coefficients. asses through (-3,2) and is parallel to the line defined by 5x+2y=-10

Answer:

10mins for 35 photos

Step-by-step explanation:

If it takes 8mins to produce 28photos, that is ratio 1:3.5

For 7 photos, divide by 3.5, that is 2mins

For 4mins, multiply by 3.5, that will be 14photos

For 21 photos, divide by 3.5, that will be 6 mins

The coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0

The coefficient of a term in a polynomial is the number that is multiplied by the variable. The degree of a term is the exponent of the variable. In the polynomial 8x^(2)+6x+8, there are three terms:

- The first term is 8x^(2). The coefficient of this term is 8, and the degree is 2.
- The second term is 6x. The coefficient of this term is 6, and the degree is 1.
- The third term is 8. The coefficient of this term is 8, and the degree is 0 (since there is no variable).

Therefore, the coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0.

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The average rate of change between the years 2002 and 2007 was  2,.939.8 (option B).

In demographics, the average rate of change refers to how much the population of a city, country, etc. changes over a year period usually by increasing or decreasing. Due to this, the rate of change can be calculated by using the following formula change in the population/ number of years.

239,839 (population in 2002) - 254,538 (population in 2007)

2007 - 2002 = 5 years (number of years)

14699 / 5 years = 2,.939.8 (option B)

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1. The height of the pyramid is 3.7 inches.

2. The length of the crossbar is 2√2 feet.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

1. We know, The height, slant height, and half of the base length form a

right-angled triangle

Therefore, h² = 4² - (3/2)².

h² = 13.75

h = 3.7 inches.

2. We know, In a 45°, 45° and 90° triangle, It is an isosceles right-angled triangle, The hypotenuse is √2 times the two similar sides.

Therefore, From the given information, The length of the crossbar is

2√2 feet.

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Answer:

1: 254 inches

2: 100.8 mi

3: 64 yards

4: 128 yards

Step-by-step explanation:

1: 4x7=28 4x7=28 9x7=63 9x7=63 9x4=36 9x4=36

28+28+63+63+36+36=

254

2: Dunno exactly, but my guess is: 6x5=30. 3x6=18. 2.8x3=8.4 3x6=18. 3x6=18. 2.8x3=8.4

8.4+8.4+18+18+18+30=

100.8

3: 2x1=2 2x1=2 10x2=20 10x2=20 10x1=10 10x1=10

2+2+20+20+10+10=

64

4: 6x8/2=24 6x8/2=24 10x5=50 6x5=30

24+24+50+30=

128 yards

Pls give brainliest :)

By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.

This can be represented as:

Snow remaining equals 0.23x.

Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:

0.23y = 30

By finding y, we obtain:

y = 30 / 0.23 ≈ 130.43

Hence, the initial snowfall measured about 130.43 inches.

We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:

130.43 - 30 = 100.43

Hence, during the blizzard, snowfall totaled about 100.43 inches.

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The chart that cοuId be used tο dispIay the data is D. Bοx pIοt; because the data is categοricaI.

A bοx pIοt, οften knοwn as a bοxpIοt, is a methοd in descriptive statistics fοr graphicaIIy dispIaying the IοcaIizatiοn, spread, and skewness grοups οf numericaI data thrοugh their quartiIes.

Bοx pIοts are used tο depict the distributiοns οf numericaI data vaIues, particuIarIy when cοmparing them acrοss variοus grοups. They are designed tο cοnvey high-IeveI infοrmatiοn at a gIance, prοviding generaI infοrmatiοn abοut the symmetry, skew, variance, and οutIiers οf a grοup οf data.

In this case, since the data set Iists the favοrite chοice οf rοck bands, the bοx pIοt can be used.

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Complete question:

A data set lists the favοrite chοice οf rοck bands. Which οf the fοllοwing charts cοuld be used tο display the data, and why?

Bar chart; because the data is categοrical

Bar chart; because the data is numerical

Bοx plοt; because the data is categοrical

Bοx plοt; because the data is numerical

slope of HI = 6, slope of IJ = -1/6, slope of HJ = 5/7, length of HI = √37, length of IJ = √37, length of HJ = √74, Triangle HIJ is isosceles

The slope of a line is found by the formula (y2-y1)/(x2-x1). The length of a line is found by the formula √((x2-x1)²+(y2-y1)²).

