Teresa ran a 20-mile marathon. Her average speed was 5 miles per hour. Approximately how long did it take her to finish the race?

No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

In a contingency table, we describe the relationship between two variables measured at the ordinal or nominal level (option a).

A contingency table is a statistical table that displays the frequency distribution of two categorical variables and helps identify any associations or dependencies between them. The table organizes the data into rows and columns, with each cell representing the frequency count or proportion of observations falling into a particular combination of categories.

By examining the distribution of frequencies across the table, patterns and relationships between the variables can be discerned. This information can be useful in various fields, such as social sciences, market research, and epidemiology, for analyzing survey responses, understanding consumer preferences, or investigating the relationship between risk factors and diseases, among other applications.

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9514 1404 393

Answer:

  B. 4/5

Step-by-step explanation:

When dilation is centered on the origin, each coordinate is multiplied by the dilation factor:

  B'y= k·By

  B'y = (2/5)(2)

  B'y = 4/5 . . . . . . . y-coordinate of B'

Answer:it is b

Step-by-step explanation:

(a) For y''+4y=sin2t+(2t+1)cos2t+tsint, we need to find a particular solution Y(t) using the method of undetermined coefficients.

Since the right-hand side of the equation contains sin(2t), cos(2t), and tsin(t), we can assume that the particular solution has the form:

Y(t) = A sin(2t) + B cos(2t) + Ct sin(t) + Dt cos(t) + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(b) For y''-4y'+4y=t^2(e^(2t)-1), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains t^2e^(2t) and t^2, we can assume that the particular solution has the form:

Y(t) = (At^2 + Bt + C)e^(2t) + Dt^2 + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(c) For y''+2y'+2y=3e^(-t)+2e(-t)cos(t)+4(t^2)e^(-t)sin(t), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains e^(-t), e^(-t)cos(t), and t^2e^(-t)sin(t), we can assume that the particular solution has the form:

Y(t) = Ae^(-t) + (Bt + C)e^(-t)cos(t) + (Dt + Et^2) e^(-t)sin(t) + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

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The band boosters had custom t-shirts made for homecoming and need to sell a certain number of shirts to cover their expenses. An equation, 10x = 25.90 + 8.15x, can be used to determine the number of shirts they need to sell to break even.

Let's break down the given information and formulate an equation to represent the situation.

The band boosters paid a setup fee of $25.90 and an additional cost of $8.15 per shirt to have the custom t-shirts made. They plan to sell each shirt for $10.

Let's represent the number of shirts they need to sell as 'x'. The cost to produce 'x' shirts would be the sum of the setup fee and the cost per shirt multiplied by the number of shirts:

Cost to produce 'x' shirts = Setup fee + (Cost per shirt × Number of shirts)

Using the given values, the equation becomes:

Cost to produce 'x' shirts = $25.90 + ($8.15 × x)

To break even, the revenue from selling the shirts should equal the cost to produce them. The revenue can be calculated by multiplying the selling price per shirt ($10) by the number of shirts sold:

Revenue from selling 'x' shirts = Selling price per shirt × Number of shirts sold

The equation representing the situation can be written as:

$10x = $25.90 + ($8.15 × x)

Simplifying the equation, we have:

10x = 25.90 + 8.15x

Now we have the equation that represents the situation.

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The complete statement:

The area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus, which has an area of 135 square inches.

The base of Charlene's rhombus is 5 inches and the height is 3 inches, giving it an area of 15 square inches.

Jerry's rhombus has a base of 15 inches and a height of 9 inches, so its area is given by:

Area of Jerry's rhombus = base × height = 15 inches × 9 inches = 135 square inches.

Now, Charlene's rhombus has a base and height that are 1/3 the base and height of Jerry's rhombus. Therefore:

Base of Charlene's rhombus = (1/3) × 15 inches = 5 inches.

Height of Charlene's rhombus = (1/3) × 9 inches = 3 inches.

The area of Charlene's rhombus can be calculated as:

Area of Charlene's rhombus = base × height = 5 inches × 3 inches = 15 square inches.

To compare the areas of the two rhombuses:

Area of Charlene's rhombus / Area of Jerry's rhombus = 15 square inches / 135 square inches.

Simplifying the fraction, we get:

Area of Charlene's rhombus / Area of Jerry's rhombus = 1/9.

Therefore, the area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus.

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Answer.

