explanation:

In this kind of questions we use the following steps to find the answer:

\( \frac{5}{8} - \frac{3}{16} \)

\( \frac{10}{16} - \frac{3}{16} \)

\( \frac{10 - 3}{16} = \frac{7}{16} \)

Is the answer to the question.

Answer:

C

Step-by-step explanation:

5/8 becomes 10/16 and then subtract that result from 17/16

500 grams would be approximately equal to 4 cups.  Understanding conversions between different units of measurement is an important skill for anyone who loves to cook or bake.

One of the most common conversions you may need to make is between grams and cups.

When converting 500 grams to cups, it is important to keep in mind that the conversion factor will depend on the type of ingredient being measured. For example, a cup of sugar weighs much differently than a cup of flour. However, in general, there is an average conversion factor of approximately 1 cup of flour being equal to approximately 125 grams.

Therefore, it is always best to use a reliable conversion chart or online converter to ensure accuracy, especially if you are following a recipe that requires precise measurements. Additionally, it is also a good idea to use a kitchen scale when measuring ingredients in grams, as it is more accurate than measuring cups.

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Answer:

Simple random sampling

Step-by-step explanation:

Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.

He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.

So, primary data collection, simple random sampling - has been used as a type of data collection.

Answer:

Relation.

Step-by-step explanation:

The numbers are on repeat

Answer:

Yes

Step-by-step explanation:

None of the coordinates share the same y value which means it pases the vertical line test.

Answer:

yes

Step-by-step explanation:

because it will be easier if the they are like terms

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

x = 20 meters

Step-by-step explanation:

Area = 140 square meters

The figure is composed of a rectangle and a triangle.

Area = (bh) + (1/2)(bh)

Area = (5)(x) + (1/2)(x)(4)

Area = 5x + 2x

Area = 7x

140 = 7x

x = 20 meters

Answer:

513.25  or 0.001

How i got the answer:

As we  that 06 + 4 = 10. 10 is not divisible by 8. It means that 4106 is also not divisible by 8. The correct answer will be 4106 divided by 8 is 513.25.

If you asking only 8 divided by 4106 the answer is 0.00194836824. In short form it is 0.001.

If you asking if 8 is divisible by 4106 the answer is 513.25. Steps are added above.

Answer: 513.25  or 0.001

Please mark me brainliest

Hope this helps.

answer is 8/4106 or 0.002

Just follow the rules for multiplication and keep going till the end

Answer:

Step-by-step explanation:

the given equation is in the form of quadratic formula i.e.ax^2+bx+c=0.

So ,here a=-1 ,b=-6 and c=-9

b^2=(-6)^2

=36

4ac=4*(-1)*(-9)

=4*9

=36

b^2-4ac=36-36

=0

number of solutions =1

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

A

Step-by-step explanation:

\(f(x) = y\) (output)

\(y = 16\\y = 2^x\\2^x = 16\\2^x = 2^4\\x = 4\)

x = number of rounds

y = number of points

In the 4th round, 16 points will be rewarded.

The value of the function at x = 4 will be 16. Then the correct option is A.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The exponent is given as

y = a(b)ˣ

The exponent function is given below.

f(x) = 2ˣ

Then the value of the variable x when the value of the function is 16.

f(x) = 16

2ˣ = 16

2ˣ = 2⁴

x = 4

The value of the function at x = 4 will be 16. Then the correct option is A.

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The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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Answer:

Step-by-step explanation:

2006053?

Answer:

2,000 + 600 + 50 + 3 = 2,653

Step-by-step explanation:

Answer:

What contributed to the decline of the Indus Valley civilization?

Select all correct answers.

Step-by-step explanation:

1) Add 3 to both sides.

\(x+3=2y\)

2) Divide both sides by 2.

\(\frac{x+3}{2} =y\)

3) Switch sides.

\(y=\frac{x+3}{2}\)

The value of {z} is equivalent to 13.

Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.

We can write -

{z} + {6z - 76} = {3z - 24}

7z - 76 = 3z - 24

7z - 3z = - 24 + 76

4z = 52

z = 13

Therefore, the value of {z} is equivalent to 13.

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