Given f(x) = -7x + 3, find the
domain if the range is 10.

Step-by-step explanation:

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The surface area of the table top that is not covered by the mirror in the form of algebraic expressions is [tex]5x^2 - 17x +6\,\,m^2[/tex] .

The length of the table top = 5x - 2 m.

The width of the table not covered by mirror is x-3 m.

The surface area of the table top not covered by the mirror is

[tex]$(5x-2)(x-3) = 5x^2 -15x -2x +6 \,\,m^2[/tex]

[tex]$=5x^2 -17x +6\,\, m^2[/tex] in the form of algebraic expressions.

Surface area of cylinder of radius r and height h = [tex]2\pi r^2 + 2\pi rh[/tex]

Surface area of a cuboid of side length a = [tex]6a^2[/tex]

Outside area for a sphere of radius r = [tex]4\pi r^2[/tex]

Surface area of a regular tetrahedron of edge length a = [tex]\sqrt{3}\,a^2[/tex]

Surface area of a right angled cone of base radius r, and lateral height l = [tex]\pi r^2 + \pi r l[/tex]

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Using the volume of the room we know that the area of the floor is 139 m² respectively.

A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.

Cuboid is short for "like a cube".

A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

A cuboid's volume is calculated by summing its length, breadth, and height.

So, let the values be:

Breadth = b

Length = 2b

Height = 2b/3

The volume of the cuboid:

V=whl

Insert values:
V=whl

972=b*2b*2b/3

972*3=b*2b*2b

2,916=b*2b*2b

2,916=5b³

b³=2916/5

b³=583.2

b=³√583.2

b=8.35 m

Now, l = 2b ⇒ 2(8.35) = 16.7 m

Now, the area of the floor is: l * b

= 16.7 * 8.35

= 139.445 m²

Rounding off: 139 m²

Therefore, using the volume of the room we know that the area of the floor is 139 m² respectively.

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Answer:

200

Step-by-step explanation:

Perimeter of parallelogram = 2(b + c)

b = 48

c = 52

Let's solve

2(48 + 52) = 200

So, the perimeter of the parallelogram is 200

The decimal that represents the amount of pine and spruce trees in Hidden Forest is

If 50% of the trees in Hidden Forest are spruce,

10% are maple, and

25% are oak, then

the remaining percentage must be pine trees.

To find the percentage of pine trees, we solve as below

100% - 50% - 10% - 25% = 15%

Therefore, 15% of the trees in Hidden Forest are pine trees.

To write a decimal that represents the amount of pine and spruce trees, we can add the percentage of spruce trees and pine trees together and convert it to a decimal:

50% + 15% = 65%

Converting 65% to a decimal, we get:

0.65

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The number of people who attended the movie are as follows;

Number of children = 162 children.

Number of adults = 81 adults.

Number of students = 50 students.

In order to determine the number of children, students, and adults that attended, we would assign a variable c to the the total number of children who attended the movie.

Since there are half as many adults as there are children, we have the following:

Number of adults = c/2.

Similarly, the number of students who attended the movie can be calculated as follows;

Number of students = 293 - (c + c/2)

Number of students = 293 - 3c/2

Since the total ticket sales were $2132, a linear equation to model it is given by:

2132 = 5c + 7(293 - 3c/2) + 12(c/2)

2132 = 5c + 2,051 - 21c/2 + 12c/2

2132 - 2051 = 5c - 9c/2

81 = c/2

c = 162 children.

Students = 293 - 3c/2

Students = 293 - 3(162)/2

Students = 293 - 243

Students = 50 students.

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The probabiltiy that when a marble is chosen from the bag at random then choosen marble is blue is 1/2.

Given that the bag has 6 red marble and 6 blue marbles. Now, a marble is chosen from the bag at random. Therefore, the probabiltiy that choosen marble is blue is:

Probability(Blue Marble)

= Number of blue marbles / Total number of marbles in the bag

= 6/ 12

= 1/ 2

Hence, the probability is 1/2.

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The complete question must be:

A bag with 6 red marbles has 6 blue marbles. A marble is chosen from the bag at random. What is the probability that it is blue? Write your answer as a fraction in simplest form.

