Solve Applications involving Uniform Motion
Question
Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 2 miles per
hour faster than her walking speed. Find Lorena's walking speed and jogging speed.

Answer:

4 pounds

Step-by-step explanation:

"About" means that you are rounding. Most of the time, when you are rounding food, you generally round to the next whole number. In this case, it is 3.75, so you round to 4.

Jolie bought ~4 pounds of turkey.

The reason you round up, is because you can have less than amount, but generally not more. Also, food's weight can change depending on temperature, heat, how it is at the moment (cooked, non-cooked, mashed, processed, unprocessed, etc.).

~

Answer:

The answer is 15/52. (Please make me as brainliest (: )

The probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have:

Eli has 8 black pens and 5 in his desk drawer. He also has 3 yellow highlighters, 4 green highlighters, and 5 pink highlighters in his pencil case.

Total pens = 8+5 = 13

The probability of choosing the blue pen = 5/13

Total highlighter = 3+4+5 = 12

The probability of choosing yellow highlighter = 3/12 = 1/4

The probability of not choosing yellow highlighter = 1 - (1/4) = 3/4

The probability that he will get a blue pen, and he will not get a yellow highlighter:

= (5/13)(3/4)

= 15/52

Thus, the probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Answer:

[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]

Step-by-step explanation:

[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x+7-7>17-7\\\\5x>10\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{10}{5}\\\\x>2[/tex]

Answer:

option D

Lines a and b are parallel and lines c and d are parallel.

Step-by-step explanation:

Given in the question four lines a , b, c, d.

If two parallel lines (a,b) are cut by a transversal(d), then corresponding angles m<7 and m<15 are congruent.

They are know as corresponding angles.

Hence lines a and b are parallel.

If two parallel lines (c,d) are cut by a transversal(d), then corresponding angles m<13 and m<15 are congruent.

They are know as corresponding angles

Hence lines c and d are parallel

Answer:

Option D.) 28 Pa

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem

[tex]P*V=k[/tex]

step 1

Find the value of k

For [tex]P=84\ Pa,V=51\ L[/tex]

substitute and solve for k

[tex]k=84*51=4,284[/tex]

step 2

If the volume is expanded to 153 L, what will the new pressure be?

we have

The equation is equal to

[tex]P*V=4,284[/tex]

For  [tex]V=153\ L[/tex]

substitute

[tex]P*153=4,284[/tex]

[tex]P=4,284/153[/tex]

[tex]P=28\ Pa[/tex]

Look at the image below :)

In case you didn't know, corresponding angles are equal to each other and are on the same side of the traversal

Therefore the answer is angle CGH

Hope this helped!  

Answer:

Step-by-step explanation:

When two lines are crossed by another line, the angles in matching corners are called corresponding angles.

When the two lines are parallel Corresponding Angles are equal.

∠AFG and ∠CGH are corresponding angles.

The lines AB and CD are parallel, therefore m∠AFG = m∠CGH.

∠CGH and ∠DGH are supplementary angles.

Therefore m∠CGH + m∠DGH = 180°

Substitute m∠DGH = 54°:

m∠CGH + 54° = 180°          subtract 54° from both sides

m∠CGH = 126°

Therefore m∠AFG = 126°.

Answer:

124.7 in²

Step-by-step explanation:

A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.

So, we can calculate the area of one right triangle and multiply by 12.

The formula for the area of one triangle is

A = ½bh

Step 1. Calculate the length of the side a

Per the Pythagorean Theorem,

[tex]\begin{array}{rcl}h^{2} + \left(\dfrac{a}{2}\right)^{2} & = & a^{2} \\\\6^{2} + \dfrac{a^{2}}{4} & = & a^{2}\\\\36 & = &\dfrac{3a^{2}}{4}\\\\144 & = & 3a^{2}\\\\\end{array}\\\\[/tex]