Slope of HI = (1-(-5))/(8-7) = 6/1 = 6
Slope of IJ = (-5-(-4))/(7-1) = -1/6
Slope of HJ = (1-(-4))/(8-1) = 5/7

Length of HI = √((8-7)²+(1-(-5))²) = √(1²+6²) = √(1+36) = √37
Length of IJ = √((7-1)²+(-5-(-4))²) = √(6²+(-1)²) = √(36+1) = √37
Length of HJ = √((8-1)²+(1-(-4))²) = √(7²+5²) = √(49+25) = √74

Triangle HIJ is isosceles because it has two sides with the same length (HI and IJ).

- slope of HI = 6
- slope of IJ = -1/6
- slope of HJ = 5/7
- length of HI = √37
- length of IJ = √37
- length of HJ = √74
Triangle HIJ is isosceles

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The mapping diagram represents a relation between the set of x-values {negative 8, negative 5, negative 1, 1, 12} and the set of y-values {negative 4, negative 2}. The arrows between the circles show how the x-values are related to the y-values.

A mapping diagram is a visual way to represent a relation between two sets of values, where the arrows show how the values in one set are related to the values in the other set. The input values are typically shown in one circle or column, while the output values are shown in another circle or column.

Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes to determine their effects on a larger scale. It is a major part of modern mathematics and is used extensively in science, engineering, and economics.

In the given question,

The mapping diagram represents a relation between the set of x-values {negative 8, negative 5, negative 1, 1, 12} and the set of y-values {negative 4, negative 2}. The arrows between the circles show how the x-values are related to the y-values.

Specifically, the arrow from negative 8 to negative 4 means that the input value of x = negative 8 is related to the output value of y = negative 4. Similarly, the arrow from negative 5 to negative 2 means that the input value of x = negative 5 is related to the output value of y = negative 2.

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The probability of exactly two heads in tossing three fair coins is 3/8.

To find the probability of exactly two heads, we need to count the number of outcomes in the sample space that have exactly two heads and divide that by the total number of outcomes in the sample space.
In the sample space {hhh, hht, hth, htt, thh, tht, tth, ttt}, there are three outcomes that have exactly two heads: hht, hth, and thh.
So the probability of exactly two heads is 3/8.

In mathematical terms, this can be represented as:
P(exactly two heads) = number of outcomes with exactly two heads / total number of outcomes
P(exactly two heads) = 3 / 8

Therefore, the probability of exactly two heads in tossing three fair coins is 3/8.

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Therefore , the solution of the given problem of angles comes out to be  Lines I and m can be inferred to be parallel by the Corresponding Angles Converse .

An angle is a shape in Euclidean geometry consisting of two rays, or sides of a circular, that split at the angle's apex and the angle's apex, which is in the middle. Where they are located, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles.

Here,

The Corresponding Angles Converse states that if two parallels are intersected by a transversal such that a set of corresponding angles are congruent, then perhaps the two lines are parallel.

This can be used to demonstrate that lines I and m are parallel.

We can infer that 1 and 2 are corresponding angles because 1 2.

We can infer that they have the same measure because they are congruent.

Let's now think about the transversal line t. Lines I and m can be inferred to be parallel by the Corresponding Angles Converse because 1 and 2 are corresponding angles and t crosses both I and m.

We have thus demonstrated that I / m.

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Answer: Your welcome!

Step-by-step explanation:

The slope of the line represents the amount of money that is donated each day, which is 25. The y-intercept represents the amount of money donated on the first day, which is 50.

The remainder when 7x⁴ - 3x is divided by x - 1 is 4.

knοwn as indeterminates) and cοefficients, which are cοmbined using the οperatiοns οf additiοn, subtractiοn, and multiplicatiοn. A pοlynοmial can have οne οr mοre variables, but each term in the pοlynοmial must have nοn-negative integer expοnents οn the variables. The degree οf a pοlynοmial is the highest pοwer οf its variables with a nοn-zerο cοefficient.