Answer:

Step-by-step explanation:

Assuming these are lengths of a line segment,

you would add AB to BC to get AC.

18 + 8 = 26

Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

The simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

From the rule exponent we know that the exponents follow the below rules,

aˣ⁺ʸ = (aˣ)*(aʸ)

(aˣ)ʸ = aˣʸ

aˣ⁻ʸ = (aˣ)/(aʸ)

The given expression is,

3√(27x¹²) that is in words "Cube root of 27x¹²"

Now we know that, 3³ = 27 and we can write from exponent formula that,

x¹² = (x⁴)³ [As 4*3 = 12]

So, now simplifying the given expression we get,

3√(3³(x⁴)³) = 3√((3x⁴)³) = 3x⁴ [Omitting the exponent 3 and cube root]

Hence the simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

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The measurements which is best estimate is given as 6m, 100grams, 2L.

Measurement is the process of quantifying a physical property of an object or phenomenon, typically by comparing it to a standard unit of measurement. This allows for precise and objective description and comparison of different quantities.

An estimate is an approximate calculation or judgment of the value, amount, size, or cost of something, based on available information and assumptions. It is often used when precise measurements or exact values are not available or practical. Estimates can be useful in planning, budgeting, and decision-making, but they should be used with caution and updated as more accurate information becomes available.

a) The best estimate for the height of a lamp post would be 6 meters (6m).

b) The best estimate for the mass of a pear would be 100 grams (100g).

c) The best estimate for the amount of water in a filled kettle would be 2 litres (2L).

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Using both hoses at the same time, it would take 10 minutes to fill up the kiddie pool. The correct option is B).

Let's call the time it takes to fill up the pool using the back hose alone "B". From the problem, we know that B = 30 minutes. We also know that the front hose fills the pool in half the time of the back hose, so the time it takes to fill up the pool using the front hose alone is 1/2 B = 15 minutes.

Now let's use the formula for "combined work" to find out how long it will take to fill the pool using both hoses at the same time. The formula is

Combined time = (time for hose A * time for hose B) / (time for hose A + time for hose B)

Let's let "A" represent the time it takes to fill up the pool using both hoses at the same time. We know that the combined time is the time it takes to fill up the pool, so A is what we're looking for.

Using the formula, we get

A = (30 * 15) / (30 + 15)

A = 10 minutes

Therefore, it will take 10 minutes to fill up the pool using both hoses at the same time. The correct answer is B.

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Answer:

- 6 > - 8

 8 > 5

- 1 < 0

Step-by-step explanation:

The exponential decay model that represents the forest cover in the world t years after 1990 is:

We can use the exponential decay model to represent the decrease in the world forest cover over time:

y = a e^(kt)

where

y is the forest cover in 10^6 hectares,

t is the time ,

a is the initial forest cover,

k is the decay rate.

Solving for a and k:

where a = 4168 million hectares  (given)

When t = 20  the forest cover was 4033 million hectares.

y = a e^(kt)

y = 4033 = 4168 e^(k*20)

4033/4168 = e^(k*20)

Taking the natural logarithm of both sides:

ln(4033/4168) = k*20

Solving for k, results to

k = ln (4033 / 4168) / 20

k = -0.00165 (to 5 dp)

therefore we can say that, the decay model is:

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Justin's pack was lighter than Sue's pack.

Therefore, the answer is B. Justin.

Answer:

Step-by-step explanation:

A sequence is a list of things in which repeats are permitted and order is important. The last term of the missing pattern is 57.

What is a sequence?

A sequence is a list of things in which repeats are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of items.

In the given sequence, the difference between the first two-term is 4, while in the next two-term is 16(4²), Therefore, in the next two-term, the difference between the two terms will be equal to 64(4³).

Therefore, the last term will be,

Hence, the last term of the missing pattern is 57.

55.2% is capital gain of Maria.