Attached my answer, hope that helps...

Plot the four vertices of the rectangle using the given coordinates:

Find the perimeter of the rectangle by adding the length of each side.

The sides of that rectangle have lengths of 14, 11, 14 and 11 units. Then, the perimeter of the rectangle is:

Since each unit on the grid represents 10 meters, multiply that result by 10 to find the real distance that Randy walked, measured in meters:

Therefore, the answer is:

If the researcher uses a cross-sectional design and obtains 25 scores for each age, to determine how many children participated in the entire study, you can follow these steps: First, you have to add up all the scores obtained for all ages.

This is done by multiplying the 25 scores by the number of ages that were considered in the study, which in this case is three (5 years, 7 years, and 10 years). Therefore, the total number of scores would be:

25 scores × 3 ages = 75 scores.

Then you divide the total number of scores by the number of scores per participant to get the total number of participants. In this case, each participant had one score. Therefore, the total number of children who participated in the entire study would be:

75 scores ÷ 1 score per child = 75 children.

This study aimed to examine the cooperation between peers by observing children at five years, seven years, and ten years old. A cross-sectional design is a research method used to compare different groups of people at one time. It involves selecting participants at different ages or from different groups to compare their performance. In this study, the researcher used a cross-sectional design and obtained 25 scores for each age to determine the number of children who participated in the entire study. In this study, the researcher had a total of 75 scores, 25 for each age of the children. Therefore, the total number of children who participated in the study would be 75, which is the total number of scores divided by one score per child. The study focused on understanding the level of cooperation between peers, and it is expected that the results of the study would help in developing strategies to improve the level of cooperation between peers among children of different ages.

In conclusion, a cross-sectional design is a research method used to compare different groups of people at one time. This method was used in this study to observe the cooperation between peers by observing children at different ages. The study obtained 25 scores for each age, which totaled to 75 scores for all ages. Therefore, the total number of children who participated in the entire study was 75, which was obtained by dividing the total number of scores by the number of scores per participant. The study's results will help develop strategies to improve cooperation among peers among children of different ages.

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Using a cross-sectional research design, the total number of children that participated in the study is 75, which is calculated by multiplying the number of children in each group (25) by the number of age groups (3).

In a cross-sectional research design, different age groups are observed at a single point in time. In this case, the groups are children at ages of five years, seven years, and ten years. Each age group includes 25 children, therefore we have 3 groups. We calculate the total number of participated children by multiplying the number of children in each group by the number of the groups. Therefore, 25 children/group × 3 groups = "75 children" participated in the entire study.

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Applying the scale factor of 1:5, Lisa del Giocondo's face was 1.6 inches long in the sketch.

If the scale factor from the sketch to real life is 1:5, then it means that every inch in the sketch represents 5 inches in real life.

Therefore, to find out how long Lisa del Giocondo's face was in the sketch, we need to multiply the real-life length of her face by the inverse of the scale factor, which is 1/5.

If her face was 8 inches long in real life, then her face in the sketch would be:

8 inches * (1/5) = 1.6 inches

Therefore, based on the scale factor given, Lisa del Giocondo's face was 1.6 inches long in the sketch.

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Plug it in.

y = -1, y1 = 1

x = 3, x1 = 1

-1 - 1 = m( 3 - 1)

-2 = 2m

m = -1

The slope is -1

y = -x +b

-1 = -3 +b

b = 2

The equation is y = -x + 2

Hope this helps.

Answer:

y=-1·x+2

Step-by-step explanation:

(1) Repetition allowed : There are 4 choices for both positions, so 4 × 4 = 16 2-digit numbers can be formed. (2) Repetition not allowed : There are 4 options for tens position, and three options for ones position. Therefore, 4 × 3 = 12 2-digit numbers can be formed.

Answer:

7 is the answer hope it will help you

Answer:

l = 12.25 m²

Step-by-step explanation:

Here, l = 3½ m = 3.5m

∴ Now, The area of a square is

= l²

= (3.5)² m

= 12.25 m²

Thus, The area of a square is 12.25 m²

-TheUnknownScientist

Answer:

B.)58?

Step-by-step explanation:

Hope I helped..

Answer:

b: 58

Step-by-step explanation:

Answer:

8/3 < 8/2

D

Step-by-step explanation:

8/3 = 2.67

8/2 = 4

So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.

