Adam drove his car 132 km and used 11 liters of fuel. How many kilometers will he cover with 14 liters of fuel?

Answer:

3

Step-by-step explanation:

To have full outfits he can only make three

Answer:

she can make 12: A

Step-by-step explanation

add up the numbers of pants, shoes , shirts you will get 12

Answer:

Concentration of solution A = 23%

and concentration of solution B = 2%

Step-by-step explanation:

Lets get started

lets say that we concentration of solution A be x% and concentration of second solution be y%

we also know that first mixture is obtained by mixing them in ratio of 2:7

so linear equation representing this situation can be written as:

2(x%)+7(y%)= 9(6.66%)    

changing percentage to decimal we get,

.02x+.07y=9(.0666)

.02x+.07y = 0.6          (equation 1 )

similarly , second mixture is obtained by mixing them in ratio of 7:3

so linear equation can be written as:

7(x%)+3(y%) = 10(16.7%)

.07x +.03y = 1.67     (equation 2)

solving equations 1 and 2  we get

x =  23 and y = 2

so concentration of solution A = 23%

and concentration of solution B = 2%

That's the final answer

Hope it was helpful !!

Answer:

[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]

Step-by-step explanation:

To write sin6x-sinx  as a product , we use formula

[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]

We have 6x in the place of 'a'  and x in the place of b

Replace it in the formula

[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]

[tex]sin(6x) - sin(x)= 2cos(\frac{6x+x}{2}) * sin(\frac{6x-x}{2})[/tex]

[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]

Answer:

--3 ±sqrt((-3)^2 -4(4)(-9))

-------------------------------

2(4)

Step-by-step explanation:

4x^2-5=3x+4

We need to get this in standard form to answer the question

Subtract 3x from each side

4x^2-3x-5=3x-3x+4

4x^2-3x-5=+4

Subtract 4 from each side

4x^2-3x-9 =0

a = 4

b = -3

c = -9

-b ±sqrt(b^2 -4ac)

---------------------------

2a

--3 ±sqrt((-3)^2 -4(4)(-9))

-------------------------------

2(4)

Answer:

--3 ±sqrt((-3)^2 -4(4)(-9))

Step-by-step explanation:

Answer:

 x = - 50

Step-by-step explanation:

-2/5 x - 2 = 18

-2x - 10 = 90

-2x = 100

 x = - 50

Answer:

A) -50

Step-by-step explanation:

The given equation -2/5 x - 2 = 18

Here we have to find the value of x.

Step 1: Isolate the constant.

Add 2 on both sides, we get

-2/5x - 2 + 2 = 18 +2

-2/5x = 20

Step 2: Multiply both sides by the reciprocal of -2/5

The reciprocal of -2/5 is -5/2

x = 20 * -5/2

x = -100/2

x = -50

Answer: x = -50

Answer:

yes

Step-by-step explanation:

3x × 2x can be broken down as

3 × x × 2 × x = 3 × 2 × x × x = 6 × x² = 6x²

Answer:

About 4

Step-by-step explanation:

Answer: B: 3 Days

Step-by-step explanation:

Let x be the number of days when Jack and Emily have the same amount of money.

Then, the total amount saved by Jack =4x+55

The total amount saved by Emily  = 13x+28

According to the question,

13x + 28 = 4x + 55

13x - 4x = 55 - 28

9x = 27

x = 3

Brainiest PLZ

Answer:

Your answer would be C because a trinomial consists of 3 parts!

Step-by-step explanation:

Answer:

[tex]2x^3-7y^3 +14[/tex]

Step-by-step explanation:

Trinomial is a expression that has 3 terms. Now we check the options that has 3 terms.Terms are separated by operators like +,- , x or \

5xy has only one term

[tex]2x-7[/tex] has two terms 2x and -7. So it is not a trinomial

[tex]2x^3-7y^3 +14[/tex] has three terms 2x^3, -7y^3 and +14. So it is a trinomial.

[tex]2y^2+7y[/tex] has two terms, So it is not a trinomial

Answer: 7 years

Step-by-step explanation:

Answer:

The rate of change is 1 mile per hour per month

Step-by-step explanation:

We are given

initial speed = 3 mph

final speed =6 mph

total number of months =3

now, we can use rate of change formula

we know that

rate of change = ( final speed - initial speed)/(total number of months)

now, we can plug values

and we get

Rate of change is

[tex]=\frac{6-3}{3}[/tex] mph per month

=1 mph per month

Jason's rate of change in biking speed is 1 mile per hour per month.