To calculate Maria's capital gain, we need to find the difference between the sale price and the purchase price, and then divide that by the purchase price. We can express this as a formula:

capital gain = (sale price - purchase price) / purchase price

Plugging in the numbers we have:

capital gain = ($55.10 - $35.50) / $35.50

Simplifying the expression:

capital gain = $19.60 / $35.50

capital gain = 0.5521

To express this as a percentage, we need to multiply by 100:

capital gain = 55.21%

Rounded to the nearest tenth of a percent:

capital gain = 55.2%

Therefore, Maria's capital gain is 55.2%.

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Answer:

[tex]\textsf{d)} \quad \sf Secant=\overleftrightarrow{\sf ED}[/tex]

[tex]\sf e) \quad Tangent = line\; \textit{b}[/tex]

[tex]\sf f) \quad Point \;of \;tangency = Point \;B[/tex]

[tex]\sf g)\quad N\:\!ame\;of\;circle=Circle\;A[/tex]

Step-by-step explanation:

A secant is a straight line that intersects a circle at two points and is drawn from outside the circle.

Therefore, the secant in the given diagram is [tex]\overleftrightarrow{\sf ED}[/tex].

A tangent is a straight line that touches a circle at only one point and is drawn from outside the circle.

Therefore, the tangent in the given diagram is line b.

The point of tangency is the point where the tangent meets the circle.

Therefore, the point of tangency in the given diagram is point B.

A circle is named by the point of its center.

As the center of the given circle is point A, then the name of the circle is Circle A.

Answer:

b= 23.4,. γ = 70°, c= 28.9

Step-by-step explanation:

To solve the triangle with given α = 65°, β = 45°, and a = 30, we can use the law of sines:

b/sin(β) = a/sin(α)

b/sin(45°) = 30/sin(65°)

b ≈ 23.4

Then, to find angle γ, we can use the fact that the sum of angles in a triangle is 180°:

γ = 180° - α - β

γ ≈ 70°

To find side c, we can again use the law of sines:

c/sin(γ) = a/sin(α)

c/sin(70°) = 30/sin(65°)

c ≈ 28.9

Therefore, the solution is b = 23.4, γ = 70°, and c = 28.9.

Note that there is no other possible solution, as the given angles and side lengths do not allow for multiple triangles to be formed.

Answer:

The perimeter of triangle ABC is

[tex]6 + 7 + \sqrt{ {6}^{2} + {7}^{2} } [/tex]

[tex]13 + \sqrt{85} = 22.2[/tex]

We know that the perimeter of the given triangle ABC is 19 units respectively.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

The provided object is a triangle with equal sides that has vertices A, B, and C. The triangle shape.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

So, we know that the perimeter of the triangle is = Sum of all 3 sides.

In this case, we will count the units of each side as follows:

AB = 6 units

BC = 7 units

AC = 6 units

Now, get the perimeter as follows:

6+7+6 = 19 units

Therefore, we know that the perimeter of the given triangle ABC is 19 units respectively.

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Step-by-step explanation:

INVERSE variation means that   y = k/x

when x =3    y = 10

 10 = k/3    shows the proportionality constant k = 30

y = 30 / x       now when x = 5      y = 6

Answer:

The answer is: y ≤ (2/3)x - 1/2

Step-by-step explanation:

Add 2y to both sides of the inequality:

2/3x ≥ 1 + 2y

Subtract 1 from both sides of the inequality:

2/3x - 1 ≥ 2y

Divide both sides by 2 to isolate y:

y ≤ 1/2(2/3x - 1)

This gives you the inequality in slope-intercept form, y ≤ (2/3)x - 1/2, where the slope is 2/3 and the y-intercept is -1/2.

To graph the boundary line, plot the y-intercept at (0, -1/2) and then use the slope to find another point. For example, if you move up 2 units and to the right 3 units from the y-intercept, you'll arrive at the point (3, 1/2). Connect these two points with a straight line to graph the boundary line.

Finally, to shade the region of the coordinate plane that satisfies the inequality, test any point above or below the boundary line to see if it's a solution to the inequality. If the point satisfies the inequality, shade the region that it's in. If it doesn't, shade the opposite region.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle

sin73° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{20}{x}[/tex] ( multiply both sides by x )

x × sin73° = 20 ( divide both sides by sin73° )

x = [tex]\frac{20}{sin73}[/tex] ≈ 20.9 ( to the nearest tenth )

a) The graph shows the mean and the values at ±1, ±2, and ±3 standard deviations from the mean.

b) -0.1213

c) 0.0653

d) 0.0171

e) EOC

Given that;

The EOC exams are normally distributed with a mean of 702.19 and a standard deviation of 35.81. A score of 700 is needed to earn 3 points.