[tex]\begin{array}{rcl}a^{2} & = & \dfrac{144}{3}\\\\a & = & \dfrac{12}{\sqrt{3}}\\\\a & = & \dfrac{12\sqrt{3}}{3}\\\\a & = & 4\sqrt{3}\\\\\end{array}[/tex]

2.Calculate the area of a small triangle

The base of a small triangle is  

b = ½a = ½ × 4√3 = 2√3

The area of one small triangle is

A = ½ bh = ½× 2√3 × 6 = 6√3 in²

3. Calculate the area of the hexagon

A = 12 × 6√3 = 72√3 = 124.7 in²

To find the area of a regular hexagon, use the formula A = (1/2) x Perimeter x Apothem, find the side length with the apothem, calculate the perimeter, and then apply the values to the formula.

To find the area of a regular hexagon with an apothem of 6 inches, you can use the formula for the area of a regular polygon, which is A = (1/2) x Perimeter x Apothem. A regular hexagon can be split into six equilateral triangles, which means each side of the hexagon is equal in length. Since the apothem corresponds to the height of each of these triangle components, you can use the fact that in an equilateral triangle, the ratio of the side to the apothem is √3:1 to find the side length. Once the side length (s) is known, you can find the perimeter (P) of the hexagon by multiplying the side length by six. Then, plug the perimeter and the apothem into the formula to calculate the area.

Step 1: Calculate the side length (s).

Step 2: Calculate the Perimeter (P).

Step 3: Calculate the area (A).

Answer:

Step-by-step explanation:

Use Pythagoras theorem

a = √ 8² + 5² = 9.4

b = √ 17² - 12² = 12.0

Answer: a=9.4 b=12.0

Step-by-step explanation:

Answer: I believe it is A

Step-by-step explanation:

In this table, you have to look at multiple things in the table. So you have to look at where it says Under 40 and that don't read the paper. So according to what I learned with this, you would have to do 36/40 and then get 0.9 which would be in percent form: 90 %.

I would recommend looking at another person's response also, before you submit this question. But hope this helps!

The probability that a person surveyed is under and does not get the news by reading the paper is A; 90%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

So,

P(a person is under 40 and doesn't get the news by reading the paper)

= 36/40

= 0.90

= 90 %  

Hence, option A is correct.

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ2

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the "y" axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

Then, we have the points:

[tex](x1, y1): (- 6, -3)\\(x2, y2) :( 6, -7)[/tex]

Substituting:

[tex]m = \frac {-7 - (- 3)} {6 - (- 6)}\\m = \frac {-7 + 3} {6 + 6}\\m = \frac {-4} {12}\\m = - \frac {1} {3}[/tex]

Thus, the equation is:

[tex]y = - \frac {1} {3} x + b[/tex]

We substitute a point to find the cut point:

[tex]-7 = - \frac {1} {3} (6) + b\\-7 = -2 + b\\b = -7 + 2\\b = -5[/tex]

Finally the equation is:

[tex]y = - \frac {1} {3} x-5[/tex]

ANswer:

[tex]y = - \frac {1} {3} x-5[/tex]

Answer:

$600

Step-by-step explanation 50 dollars every month for 12 months you would do 12 *50 and it gives you 600

Answer:

By the end of 12 months, Esther would have $600.

Step-by-step explanation:

As Esther deposits $50 each month in her account, and the account does not produce interests, it is just an addition of money each time she puts $50 in it. That money won't increase until she puts another $50 at the end of the following month. Therefore, by the end of twelve months, she would have $600 (50 x 12 = 600).

Final answer:

The number of 4-letter passwords using the letters A-Z with repetition allowed is 456,976, while without repetition it's 358,800.

Explanation:

When calculating the number of 4-letter passwords that can be made using the letters A through Z, two scenarios are considered: one where repetition of letters is allowed, and one where it is not allowed.

Scenario a) Repetition of letters is allowed

For each position in the 4-letter password, there are 26 possibilities (since there are 26 letters in the alphabet). Because repetition is permitted, each of the four positions can be filled by any of the 26 letters. Thus, the total number of possible passwords can be found by multiplying the number of choices for each position: 26 x 26 x 26 x 26 = 456,976.