Jason is training for a marathon bike ride. His average speed increases from 3 miles per hour to 6 miles per hour in 3 months. To find the rate of change in the miles per hour that Jason bikes, we use the formula:

Rate of Change = (Final Speed - Initial Speed) / Time Period

The final speed is 6 miles per hour, the initial speed is 3 miles per hour, and the time period is 3 months. Therefore:

Rate of Change = (6 - 3) mph / 3 months

Rate of Change = 3 mph / 3 months

Rate of Change = 1 mph per month

Therefore, Jason's rate of change in biking speed is 1 mile per hour per month.

Answer: Choice D) Opposite sides of a parallelogram are congruent

Likely a typo has been made because A, B, C, and D aren't shown. I think your teacher meant to say PQ = RS and QR = PS

A parallelogram has properties that the opposite sides are parallel, and it can be proven that the opposite sides are congruent as well.

Answer:

D is the right answer hope this helps!!!!!!!!

Answer:

(a). [tex]h=\frac{3V}{B}[/tex]

(b). 18 cm.

Step-by-step explanation:

We have been given the volume of pyramid is given by the formula [tex]V=\frac{1}{3}Bh[/tex], where B is the area of the base and h is the height.

(a). Let us solve the given formula for h as:

[tex]V=\frac{1}{3}Bh[/tex]  

Multiply both sides by [tex]3[/tex]:

[tex]3\cdotV=3\cdot\frac{1}{3}Bh[/tex]  

[tex]3V=Bh[/tex]

Divide both sides by B:

[tex]\frac{3V}{B}=\frac{Bh}{B}[/tex]

[tex]\frac{3V}{B}=h[/tex]

Switch sides:

[tex]h=\frac{3V}{B}[/tex]

(b). To find the height for the given pyramid, we will substitute the given values as:

[tex]h=\frac{3(216\text{ cm}^3)}{36\text{ cm}^2}[/tex]

[tex]h=\frac{648\text{ cm}}{36}[/tex]

[tex]h=18\text{ cm}[/tex]

Therefore, the height of the pyramid is 18 cm.

Answer:

Chicken=97/221=0.44

Cow=47/221=0.21

Human=77/221=0.35

Step-by-step explanation:

[tex]a,b-the\ numbers\\\\a-b=34\to a=34+b\\\\a^2+b^2\to minimum\\\\\text{substitute:}\\\\(34+b)^2+b^2\to minimum\\\\f(b)=(34+b)^2+b^2\qquad\text{use}\ (x+y)^2=x^2+2xy+y^2\\\\f(b)=34^2+(2)(34)(b)+b^2+b^2\\\\f(b)=1156+68b+2b^2\to f(b)=2b^2+68b+1156\\\\y=ax^2+bx+c\\\\if\ a>0\ then\ a\ parabola\ op en\ up\\if\ a<0\ then\ a\ parabola\ op en\ down\\\\if\ a>0\ then\ a\ parabola\ has\ a\ minimum\ at\ a\ vertex\\if\ a<0\ then\ a\ parabola\ has\ a\ maximum\ at\ a\ vertex[/tex]

[tex]\text{We have}\ a=2>0.\ \text{Therefore the parabola has the minimum at the vertex.}\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a};\ k=f(h)\\\\\text{We have}\ a=2\ \text{and}\ b=68.\ \text{Substitute:}\\\\h=\dfrac{-68}{2(2)}=\dfrac{-68}{4}=-17\\\\k=f(-17)=2(-17)^2+68(-17)+1156=2(289)-1156+1156=578[/tex]

[tex]\text{Therefore}\ b=-17\ \text{and}\ a=34+b\to a=34+(-17)=17.\\\\Answer:\ a^2+b^2=17^2+(-17)^2=289+289=578[/tex]

The minimum sum of their squares is [tex]\(578\)[/tex].The sum of their squares is a minimum when each number is half the difference between them.The sum of their squares is[tex]\(2 \times \left(\frac{34}{2}\right)^2\)[/tex].

Let the two numbers be [tex]\(x\)[/tex] and [tex]\(y\)[/tex], where [tex]\(x > y\)[/tex]. Given that the difference between the numbers is 34, we can express [tex]\(y\)[/tex] in terms of [tex]\(x\) as \(y = x - 34\)[/tex].

We want to find the minimum value of the sum of their squares, which is [tex]\(x^2 + y^2\)[/tex]. Substituting [tex]\(y\)[/tex] with [tex]\(x - 34\)[/tex], we get:

[tex]\[S = x^2 + (x - 34)^2\] \[S = x^2 + x^2 - 68x + 1156\] \[S = 2x^2 - 68x + 1156\][/tex]

To find the minimum value of [tex]\(S\)[/tex], we take the derivative of [tex]\(S\)[/tex] with respect to [tex]\(x\)[/tex] and set it equal to zero:

[tex]\[\frac{dS}{dx} = 4x - 68\][/tex]

Setting the derivative equal to zero gives us:

[tex]\[4x - 68 = 0\] \[x = \frac{68}{4}\] \[x = 17\][/tex]

