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Unit 8.5, Lesson 14: Practice Problems

4. Here is a graph. The horizontal axis represents time and the vertical axis represents distance from school.
Write a possible story for the graph.

From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)

b, c, d, and f are true

The opposite angles of a parallelogram are congruent (b)

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)

Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)

Transitive property, like c (f)

The action that would reduce the amount the person paid in taxes to 1,000 is option (D) Receiving a $49,000 tax credit

In this scenario, the person has $50,000 in taxable income and pays a 10% income tax rate, which amounts to $5,000 in taxes. To reduce the tax liability to $1,000, the person needs to receive a tax credit of $49,000. Tax credits directly reduce the amount of tax owed, whereas tax deductions reduce taxable income.

A tax deduction of $4,000 would lower the taxable income to $46,000, resulting in a lower tax liability of $4,600, which is not low enough to reach $1,000. Therefore, a tax credit of $49,000 is needed to reduce the tax liability to $1,000.

Therefore, the correct option is (D) Receiving a $49,000 tax credit

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The given question is incomplete, the complete question is:

A person has $50,000 in taxable income for a year and pays a 10 percent income tax rate, equal to $5,000. Which action would reduce the amount the person paid in taxes to $1,000?

A.Receiving a $4,000 tax deduction

B.Receiving a $4,000 tax credit

C. Receiving a $49,000 tax deduction

D. Receiving a $49,000 tax credit

The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.

To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.

In this case, the company should use the adjusted R² approach instead of the p-value approach.

The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).

Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.

It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.

This could result in a less accurate recommendation system.

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The z- score that has 20.9 of the distribution's area to its right is roughly 0.84.

To find the z- score that has 20.9 of the distribution's area to its right, we can use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we can look for the area to the left of the z- score with an area of 1-0.209 = 0.791. The closest value we can find in the table is 0.7901, which corresponds to a z- score of 0.84.

Alternatively, we can use a calculator with a normal distribution function.However, 0, 1) = 0, If we use the formula" normalcdf(z. 209" to find the z- score, we get z = 0.84.

therefore, the z- score that has 20.9 of the distribution's area to its right is roughly 0.84.

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Answer:

To write the equation of the line that passes through the points (2, 7) and (0, -5), we can use the slope-intercept form of a linear equation, which is:

y = mx + b

Where m is the slope of the line, and b is the y-intercept.

First, we can find the slope of the line by using the formula:

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

Where (x1, y1) = (2, 7) and (x2, y2) = (0, -5)

m = (-5 - 7) / (0 - 2)

m = -12 / -2

m = 6

So the slope of the line is 6.

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Where (x1, y1) = (2, 7)

y - 7 = 6(x - 2)

Simplifying this equation, we get:

y - 7 = 6x - 12

y = 6x - 5

So the equation of the line that passes through the points (2, 7) and (0, -5) is y = 6x - 5.

Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.

Explain average

The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.

According to the given information

Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:

Y = (X1 + X2 + X3 + X4 + X5) / 5

Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:

E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)

Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:

E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4

Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:

E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)

Thus, we can simplify the expression as:

E(Y|X1=150) = (4E(X) / 4) = E(X) = 100

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Answer:

48 ounces

Step-by-step explanation:

12*4= 48

The current in the circuit when the resistance is 12 ohms is 40 amps.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

We can use the inverse proportionality formula to solve this problem, which states that:

current (in amps) x resistance (in ohms) = constant

Let's call this constant "k". We can use the information given in the problem to find k:

24 amps x 20 ohms = k

k = 480

Now we can use this constant to find the current when the resistance is 12 ohms:

current x 12 ohms = 480

current = 480 / 12

current = 40 amps

Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.

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Answer:

The formula for the area of a trapezoid is:

Area = (b1 + b2) / 2 x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height.

We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).

Substituting the given values into the formula for the area of a trapezoid, we get:

96 = (11 + b2) / 2 x 8

Multiplying both sides by 2 and dividing by 8, we get:

24 = 11 + b2

Subtracting 11 from both sides, we get:

b2 = 13

Therefore, the length of the other base is 13 ft.

Answer:

135.07 mm2

Step-by-step explanation:

height = 10.39 mm

area = 135.07 mm2

Similarly, if the spread of the training group's distribution is smaller than the spread of the no training group's distribution.

The training group ran faster on average, than the no training group.

To determine which pair of dot plots provides the strongest statistical evidence that the training group ran faster.

Compare the center and spread of the two groups.

The center of the training group's distribution is consistently to the left (i.e., lower times) of the center of the no training group's distribution.

Overlap between the two distributions, then we can conclude that the training group ran faster on average, than the no training group.

100 by adding data.

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We need to examine the dotplots and summary statistics of the two groups to determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, on average, than the no training group.

To determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, we need to compare the centers and spreads of the two groups. If the center of the training group is shifted to the left (smaller times) compared to the center of the no training group, and if the spread of the training group is smaller than the spread of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.

Without seeing the actual dotplots, we cannot make a definitive determination. However, we can describe what to look for in the dotplots. Specifically, we want to see a clear separation between the centers of the two groups, and we want to see less overlap between the dots in the training group than in the no training group.

In addition, we can calculate summary statistics for the two groups, such as the mean and standard deviation, to help us compare the centers and spreads of the two groups. If the mean of the training group is significantly smaller than the mean of the no training group, and if the standard deviation of the training group is significantly smaller than the standard deviation of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.

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(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°

(4) m∠1=88°m∠2=42° m∠3=113°

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.

A triangle is a closed two-dimensional shape with three straight sides and three angles.

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)

(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)

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The product of two terms gives the walkway's area around the garden: 15x+13.5.

A rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.

Area of garden = 4(4.5x + 3.5) = 18x+14

The combined area of the garden and the walkway = 5.5​(6x+5​) =33x+27.5

The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:

Aw=combined area -Area of garden

=33x+27.5-18x-14

=15x+13.5

Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.

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The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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Answer:

The Correct answer is sinA/3.2=sin110°/4.6

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.

Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.

Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.

As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.

Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.

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Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

How to solve the question?

To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check each option:

A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm

To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:

XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm

YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm

XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm

YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm

Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.

C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm

YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm

YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm

XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm

The first combination is less than the third side, so a triangle cannot be formed with these side lengths.

Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

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Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

By dividing the overall elevation change (12 metres) by the total time required (4 seconds),

it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.

=> Elevation change equals 12 metres

=> Total duration: 4 seconds

=>  12 meters / 4 seconds

=> 3 meters/second

As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.

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The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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a) Classroom:

Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m

Area = length x breadth = 10m x 8m = 80m^2

Volume = length x breadth x height = 10m x 8m x 3m = 240m^3

b) Box:

Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm

Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2

Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3

c) Cabinet:

Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm

Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2

Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3

Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.

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The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).

Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:

V_small = π(2²)(4) = 16π cubic inches

Using these dimensions, we can calculate the volume of the larger can using the same formula:

V_large = π(6²)(12) = 432π cubic inches

Now, let's compare the volumes of the small and large cans. We have:

V_large = 432π cubic inches > 16π cubic inches = V_small

Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:

V_large = 432π cubic inches 3

V_small = 3(16π) cubic inches = 48π cubic inches

We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.

Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.

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Complete Question:

A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?

a) The radius of the larger can will be 5 inches.

b) The volume of the larger can will be 3 times the volume of the smaller can

c) The radius of the larger can will be 8 inches.

d) The volume of the larger can is 3 times the volume of smaller can

Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)

The shortest driving distance between the stadium and the animal shelter is given as follows:

10 blocks.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates are given as follows:

Since the spaces are filled by houses, we cannot apply the formula, hence the shortest distance is:

6 - (-3) + 3 - 2 = 9 + 1 = 10 blocks.

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The point of intersection in the first quadrant is (3, 4) from the equation of circle.

We can start by substituting the equation of the line into the equation of the circle and solving for z and y.

The equation for the circle is:

(x - h)^2 + (y - k)^2 = r^2

Substituting h = 0, k = 3, and r = 3, we get:

x^2 + (y - 3)^2 = 9

Now, we substitute y = 2z + 3 into the equation:

x^2 + (2z + 3 - 3)^2 = 9

Simplifying, we get:

x^2 + 4z^2 = 9

Since we are looking for a point in the first quadrant, both x and z must be positive. We can solve for z in terms of x:

4z^2 = 9 - x^2

z^2 = (9 - x^2)/4

z = sqrt[(9 - x^2)/4]

Substituting this into the equation y = 2z + 3, we get:

y = 2sqrt[(9 - x^2)/4] + 3

To find the point of intersection in the first quadrant, we need to find a value of x that satisfies both this equation and the equation of the circle. We can substitute the equation for y into the equation for the circle:

x^2 + [2sqrt((9 - x^2)/4)]^2 = 9

Simplifying, we get:

x^2 + (9 - x^2)/2 = 9

Multiplying both sides by 2:

2x^2 + 9 - x^2 = 18

Solving for x:

x^2 = 9

x = 3

Substituting x = 3 into the equation for y, we get:

y = 2sqrt[(9 - 3^2)/4] + 3 = 4

Therefore, the point of intersection in the first quadrant is (3, 4).

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The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.

Total number of children is equal to 15

Total amount of money distributed among 15 children = $9

To find out how much each child receives,

We can divide the total amount of money by the number of children.

In this case, there are 15 children and $9 to split.

So, the amount of money each child receives is equal to,

(Total amount of money )/ ( total number of children )

= $9 ÷ 15

= $0.60

Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.

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