Fοr example, the pοlynοmial 3x² - 2x + 5 has a degree οf 2, with the term 3x² being the highest degree term. The cοefficient οf the term 3x^2 is 3, and the cοefficient οf the term -2x is -2.

Pοlynοmials are used in a variety οf mathematical applicatiοns, including algebra, calculus, and geοmetry. They are used tο represent mathematical functiοns, tο apprοximate cοmplex curves, and tο sοlve equatiοns. Sοme cοmmοn οperatiοns οn pοlynοmials include additiοn, subtractiοn, multiplicatiοn, divisiοn, and factοring.

Tο find the remainder when the pοlynοmial 7x⁴ - 3x is divided by x - 1, we can use pοlynοmial lοng divisiοn οr synthetic divisiοn.

7x³ + 7x² + 7x + 4

x - 1 | 7x⁴ + 0x³ - 3x² + 0x + 0

     - (7x⁴ - 7x³)

           7x³ - 3x²

           - (7x³ - 7x²)

                 4x² + 0x

                 - (4x² - 4x)

                        4x

                        - (4x - 4)

                             4

Therefore, the remainder when 7x⁴ - 3x is divided by x - 1 is 4.

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The points of the equation are: (-3, 0), (-9, 0), and (0, 0). Be sure to select the appropriate number.

To find the points of the equation f(x) = (3x2 + 18x + 27)/(x2 + 3x4), you need to set the numerator and denominator of the equation equal to 0. Then you can solve for the points.

Setting the numerator equal to 0:
3x2 + 18x + 27 = 0
Solve for x: x = -3 and x = -9

Setting the denominator equal to 0:
x2 + 3x4 = 0
Solve for x: x = 0

Therefore, the points of the equation are: (-3, 0), (-9, 0), and (0, 0). Be sure to select the appropriate number.

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a) The equation of the circle is x² + y² 169.

b) The coordinates of the other endpoint of the diameter are (-5, 12).

The equation of a circle is given by:

(x-a)² + (y-b)² = r²

Where (a, b) is the centre of the circle and r is the radius.

In this case, the centre of the circle is at (0, 0), so the equation of the circle simplifies to: x^2 + y^2 = r^2

To find the radius, we can use the distance formula between the centre and the point

P: r = √((5-0)^2 + (-12-0)²) = √(25 + 144) = √169 = 13

Therefore, the equation of the circle is: x² + y² = 13^2 or x² + y² = 169

To find the coordinates of the other endpoint of the diameter that passes through the point P, we can use the fact that the diameter is a straight line that passes through the centre of the circle. The slope of this line is: m = (-12-0)/(5-0) = -12/5

The equation of this line is: y = -12/5x

Since the other endpoint of the diameter also lies on the circle, we can substitute this equation into the equation of the circle: x² + (-12/5x)² = 169

Solving for x, we get: x = -5 or x = 5. Since the point P has an x-coordinate of 5, the other endpoint of the diameter must have an x-coordinate of -5.

Substituting this value of x back into the equation of the line, we get: y = -12/5(-5) = 12

Therefore, the coordinates of the other endpoint of the diameter are (-5, 12).

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IQR difference = 5

The interquartile range (IQR) is a measure of variability that describes the spread of a set of data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of the data.

The formula for calculating the IQR is:

IQR = Q3 - Q1

The Upper Quartile - Lower Quartile is the definition of the interquartile range.

The answer to the query is

Mount Vernon data set: 55, 60, 65, 70, 75, 80, 85 and 90

Lakewood data set = 65, 70, 75, 80 and 85

Mount Vernon median = 70+75/2 = 77.5

55+60+65+70/4 = 62.5 is the median for the lower half of the collection.

Upper half of set median: 82.5 (75, 80, 85, 90 divided by 4).

Mount Vernon's IQR is 82.5 minus 62.5, or 20.

Likewise, in the instance of Lakewood,

Average: 75

Lower half of the set median equals 65+70/2 = 67.5

Upper half of set median equals 80+85/2 = 82.5

IQR = 82.5 - 67.5 = 15

Hence, IQR difference = 20-15 = 5

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1) The radius of the small circle r is 5√5 and 2) The shaded area will be 13.5π cm².