Now, We can formulate;

a) The graph shows the mean and the values at ±1, ±2, and ±3 standard deviations from the mean. Each mark differs from the one below by the value of the standard deviation, 36.18. The central mark is the mean, 704.39.

b) As you know, the z-score is computed from ...

 z = (x -µ)/σ

 z = (700 -704.39)/36.18

 z = -0.1213

c) Same formula, different numbers.

 z = (22 -21.65)/5.36

 z = 0.0653

d) Likewise, ...

 z = (530 -528)/117

 z = 0.0171

e) EOC would be the easiest. The required score has the lowest z-value, so the applicant only needs to do better than a smaller number of peers.

Actually, the answer to this depends on why the thresholds vary. If we assume that the threshold on each test is set appropriate to the desired knowledge and ability, the test-taker would find his knowledge and ability allows him to do better on the ACT than on the other tests.

On the other hand, if the scores are representative of test taker populations all with the same knowledge and ability, less of that knowledge is required to achieve the necessary score on the EOC.

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Complete question is,

In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation

scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39

and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.

the values of each standard deviation above and below the mean, and make sure to add in the value

of the mean. Answers only are fine.

free

(Graph below)

b. What would be the z-score for a 700 on the EOC? Show work.

C. You can also earn math credit by scoring a remediation free score on the ACT. ACT tests have a mean

value of 21.65 and a standard deviation of 5.36. What would be a Z-score for a 22 on the ACT? Show work.

d. You can also earn math credit by scoring a remediation free score on the SAT. SAT tests have a mean value

of 528 and a standard deviation of 117. What would be a z-score for a 530 on the SAT? Show work.

e. Of the three testing options, which would be statistically easier to earn? Circle the answer and explain

your reasoning. EOC ACT SAT​

The surface area of the figure shown is,

⇒ 204 cm²

We have o given that;

Upper cube has side = 3 cm

And, Lower cube has side = 5 cm

We know that;

Surface area of cube = 6a²

Hence,

The surface area of the figure shown is,

⇒ 6 × 3² + 6× 5²

⇒ 6 × 9 + 6 × 25

⇒ 54 + 150

⇒ 204 cm²

Thus, The surface area of the figure shown is,

⇒ 204 cm²

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Answer:

The formula for continuous compounding is given as:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the annual interest rate (as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

To find the time for an investment to double, we can set A/P = 2 and solve for t:

2 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting r = 0.0575 (since 5.75% = 0.0575 as a decimal), we get:

t = ln(2)/0.0575 ≈ 12.06 years

Therefore, at an annual interest rate of 5.75% compounded continuously, it takes approximately 12.06 years for an investment to double.

Using a trigonometric relation we can see that the value of the missing side is x = 3.9

We can use the trigonometric relation:

cos(75°) = adjacent cathetus/hypotenuse

Where the adjacent cathetus is x, and the hypotenuse measures 15 units, then we can replace these values to get.

cos(75°) =x/15

Solving this for x we get.

15*cos(75°) =x

3.9 = x

So the correct option is D, the length of the missing side is 3.9 units.

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1. The measure of <POQ  = π/3.

2. (-0.5, 0.87) and (0.5, -0.87) are on circle.

3. R is on the positive y axis.

We have,

The arc PQ has a length of 5.

1. Circumference of circle

C = 2πr

C = 2π(1)

and, Arc length = [tex]\theta[/tex] /360 x 2πr =π/3

[tex]\theta[/tex] = π/3

So, the measure of <POQ  = π/3

2. Q has approximate coordinates (0.5, 0.87)

Then (-0.5, 0.87) and (0.5, -0.87) are on circle.

3. <POR = π/2

x = r cos π/2 = 0, y= r sin π/2= 1

Thus, R is on the positive y axis.

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