Scenario b) Repetition of letters is not allowed

When repetition of letters is not allowed, the number of choices decreases for each subsequent position in the password. The first position can be filled by any of the 26 letters, the second can be filled by 25 remaining letters (since one letter has been used), the third position by the 24 remaining letters, and the fourth by 23 remaining letters. Thus, the calculation would be: 26 x 25 x 24 x 23 = 358,800.

Answer:

Summation: [tex]\sum_{n=1}^4(3n+12)[/tex]

Explicit formula: [tex]a_n=3n+12[/tex]

Step-by-step explanation:

The given series is 15 + 18 + 21 + 24.

The first term of this series is [tex]a_1=15[/tex].

The common difference is [tex]d=18-15=3[/tex]

The explicit formula is given by: [tex]a_n=a_1+d(n-1)[/tex].

We plug in the known values to get:

[tex]a_n=15+3(n-1)[/tex]

[tex]a_n=15+3n-3[/tex]

The explicit formula is [tex]a_n=3n+12[/tex]

The summation that represents the series is: [tex]\sum_{n=1}^4(3n+12)[/tex]

Answer:

3 12

Step-by-step explanation:

Answer:

The sequence of transformation is reflected across the y-axis and translated 2 units down

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) translate h units to the right

∴ Its image is (x + h , y)

- If point (x , y) translate h units to the left

∴ Its image is (x - h , y)

- If point (x , y) translate k units up

∴ Its image is (x , y + k)

- If point (x , y) translate k units down

∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of figure ABCD are:

  A (-1 , 3) , B (1 , 0) , C (2 , 3) , D (1 , 4)

∵ The vertices of figure A"B"C"D" are:

  A" (1 , 1) , B" (-1 , -2) , C" (-2 , 1) , D" (-1 , 2)

* Lets compare between ABCD and A"B"C"D"

∵ All x-coordinates has opposite signs

  -1 ⇒ 1 , 1 ⇒ -1 , 2 ⇒ -2 , 1 ⇒ -1

∴ The ABCD is reflected across the y-axis

∵ All y-coordinates subtracted by 2

 3 ⇒ 1 , 0 ⇒ -2 , 3 ⇒ 1 , 4 ⇒ 2

∴ The ABCD is translated 2 units down

* The sequence of transformation is reflected across the y-axis

  and translated 2 units down

ANSWER

Brayden should have expanded the parenthesis first.

EXPLANATION

The expression Brayden is trying to simplify is

[tex]4n - {( n - 2)}^{2} [/tex]

To simplify this expression, the first thing to do is to expand the perfect square to obtain:

[tex]4n - {( n}^{2} - 4n + 4)[/tex]

We can now distribute the negative to the terms in the parenthesis.

[tex]4n - { n}^{2} + 4n - 4[/tex]

Answer:

He should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.

Step-by-step explanation:

Given that Brayden is simplifying the expression [tex]4n-(n-3)^2[/tex]. He begins by distributing the negative to the terms inside the parentheses. Which is basically the wrong step for the given problem.

Now we need to find about what should he have done instead.

According to order of operations, we should begin with exponent first.

So that means he should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.

Answer:

[tex]\large\boxed{A)\ y=-2x+15}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(10,\ -5).[/tex]

[tex]\text{Put the coordinates of the point to the equation.}\ x=10,\ y=-5:\\\\-5=-2(10)+b\\\\-5=-20+b\qquad\text{add 20 to both sides}\\\\b=15[/tex]

Answer:

Correct choice is D). 8y + 96​.

Step-by-step explanation:

Given expression is [tex]8\left(y+12\right)[/tex].