Area of circle A = 125 π, Radius of circle R = 15, We need to find the radius of the small circle r. By comparing both circles,Area of circle A = πR² 125π = π × 15² 125π = π × 225, 125π = 225 πr², r² = (125π) / πr² = 125r = √125r = 5√5. Hence, the radius of the small circle r is 5√5.

A circle of radius 9 cm with a sector of angle 60° cut out. We know that the area of the circle is given by ,Area of circle = πr² Where, r = 9 cm Area of circle = π × 9²= π × 81= 81 π. Since we have cut a sector of 60°,The remaining angle = 360° - 60° = 300° Fraction of the circle left = (300/360) = 5/6

Therefore,The area of the circle left = (5/6) × 81 π= 67.5 π. The area of the shaded portion = (Area of circle) – (Area of the circle left) Area of the shaded portion = 81 π – 67.5 π= 13.5 π cm², Hence, the shaded area is 13.5π cm².

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Answer:

scatter plot with points plotted at 1 comma 2, 1 comma 3, 3 comma 2, 3 comma 3, 4 comma 2, 4 comma 5, 5 comma 6, 6 comma 6, 7 comma 8, 8 comma 7, 9 comma 10, and 10 comma 9, with a line drawn through the points 4 comma 5 and 5 comma 6.

Step-by-step explanation:

The scatter plot shows a collection of points on a coordinate plane. To determine which of the given graphs shows a line that fits the data, we need to analyze the points and their distribution.

From the given points, we can observe that there is no clear linear relationship between the x and y variables. However, we can see that there is a cluster of points between (4,2) and (7,8), and the rest of the points are scattered around this cluster. Therefore, any line that fits the data should pass through this cluster of points.

Now, let's analyze each option:

The first option shows a line passing through (6,6) and (7,7). While these two points are part of the cluster, the line does not seem to fit the rest of the data very well.

The second option shows a line passing through (4,5) and (5,6). These points are also part of the cluster, and the line seems to fit the data reasonably well.

The third option shows a line passing through (3,3) and (4,4). These points are near the edge of the cluster, but the line seems to fit the data reasonably well.

The fourth option shows a line passing through (1,2) and (7,8). While these two points are part of the cluster, the line does not seem to fit the rest of the data very well.

Based on the analysis above, the second and third options seem to be the best fits for the data. However, the second option seems to be a slightly better fit than the third option since the line passes through two points that are closer to the center of the cluster. Therefore, the answer is:

scatter plot with points plotted at 1 comma 2, 1 comma 3, 3 comma 2, 3 comma 3, 4 comma 2, 4 comma 5, 5 comma 6, 6 comma 6, 7 comma 8, 8 comma 7, 9 comma 10, and 10 comma 9, with a line drawn through the points 4 comma 5 and 5 comma 6.

Answer: B

scatter plot with points plotted at 1 comma 2, 1 comma 3, 3 comma 2, 3 comma 3, 4 comma 2, 4 comma 5, 5 comma 6, 6 comma 6, 7 comma 8, 8 comma 7, 9 comma 10, and 10 comma 9, with a line drawn through the points 4 comma 5 and 5 comma 6

Step-by-step explanation:

The value of hypotenuse for given right angles triangle is :

Part 1:  c = 1.5

Part 2: c = 3.5

Part 1:

a = 3, c = ?

using sin function.

sin 30 = 3/c

c = 3 * sin 30

c = 1.5

Part 2:

a = 7√3

cos 30 = 7√3 / c

c = cos 30 * 7√3

c = 7/2

c = 3.5

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Answer:

1)  12<x<15 is:   f(x) = -5(x-12)^2 + 80

2) 15<x<17 is:    f(x) = 35

3) 27<x<30 is:  f(x) = 2.5x-22.5

Step-by-step explanation:

See the attached image.

1)  Plot all the lines as shown

2)  Add the inequalities, which will produce the colored regions on DESMOS.

3)  Assume that the function having the greatest value in each region is the function that determines the roller coaster's height  (My assumption - it is not clear in the problem which function should dominate)

4) for the three regions listed with no corresponding function, identify the line having the greatest value.  Thiose are the functions that are noted on the graph and in the answer box above.