Since [tex]\(y = x - 34\)[/tex], we substitute [tex]\(x = 17\)[/tex] to find [tex]\(y\)[/tex]:

[tex]\[y = 17 - 34\] \[y = -17\][/tex]

So the two numbers are 17 and -17. The sum of their squares is:

[tex]\[17^2 + (-17)^2 = 289 + 289\] \[= 578\][/tex]

However, since we are looking for the minimum sum of squares, we can also use the property that the sum of squares is minimum when the numbers are equidistant from their mean. The mean of the two numbers is [tex]\(\frac{34}{2}\)[/tex], so the numbers would be [tex]\(\frac{34}{2}\)[/tex] and [tex]\(-\frac{34}{2}\)[/tex]. The sum of their squares is:

[tex]\[2 \times \left(\frac{34}{2}\right)^2 = 2 \times 289\] \[= 578\][/tex]

Answer:

4/5 pi ,  14pi/5, etc

-16pi/5, -26pi/5, etc

Step-by-step explanation:

To find coterminal angles you add or subtract 2pi from the angle

Rewrite 2pi with a common denominator of 5

2pi * 5/5 = 10pi/5

-6/5 *pi + 10pi/5  = 4/5 pi

4/5pi + 10pi/5 = 14pi/5

etc

you can keep adding 2pi

or you can subtract 2pi

-6pi/5 - 10pi/5 = -16pi/5

-16pi/5 - 10pi/5 = -26pi/5

etc

you can keep subtracting 2pi

Answer:

The graph of y = 6x increases at a faster rate than the graph of y = 2x.

Step-by-step explanation:

y=6x and y=2x are proportional relationships of linear functions. It has the form y=mx where m is the rate of change or increase. 6>2 so y=6x will increase faster than 2.

We know the last two statements are not possible because a translation of a graph must be done through addition or subtraction.

1.  -3(2x-3) = 25-8x is given.

2.  -6x+9 = 25-8x  simplified the left hand side

3. 2x+9 = 25 eft hand side of the equation and simplified

4. 2x = 16 equation are brought to the right side of the equation and simplified

5.  the whole equation is divided by 2 in order to get the value of 'x' i.e. x = 8.

We are provided with an equation and are required to give reasons on how we got the final answer.

(1.) The equation is -3(2x-3) = 25-8x is given.

(2.) In this step, we have simplified the left hand side of the equation by opening the bracket i.e. -6x+9 = 25-8x

(3.) Here, the terms containing 'x' are brought to the left hand side of the equation and simplified i.e. 2x+9 = 25

(4.) Now, the constant terms of the equation are brought to the right side of the equation and simplified i.e. 2x = 16.

(5.) Lastly, the whole equation is divided by 2 in order to get the value of 'x' i.e. x = 8.

Answer:

392 ft

Step-by-step explanation:

Hello, Let me help you with this

to find the real length and width you can use a rule of three

Step 1

length=8 in

Let

if

2.5 in ⇔ 35 ft

8 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{8\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=8\ in\\x*2.5\ in=8\ in *35\ feet\\x=\frac{8\ in *35\ feet}{2.5\ in}\\ x=112\ ft[/tex]  

Step 2

width=6 in

Let

if

2.5 in ⇔ 35 ft

6 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{6\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=6\ in\\x*2.5\ in=6\ in *35\ feet\\x=\frac{6\ in *35\ feet}{2.5\ in}\\ x=84\ ft[/tex]  

Step 2

find the perimeter using

Perimeter = 2*length +2* width

replacing

Perimeter= 2*112 ft +2* 84 ft

Perimeter=224 ft +168 ft

Perimeter=392 ft

Have a nice day

Answer:

CN Tower = 550 m and church tower = 160 m

Step-by-step explanation:

The first equation x + y = 710 is correct

but the second one is

x - y = 390    

Note x = height of the CN tower and y = height of the church.

x + y = 710

x - y = 390

If we add the 2  above equations we eliminate y so

2x = 1100

x = 550 m

and y = 710 - 550 =  160 m

The percent markup is 62.5%

The work is provided in the image attached.

Answer:

y < -3

Step-by-step explanation:

Isolate the variable, y. Treat the > sign like an equal sign, what you do to one side, you do to the other.

8 - 5y > 23

Do the opposite of PEMDAS (Parenthesis, Exponent (& roots), Multiplication, Division, Addition, Subtraction).

First, subtract 8 from both sides

8 (-8) - 5y > 23 (-8)

-5y > 23 - 8

-5y > 15

Isolate the variable. Divide -5 from both sides. Note that when dividing a negative number from both sides, you must flip the sign.