Now question says to simplify that expression using distributive property then find the correct matching choice from the given choices:

A). 8y=12

B). 20y

C). 20 - y

D). 8y + 96​

So let's distribute 8 by using distributive property

[tex]a\left(b+c\right)=a\left(b\right)+a\left(c\right)[/tex]

[tex]8\left(y+12\right)=8\left(y\right)+8\left(12\right)[/tex]

[tex]8\left(y+12\right)=8y+96[/tex]

Hence correct choice is D). 8y + 96​.

Answer:

I think it's B.

Step-by-step explanation:

Because the equation is 1 - 0.144/24 should represent the amount of emails to be answered after one day.

Answer:

D. The decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed.

Step-by-step explanation:

An exponential decay function is,

[tex]f(x)=a(1-r)^x[/tex]

Where, a is initial value,

r is rate of change per period,

x is the number of periods,

(1-r) is decay factor that shows the periodic rate of change in the initial value.

Given expression that represents the number of such customers after n days is,

[tex]15,000(1-\frac{0.144}{24})^{24n}[/tex]

By comparing,

15,000 is the initial number of customers who are due to be renewed,

[tex]\frac{0.144}{24}[/tex] is the change per hour in the number of customers,

24n is the total number of hours,

[tex](1-\frac{0.144}{24})[/tex] is the decay factor or decay rate that reveals the hourly rate of change in the number of customers,

Hence, option 'D' is correct.

Answer:

45°

Step-by-step explanation:

Each corner of a square is a right angle. That is 90° which divided by 2 equals 45°

Answer:

Step-by-step explanation:

I believe the correct option would be the 1st option because I just took the test and I got this correct! Hope this helps :)

Answer:

the answer to that is the very first response.

Step-by-step explanation:

you see, 6(4x+5) is equal to saying (6•4x) + (6•5). hope this helped!

It’s the first answer choice, the second answer choice, and the forth one.

Answer:

41.7 % to the nearest tenth.

Step-by-step explanation:

5 out of did not arrive on time.

As a percentage this is 5*100 / 12

= 41.7 % .

Answer:

(a) Option 3

(b) Option 1

(c) Option 2

Step-by-step explanation:

Given information: m∠ABC = m∠CBD

Prove: BC bisects ∠ABD.

Proof:

[tex]m\angle ABC=m\angle CBD[/tex]             (Given)

Definition of congruent: Two angles are congruent if their measures are equal.

[tex]\angle ABC\cong \angle CBD[/tex]         (Definition of bisect)

Definition of bisect: If a line divides an angle in two equal parts, then the line is called angle bisector.

BC bisects ∠ABD                    (Definition of bisect)

Hence proved.

An angle bisector divides the angle into two equal parts. The justification of each step of the flowchart is as follows

From the question, we are given that:

[tex]\angle ABC =\angle CBD[/tex]

This represents the first step of the flowchart.

So, the justification is (3) Given

From the figure, we have that:

[tex]\angle ABC \cong \angle CBD[/tex]

This represents the second step of the flowchart.

[tex]\cong[/tex] mean congruent

So, the justification is (1) Definition of congruent

Lastly:

Line BC bisects [tex]\angle ABC[/tex].

This represents the third step of the flowchart.

So, the justification is (2) Definition of bisect

Because line BC divides [tex]\angle ABC[/tex] into two equal halves.

Read more about bisections at:

https://brainly.com/question/2866798

Answer:

90

Step-by-step explanation:

A right triangle is a triangle that has a right angle.  A right angle is an angle that is 90 degrees.

A 90 degree angle. That’s the answer .

Answer:

a. blue 16x + 5

a. red 4x + 5

b. 12x

c. blue 53

c. red 17

Step-by-step explanation:

a.

The perimeter of a polygon is the sum of the lengths of the sides of the polygon.

Blue triangle:

side lengths: 4x + 2, 5x - 4, 7x + 7

perimeter = 4x + 2 + 5x - 4 + 7x + 7 = 16x + 5

Red triangle:

side lengths: x + 3, x + 7, 2x - 5

perimeter = x + 3 + x + 7 + 2x - 5 = 4x + 5

b.

We subtract the perimeter of the red triangle from the perimeter of the blue triangle.