5) Take a break

a) 6% of 34 is 2.04
b) 17 is 50% of 34

c) 18 is 30% of 60

d) 7% of 49 is 3.43.

a. To find 6% of 34, you can multiply 34 by 0.06 (which is the decimal equivalent of 6%): 34 * 0.06 = 2.04. So 6% of 34 is 2.04.

b. To find what percent 17 is of 34, you can divide 17 by 34 and then multiply by 100 to convert the decimal to a percentage: (17/34) * 100 = 50%. So 17 is 50% of 34.

c. To find what number 18 is 30% of, you can divide 18 by 0.30 (which is the decimal equivalent of 30%): 18 / 0.30 = 60. So 18 is 30% of 60.

d. To find 7% of 49, you can multiply 49 by 0.07 (which is the decimal equivalent of 7%): 49 * 0.07 = 3.43. So 7% of 49 is 3.43.

8. Unfortunately, I cannot see the number line that you are referring to, so I cannot provide an answer for this part of the question.

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the first question answer is 15/17

There is only one solution when you solve the system of equations 2x+y=7 and y=-2x+7. The one solutions is (2, 3).

To find the solution, you can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation.

First, solve the second equation for y:
y = -2x + 7

Now, substitute this expression for y into the first equation:
2x + (-2x + 7) = 7

Simplify the equation:
2x - 2x + 7 = 7

Combine like terms:
7 = 7

This equation is always true, which means that there is only one solution for this system of equations. The solution is the point where the two lines intersect, which is (2, 3).

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Option (c) has the same equation as above after simplification, so the answer is (c):y-8=-0.2(x+10).

Simplification involves reducing an expression, equation, or problem to a simpler form. This can involve performing operations such as combining like terms, factoring, or canceling out common factors.

Point-slope form is a way of writing the equation of a straight line in two-dimensional space, using a given point on the line and the line's slope.

The point-slope form equation for a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1).

In the given question,

To write the equation of a line in point-slope form, we need to use the formula:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is any point on the line.

We are given two points on the line: (-10, 8) and (10, 4). We can use these points to find the slope of the line:

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

= (4 - 8) / (10 - (-10))

= -0.15

Now we can use the point-slope form with the point (-10, 8) and slope -0.15:

y - 8 = -0.15(x - (-10))

Simplifying this equation, we get:

y - 8 = -0.15(x + 10)

Option (c) has the same equation as above after simplification, so the answer is (c):

y-8=-0.2(x+10).

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1. 1-cos²x / sinx = sin²x / sinx = sinx
2. Cos X – Cos x = 0
3. (sin^2 + tan^2 u + cos^2 u) / (sec u) = (1 + tan^2 u) / (sec u) = sec^2 u / sec u = sec u
4. (sec^2 x – tan^2 c) / (cos^2 x + sin^2 x) = (1/cos^2 x - sin^2 x / cos^2 x) / 1 = (1 - sin^2 x) / cos^2 x = cos^2 x / cos^2 x = 1
5. (sec^2 + csc^2 x) - (tan^2 x + cot^2 x) = (1/cos^2 x + 1/sin^2 x) - (sin^2 x / cos^2 x + cos^2 x / sin^2 x) = (sin^4 x + cos^4 x) / (sin^2 x cos^2 x) = 1 / (sin x cos x)
6. tan x cot x = (sin x / cos x) * (cos x / sin x) = 1
7. cot u sin u = (cos u / sin u) * sin u = cos u
8. sec (-x) cos (-x) = (1 / cos (-x)) * cos (-x) = 1
9. cot (-θ) tan (-θ) = (cos (-θ) / sin (-θ)) * (sin (-θ) / cos (-θ)) = 1
10. sec^2 (-x) – tan^2 (-x) = (1/cos^2 (-x)) - (sin^2 (-x) / cos^2 (-x)) = (1 - sin^2 (-x)) / cos^2 (-x) = cos^2 (-x) / cos^2 (-x) = 1
11. sec u sin u = (1 / cos u) * sin u = sin u / cos u = tan u

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Answer:

y < 2x + 4

Step-by-step explanation:

y+4<-2(x-4)

y + 4 < -2x +8

y < 2x + 4

They are not the same as the upper and lower limits used in other statistical calculations.