There is more left if 8 is divided by 2 than when it is divided by 3

[Answer]8/3 < 8/2

[Answer] D

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

8/3 < 8/2

Step-by-step explanation:

D. When fractions have equivalent numerators, the one with the lesser denominator is the greater fraction.

8/2 = 4

8/3 = 2.667

Answer:

-1.7 = rational

1.083 = rational

1.22345721 = rational

-1.090909 = rational

Step-by-step explanation:

Answer:

\(\sqrt{85}\) or 9.21954

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

\(d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }\)

d = distance

\((x_{1}, y_{1})\) = coordinates of the first point

\((x_{2}, y_{2})\) = coordinates of the second point

Answer:

the last option hope this helps

Step-by-step explanation:

Answer:

+ 45 - 45 < 16 - 45 is answer

Step-by-step explanation:

The problem asks us to find the width of a rectangular garden with a given perimeter of 40 ft and a length of 10 ft, with the width represented by x.

The perimeter of a rectangle can be found by adding the lengths of all its sides. In this case, the formula for the perimeter is: P = 2L + 2W, where L is the length and W is the width of the rectangle. We are given that the perimeter of the garden is 40 ft, and the length is 10 ft. Substituting these values in the formula gives:

40 = 2(10) + 2x

Simplifying this equation, we get:

40 = 20 + 2x

20 = 2x

x = 10

Therefore, the width of the garden is 10 ft.

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The width of the garden is 10 ft. The problem asks us to find the width of a rectangular garden with a given perimeter of 40 ft and a length of 10 ft, with the width represented by x.

The perimeter of a rectangle can be found by adding the lengths of all its sides. In this case, the formula for the perimeter is: P = 2L + 2W, where L is the length and W is the width of the rectangle. We are given that the perimeter of the garden is 40 ft, and the length is 10 ft. Substituting these values in the formula gives:

40 = 2(10) + 2x

40 = 20 + 2x

20 = 2x

x = 10

Therefore, the width of the garden is 10 ft.

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Answer:

4 Hz

Step-by-step explanation:

Formula: frequency = velocity/wavelength

f = 80/20

f = 4

Answer:

180 degrees

Step-by-step explanation:

Angle RQS + Angle RQS = 180 degrees

Answer:

RQS = 102 TQS= 78

Step-by-step explanation:

Answer:300cm

Step-by-step explanation:

The cost of 12 tickets is $180.

Given that, three concert tickets cost $45.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, the cost of one ticket

= 45/3

= $15

So, the cost of 12 tickets = 12×15

= $180

Therefore, the cost of 12 tickets is $180.

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\((\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{3}{4}})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{\frac{5}{4}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{5}{4}}-\stackrel{y1}{\left( -\frac{3}{4} \right)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{~~ \frac{5 }{4 }+\frac{3}{4} ~~}{-2} \\\\\\ \cfrac{~~ \frac{ 5+3}{ 4} ~~}{-2}\implies \cfrac{~~ \frac{8 }{4 } ~~}{-2}\implies \cfrac{2}{-2}\implies -1\qquad \impliedby m\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left(-\frac{3}{4} \right)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4})\implies {\large \begin{array}{llll} y+\cfrac{3}{4}=-(x-4) \end{array}}\)

Answer:

\(-3\frac{1}{2}\)

Step-by-step explanation:

\(2\frac{1}{6}-5\frac{2}{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\\quad 2\frac{1}{6}=\frac{13}{6}\\\\\frac{13}{6}-5\frac{2}{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\\quad 5\frac{2}{3}=\frac{17}{3}\\\\\frac{13}{6}-\frac{17}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}6,\:3:\quad 6\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\=\frac{13}{6}-\frac{34}{6}\\\\=\frac{13-34}{6}\\\\=\frac{-21}{6}\\\\=-\frac{21}{6}\\\\=-\frac{7}{2}\\\)

\(\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{7}{2}=3\frac{1}{2}\\\\=-3\frac{1}{2}\)

Answer:

-3 1/2 or -7/2 or -3.5

The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

Let the number be x,

Twice the difference of three times a number and five = 2(3x - 5)

The sum of four times a number and six is  (4x + 6)

2(3x - 5) ≤ (4x + 6)

6x - 10 ≤ 4x + 6

6x - 4x ≤ 6 + 10

2x ≤ 16

x ≤ 8

x can be any positive number less than or equal to 8.

Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

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