Shirley went shopping in a mall. She reached the mall 12.5 minutes later than her usual time. While returning she took 20 minutes more than twice her usual time to reach home. If the usual time she takes to reach the mall is 40 minutes, find the total number of minutes Shirley spent going and coming back from the mall.

Answer:

b = 3.5

a = 7

Step-by-step explanation:

Hello!

This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.

There are some important Rules:

We can first solve for the leg that is opposite to the 30° angle.

Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:

The length of b is 3.5.

We can multiply 3.5 by 2 to find the length of a.

The length of a is 7.

Answer:

x = y = 6.5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 13[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = y = 6.5[tex]\sqrt{2}[/tex]

The new values for the mean and the standard deviation are 38 and 5 respectively.

The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].

In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.

We let the new population formed be over the variable k.

Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.

Thus, the new mean can be calculated as:

[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]

Thus, the new mean is 38.

Thus, the new standard deviation can be calculated as:

[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]

Thus, the new standard deviation is 5.

Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.

Learn more about the mean and the standard deviation at

https://brainly.com/question/26941429

#SPJ1

Answer:

8

Step-by-step explanation:

F=ma

10=5m

4m=10*4/5

4m=8

So the answer is 8

Answer:

Step-by-step explanation:

The rate of change of stamp collection was $57.5 per year.

Rate is comparison of two related quantities.

Often the second quantity is time (per second, per hour, etc) but it can be anything.

Can be in the style "this per that" or as a single number calculated using division.

Example: Sam makes 3 pancakes every 6 minutes, that is a rate of:

• 3 pancakes per 6 minutes

• 0.5 pancakes per minute

• 30 pancakes per hour

• an hourly rate of 30

By formula the rate of change = Change in cost/ Time taken

=( $980 - $420)/ 8years

= $460/ 8 years

= $57.5 per year

Thus the rate of change of stamp collection was $57.5 per year.

Learn more about rate here :

https://brainly.com/question/12786410

#SPJ4

The purpose of the coordinate graphing system described by Descartes in his book "Discourse on Method" is to use algebraic methods to solve geometric problems. That is option A.

The coordinate graphing system is used on graphical systems to describe the relationship or location between two points on different axes such as X and y axis.

According to Descartes in his book "Discourse on Method" he developed a connection between Algebra and geometry.

Therefore, the main purpose for the coordinate graphing system is to use algebraic methods to solve geometric problems.

Learn more about geometry here:

https://brainly.com/question/19241268

#SPJ1

Answer:

The answer that you are looking for is A.

Have a great day!

Step-by-step explanation:

Please mark me brainliest!

The cost of one gizmo is $18.

The cost of one thingamajigs is $9

3g + 6t = 102 equation 1

5g + 11t = 179  equation 2

Where:

Multiply equation 1 by 5 and equation 2 by 3

15g + 30t = 510 equation 3

15g + 33t = 537 equation 4

Subtract equation 3 from equation 4

3t = 27

t = 27 / 3

t = $9

Substitute for t in equation 1

3g + 6(9) = 102

3g + 54 = 102

3g = 102 - 54

3g = 48

g = 48 / 3

g = $18

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

Using Algebraic equation, Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

Let's review all the information given for solving this question:

Rate per hour of Job A = US$ 6.20

Rate per hour of Job B = US$ 6.50

Earnings received by Kathy during the week = US$ 140.60

Total time worked by Kathy during the week = 22hours

Hours at job A = x

Hours at job B = 22 -x

In order to find how many hours Katy worked at each job: This is the Algebraic equation that we'll use:

6.20x + 6.50 (22 - x) = 140.60

6.20x + 143- 6.50x = 140.60

-0.3x = 140.60 - 143

-0.3x = - 2.4

    x = -(2.4)/-(0.3)

x = 14.3/0.3 = 8 (Dividing by 0.3 at both sides)

Kathy worked 8 hours at job A.

Hours at job B = 22 - x. Put x = 11 we get

Hours at job B = 22 -11

= 11

Hence, using Algebraic equation Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

Learn more about Algebraic equation here

https://brainly.com/question/14781054

#SPJ4

Answer:

  14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

  V = s³ . . . . volume in terms of edge length (s)

  dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

  dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

Answer:

y = -1.5x + 3.5

Step-by-step explanation:

Slope intercept form is y=mx+b.

3x + 2y = 7

2y = -3x + 7

y = -1.5x + 3.5

Answer:

-3/2x+7/2=y

Step-by-step explanation:

The  truncation error for s3  is 0.008

The  truncation error serves as the  difference between a truncated value as well as  the actual value.

This truncated quantity can be a numeral having a fixed number of allowed digits.

Therefore the value of S_3=0.008

Learn more about Truncation error on:

https://brainly.com/question/23653751

#SPJ1

The reflection of BC over I is shown below.

See the attached figure for a better explanation:

1. By the unique line postulate, you can draw only one line segment: BC

2. Using the definition of reflection, reflect BC over l.

3. By the definition of reflection, C is the image of itself and A is the image of B.

4. Since reflections preserve length, AC = BC

Therefore, the reflection of BC over I is shown.