16x + 5 - (4x + 5) =

= 16x + 5 - 4x - 5

= 12x

c.

Blue triangle:

perimeter = 16x + 5 = 16(3) + 5 = 48 + 5 = 53

Red triangle:

perimeter = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot.  

This line may pass through some of the points, none of the points, or all of the points.

Step-by-step explanation:

1.  Prepare a scatter plot of the data on graph paper.

2.  Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3.  Find two points that you think will be on the "best-fit" line.  

4.  We are choosing the points (9, 260) and (30, 530).  

You may choose different points.  

5.  Calculate the slope of the line through your two points (rounded to three decimal places).

[tex]\frac{530-260}{30-9} =\frac{270}{21} =12.857[/tex]

6.  Write the equation of the line.  

[tex]y-y_{1} m(x-x_{1} )\\y-260=12.857(x-9)\\y=12.857(x-9)+260[/tex]

7.  This equation can now be used to predict information that was not plotted in the scatter plot.  

Question: Predict the total calories based upon 22 grams of fat.

y=12.857(22-9)+260

y=12.857(13)+260

y=427.141

ANS: 427.141 calories

The equation for the line of best fit is written as ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope determined by minimizing the sum of squared errors (SSE). You substitute various x-values to calculate the resulting y-values, then plot these points to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are used to measure the goodness of fit.

To write an equation for the line of best fit, or the least-squares regression line, you would use the formula ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. Generally, 'b' is determined by minimizing the sum of the squared differences between the observed (actual) and predicted values of y, also known as the sum of squared errors (SSE). To do this, you would typically use statistical techniques or software that perform these calculations. Let's consider an example, the equation of the best-fit line is ŷ = -173.51 + 4.83x. Here, -173.51 is the value of 'a', and 4.83 is the value of 'b'.

While working with any specific equation, you can create a table of values by substituting different values for 'x' and calculating the resulting values for 'y'. You then plot these points and draw a line through them to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are also used to measure the goodness of fit of the regression line.

Remember, while your sample data might give you a best-fit line for your sample, testing the significance of the correlation coefficient is needed to confirm the suitability of this line for the overall population.

https://brainly.com/question/10077221

#SPJ11

ANSWER

9.7 units

EXPLANATION

According to the Pythagoras Theorem, the square of the hypotenuse is equal to the sum of the squares of the two shorter legs

[tex] {x}^{2} + {7}^{2} = {12}^{2} [/tex]

This implies that,

[tex] {x}^{2} + 49= 144[/tex]

Group similar terms,

[tex] {x}^{2} = 144 - 49[/tex]

[tex] {x}^{2} = 95[/tex]

[tex]x = \sqrt{95} [/tex]

[tex]x = 9.7 \: units[/tex]

to the nearest tenth.

Answer:

Jim is 5, Dad is 20

Step-by-step explanation:

Since dad is 4 times as old as Jim that means 5 x 4=20 and in ten years Jim will be 15 and Dad will be 30 and 15 x 2 is 30.

Hope this helps!

Answer:

-3x+25

16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

-5(3 - 5) + 2(3) =

-5(-2) + 2(3)

10 + 6 =

16

Not sure what the question is, but I guess it's to prove that

[tex]\cos3A=4\cos^3A-3\cos A[/tex]

Expand the left side as

[tex]\cos3A=\cos(2A+A)=\cos2A\cos A-\sin2A\sin A[/tex]

and use the double angle identities to write

[tex]\cos3A=(\cos^2A-\sin^2A)\cos A-2\sin^2A\cos A[/tex]

[tex]\cos3A=\cos^3A-3\sin^2A\cos A[/tex]

Recall the Pythagorean identity:

[tex]\cos3A=\cos^3A-3(1-\cos^2A)\cos A[/tex]

[tex]\cos3A=\cos^3A-3\cos A+3\cos^3A[/tex]

[tex]\implies\cos3A=4\cos^3A-3\cos A[/tex]

as required.