A accumulation of numerical data that has been methodically gathered, arranged, and examined is referred to as statistical data. Numerous phenomena, including economic patterns, demographic traits, health outcomes, and more, are described and measured using this data. Numerous techniques, such as surveys, experiments, observations, and administrative documents, can be used to gather statistical data. After being gathered, the data can be examined statistically to reveal patterns, connections, and trends that can be used to guide policy development and decision-making.

given

This is a histogram showing the frequency distribution of the weights of 30 students. Each bar represents a weight range, and the height of the bar represents the frequency of students in that weight range.

To find the upper and lower boundaries for each weight range, we can use the following formula:

Lower bound = midpoint of the previous range + 0.5

Upper bound = midpoint of the current range - 0.5

For example, the lower bound of the first range (60-64) is:

Lower bound = midpoint of previous range + 0.5

= 57

Upper bound = midpoint of current range - 0.5

= 61.5

We can apply the same formula to find the upper and lower bounds for the other ranges in the histogram. The results are:

60-64: lower bound = 57, upper bound = 61.5

65-69: lower bound = 62, upper bound = 66.5

70-74: lower bound = 67, upper bound = 71.5

75-79: lower bound = 72, upper bound = 76.5

80-84: lower bound = 77, upper bound = 81.5

85-89: lower bound = 82, upper bound = 86.5

90-94: lower bound = 87, upper bound = 91.5

95-99: lower bound = 92, upper bound = 96.5

They are not the same as the upper and lower limits used in other statistical calculations.

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The value for k has to be taken, to ensure that the probability, that - when we take a distance measurement y in practice - this distance measurement lies inside the interval [x – ko, x + ko), equals 99% is  0.516.

To find the value of k that ensures that the probability that the distance measurement lies inside the interval [x – ko, x + ko) equals 99%, we can use the standard normal distribution table.

First, we need to find the z-score that corresponds to the 99% probability. This is found by looking at the standard normal distribution table and finding the z-score that corresponds to a cumulative probability of 0.995 (since the probability is split between both sides of the mean, we need to look for 0.995 instead of 0.99).

The z-score that corresponds to 0.995 is approximately 2.58.

Now, we can use the formula for the z-score to find the value of k:

z = (y - x)/o

Since we are looking for the value of k that corresponds to the interval [x – ko, x + ko), we can plug in the values for the z-score and the standard deviation:

2.58 = (x + ko - x)/0.2

Solving for k, we get:

k = 2.58 * 0.2

k = 0.516

Therefore, the value for k that ensures that the probability that the distance measurement lies inside the interval [x – ko, x + ko) equals 99% is 0.516.

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The ratio of similarity  DEFG to TSRQ is '3: 1'.

Two quadrilaterals are considered similar if they have the same shape but may have different sizes. Similar quadrilaterals have corresponding angles that are congruent, and their corresponding sides are in proportion to each other.

The ratio of similarity is a measure of how much two geometric figures are enlarged or reduced to become similar.

Here we have

Quadrilateral DEFG and Quadrilateral TSRQ.

Where DEFG similar to TSRQ

Hence, the ratio of corresponding sides will be equal

=> DE/TS  = EF/SR  = FG/RQ = DG/TQ

=> 24/8  = 24/8  = 24/8 = 24/8 = 3/1

Therefore,

The ratio of similarity  DEFG to TSRQ is '3: 1'.

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The values of y that make the inequality 5y<41 true are B. 7 and D. 6.5.

To find the values of y that make the inequality true, we can first isolate y by dividing both sides of the inequality by 5:

5y<41

y<41/5

y<8.2

This means that any value of y less than 8.2 will make the inequality true.

Looking at the given options, we can see that B. 7 and D. 6.5 are both less than 8.2, so they are the correct answers.

A. 8 and C. 8.5 are both greater than or equal to 8.2, so they do not make the inequality true. E. 9 is also greater than 8.2, so it does not make the inequality true.

Therefore, the correct answers are B. 7 and D. 6.5.

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