Know more about reflection here:

https://brainly.com/question/1908648

#SPJ4

The question you are looking for is here:

C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.

Given the parameters in the diagrams, we have;

4. ∆ABC ≈ ∆DEF by ASA

5. UW ≈ XZ by CPCTC

6. QR ≈ TR by CPCTC

4. The given parameters are;

<B = <E = 90°

AB = DE Definition of congruency

<A = <D Definition of congruency

Therefore;

5. Given;

XY is perpendicular to WZ

UV is perpendicular to WZ

VW = YZ

<Z = <W

Therefore;

∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate

Which gives;

6. Given;

PQ is perpendicular to QT

ST is perpendicular to QT

PQ ≈ ST

From the diagram, we have;

<SRR ≈ <PRQ by vertical angles theorem;

Therefore;

∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate

Which gives;

Learn more about congruency postulates here:

https://brainly.com/question/26080113

#SPJ1

Answer: K

Step-by-step explanation:

I. Correct. When t=0, h=c, so if you alter the value of c, the h-intercept changes.

II. Correct, the maximum value of [tex]-at^2 +bt[/tex] will stay the same, but you are changing c, which is the amount you are always adding to it, meaning the maximum will change.

III. Correct. If you plug into the quadratic formula setting h=0, it is easy to see changing the value of c will change the solutions.

The correct statement regarding the quadratic function is:

K. I, II and III.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

If a > 0, it has a maximum value, and if a < 0, it has a minimum value.

The extreme value is [tex](x_v,y_v)[/tex], in which:

The solutions are:

In this problem, we have a function h(t). Changing the coefficient c, the h-intercept h(0) changes. Looking at the formulas in the bullet point, the value of [tex]\Delta[/tex] changes, meaning that both the maximum value [tex]y_v[/tex] and the t-intercepts [tex]t_1[/tex] and [tex]t_2[/tex] will change, so option K is correct.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

The correct answer is x = 9

What is a parallelogram in math?

Diagonals of a parallelogram bisect each other.

For quadrilateral LMNO to be a parallelogram, LP must equal PN, and OP must equal PM.

Set OP equal to PM and solve for x.

PM = OP

3x - 9 = 18

Add 9 to both sides.

3x = 27

Divide both sides by 3.

x = 9

Therefore, the value of x = 9

Learn more about parallelogram

brainly.com/question/23857659

#SPJ4

The complete question is -

Determine the value of x that would make quadrilateral LMNO a parallelogram.

3

9

11

18

Answer: x=9

Step-by-step explanation:

Becca needs approximately 5 bottles of engine oil to completely fill her car engine.

Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:

Space = 3.6 - 1.2

Space = 2.4 quarts.

By applying direct proportion, we have:

1 bottle = 0.5 quart.

x bottles = 2.4 quarts.

Cross-multiplying, we have:

0.5x = 2.4

x = 2.4/0.5

x = 4.8 ≈ 5 bottles.

Read more on direct proportion here: brainly.com/question/1266676

#SPJ1

The common difference is (1,0.38).

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term.

x1 = 1 , y1 = 24

x2 = 2, y2 = 24.38

x3 = 3 , y3 = 24.76

x4 = 4 , y4 = 25.14

Thus the common difference equals :-

x2 - x1 = x3 - x2 = x4 - x3 = 1

y2 - y1 = y3 - y2 = y4 - y3 = 0.38.

Thus the common difference is (1,0.38).

Learn more about arithmetic progression (AP) here :

https://brainly.com/question/1069426

#SPJ4

Answer:

(12,1)

Step-by-step explanation:

We know that ordered pairs are in the format of (x,y).

This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:

[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]

Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).

Answer:

(12,1)

Step-by-step explanation:

In the ordered pair, x=12

plug 12 back in the equation

12-3y=9

-3y=-3

3y=3

y=1

The maximum height of the ball that is displayed by the graph is: D. 108 feet.

A graph is a statistical diagram that displays the relation between two variables. One of the variables is plotted on the x-axis (horizontal axis) against the other variable on the y-axis (vertical axis).

The variable on the x-axis (horizontal axis) is the input, while the variable on the y-axis (vertical axis) is the output.

Considering the given graph in the image above, we have the following variables:

On the x-axis (horizontal axis): time which is the input

On the y-axis (vertical axis): height of the ball which is the output.

Thus, the peak of the line represents the maximum height the ball reaches. The maximum height which is the peak is approximately 109 feet.

Therefore, the maximum height is: D. 109 feet.

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ1

Answer:

109 feet

Step-by-step explanation:

just took the lesson

The parent function of g(x) = |x - 7| +6 is f(x) = |x|

The function is given as:

g(x) = |x - 7| +6

The above function is an absolute function, and the parent function is f(x) = |x|

Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|

When f(x) is reflected across the x-axis, we have:

f'(x) = -|x|

When f(x) is reflected across the y-axis, we have:

f'(x) = |x|

When f(x) is stretched horizontally by a factor k

g'(x) = |kx|

When f(x) is stretched vertically by a factor k

g'(x) = k|x|

When f(x) is shifted horizontally by k units

f'(x) = |x ± k|

When f(x) is shifted vertical by k units

f'(x) = |x| ± k

See attachment for the graph of g(x)

Read more about function transformation at:

https://brainly.com/question/

#SPJ1

Answer:

t = 60/n

Step-by-step explanation:

The original equation we know is y = k/n

Since 12 people can assemble the set in 5 hours, when y is 5, n will be 12.

We can now input that value into the equation.

--> 5 = k/12

--> 5(12) = k/12 (12)

--> 60 = k

--> k = 60

The equation to represent the situation can be written as:

t = 60/n

and that is our final answer!

12 people can assemble in 5hours

So

Equation

Or

For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Given that the distance formula =

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

Let say that Angle ABC has the vertices of A (-4, -2),  B (-5,1). C (0,2) and Angle DEF   has the vertices of D (7, -4), E (4,-5), F (3,0)

So lets prove it:

AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Do the same for DF:

DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.

Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Learn more about congruent Angle from

https://brainly.com/question/2938476

#SPJ

Answer:

72

Step-by-step explanation:

This shape is a prism; it's a 3-D shape with 6 sides. Basically, it's a box.

All 6 sides are rectangles.

Surface area means that we'll find the area of all 6 rectangles and add them up.

There's a front and back, left and right, and a top and bottom.

The area of a rectangle is length×width or base×height.



The front and back are identical.

Area = length×width

Area = 6×3 = 18

Since the front and back are the same, two of the rectangles have area = 18.



The left and right are the same:

Area = 3 × 2

Area = 6

Two faces have area = 6.

The top and bottom are the same.

Area = 6 × 2

Area = 12

Again, two faces have area = 12.

To find the total surface area, add up all 6 areas.

A =18+18+6+6+12+12

A = 72

Answer:

BrainlyMidIsBusy Sucks

the value of the given figures in the other units can be found to be:

A meter is 100 cm so:

= 0.006 x 100

= 0.6 cm

A kilometer is 1,000,000 mm so:

= 17,605 /  1,000,000

= 0.017605 km

A kilometer is 10,000 dm:

= 1,001,00 dm / 10,000

= 10.01 km

Find out more on converting units of length at https://brainly.com/question/8426032

#SPJ1

Using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.

According to the questions,

Three schools have a chess tournament and four players come from each school. Each player plays against each other from his/her own school.

Formula for Combinations [tex]nC_{r}[/tex] = [tex]\frac{(n-r)!}{r!}[/tex]

[tex]4C_{2}[/tex] = [tex]\frac{4*3}{1*2}[/tex]

     = 6

They are 6 ways to select two schools. Given those 2 schools they are

[tex]4^{2}[/tex] = 16 ways to pair up players 1 from each school. They are 3 games played by each of those 3 pairs.

The total number of games played against other school.

6×16×3 = 288.

Similarly using combinations we can find the number of games played against schoolmates. To find this 4 combinations of 2 is 6 ways to select a pair from the 4 people at given school. They are four schools and they play one game each.

6×4×1 = 24

Thus using combinations, the number of games played against schoolmates is 24.

In order to find the number of games of chess are played only if we add the total number of games played against other school and the total number of games played against schoolmates.

288+24 = 312

Hence, using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.

Learn more about combinations here

https://brainly.com/question/9283678

#SPJ4

When calculating correlation and regression both sets of data must be Statistical.

According to the statement

we have to find the type of data when we calculate the correlation and regression both sets.

so, The difference between these two statistical measurements is that correlation measures the degree of a relationship between two variables (x and y), whereas regression is how one variable affects another.

And when we calculate both then data sets must be a statistical data. because correlation summarizing direct relationship between two variables  and regression predict or explain numeric response. So, without statistical data this is not possible to calculate correlation and regression both sets.

so, When calculating correlation and regression both sets of data must be Statistical.

Learn more about DATA here https://brainly.com/question/13763238

#SPJ4

Answer:

A

Step-by-step explanation:

The rule for a 180 degree clockwise rotation is (-x, -y). After applying this to the figure, it must be translated one unit right to match the image.

Answer:

m = [tex]\frac{1}{2}[/tex] , m = 5

Step-by-step explanation:

assuming you mean

2m² - 11m + 5 = 0

consider the product of the factors of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × 5 = 10 and sum = - 11

the factors are - 10 and - 1

use these factors to split the m- term

2m² - 10m - m + 5 = 0 ( factor the first/second and third/fourth terms )

2m(m - 5) - 1(m - 5) = 0 ← factor out (m - 5) from each term

(m - 5)(2m - 1) = 0 ← in factored form

equate each factor to zero and solve for m

2m - 1 = 0 ⇒ 2m = 1 ⇒ m = [tex]\frac{1}{2}[/tex]

m - 5 = 0 ⇒ m = 5