(-5y)/-5 > (15)/-5

y < 15/-5

y < -3

y < -3 is your answer

~

Final answer:

Mark solved 90% of the problems correctly on his math quiz, calculated by dividing 18 (correct answers) by 20 (total questions) and then multiplying by 100%.

Explanation:

To calculate the percent of problems Mark solved correctly on his math quiz, we use the formula for percentages, which is: (Number of items of interest ÷ Total number of items) × 100%

In this case, Mark solved 18 out of 20 problems correctly. So, we set up the calculation as follows:

(18 ÷ 20) × 100% = 0.9 × 100% = 90%

Therefore, Mark got 90% of the problems correct on his quiz.

Answer:

r ≈ 0.98

Step-by-step explanation:

The correlation coefficient is easily calculated by almost any scientific or graphing calculator, or by a spreadsheet. It is mainly a matter of data entry and invoking the appropriate function. Here, the correlation coefficient is computed as about 0.97716, or 0.98 when rounded to the nearest hundredth.

Answer:

The correlation coefficient is 0.0002273427

Step-by-step explanation:

Given the data of heart rate and we have to find the correlation coefficient which can be calculated as

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2} ] [n\sum y^{2}-(\sum y)^{2} ] }} }[/tex]

       = [tex]=\frac{12(7949)-68(1341)}{\sqrt{[12(430)-4624][12(152729)-1798281]} }[/tex]

       = [tex]\frac{4200}{(536)(34467)}[/tex]

       = 0.0002273427

f(t) = 2283·(30069/2283)^(t/40) . . . . . t = years after 1960

In simplest terms, the exponential function can be written from the initial value, the ratio of given values, and the time period over which that ratio was effective. The form is ...

... f(t) = (initial value) · (ratio of values)^(t/(time period))

This works for both increasing and decreasing exponentials.

_____

Using e as a base

It can be converted to an exponential with "e" as the base by taking logarithms.

ln(f(t)) = ln(2283) + (t/40)·ln(30069/2283) = ln(2283) + 0.06445011·t

Taking antilogs, this is ...

... f(t) = 2283·e^(0.06445011·t)

_____

Comment on accuracy

The final number (30,069) when including cents (30,069.00) has 7 significant digits. In order to get the function f(t) to reproduce that number to 7 significant digits, the multiplier of t in the exponential function must be accurate to 7 significant digits. (Fairly commonly, you will see it rounded to 2 or 3 significant digits. It cannot give 30069 even to 5 digits in that case.)

Answer:

$307.5.

Step-by-step explanation:

We have been given that Elena's aunt bought her a $150 savings bond when she was born.When Elena is 20 years old, the bond will have earned 105% in interest.  

To find bond's value after 20 years we will add 105% of 150 to 150.

[tex]\text{Bond's value after 20 years}=150+(\frac{105}{100}\times 150)[/tex]

[tex]\text{Bond's value after 20 years}=150+(1.05\times 150)[/tex]

[tex]\text{Bond's value after 20 years}=150+157.5[/tex]

[tex]\text{Bond's value after 20 years}=307.5[/tex]

Therefore, the bond will be worth $307.5, when Elena will be 20 years old.

Using the formula for future value, the $150 savings bond bought for Elena that earned 105% interest by the time she's 20 years old will be worth $307.50.

The question involves calculating the future value of a savings bond when it will have earned a specific percentage in interest. In Elena's case, her aunt bought her a $150 savings bond, and this bond will have earned 105% in interest by the time Elena is 20 years old.

Calculating the future value of the bond can be done using the formula:

Future Value (FV) = Present Value (PV) × (1 + Interest Rate (i))ⁿ

For Elena's savings bond:

Inserting these values into the formula, we get:

FV = $150 × (1 + 1.05)

Therefore, the future value of the bond when Elena is 20 years old will be:

FV = $150 × 2.05

FV = $307.50

So, Elena's bond will be worth $307.50 when she is 20 years of age.

Answer:

Row 2

Step-by-step explanation:

To find the mean, we add all the numbers and divide by the number of numbers

Row 1:  

(6+5+3+0+4)/5 = 18/5 = 3.6

Row 2:  

(4+5+3+5+6)/5 = 23/5 = 4.6

Row 3:  

(7+1+4+5+3)/5 = 20/5 = 4.0

Row 4:  

(4+2+5+6+3)/5 = 20/5 = 4.0

The greatest mean , or the largest mean is 4.6  or Row 2

Answer:

The answer is B) Row 2

Step-by-step explanation:

If you need any help with this question please ask me! :)

Final answer:

The cheerleaders can be lined up in 3,628,800 ways.

Explanation:

To solve this problem, we need to consider the arrangement of the cheerleaders in two rows of five people each. Since each cheerleader in the back row must be taller than the one immediately in front, we can start by arranging the taller cheerleaders in the back row.

There are 10 different heights, so we have 10 choices for the tallest cheerleader in the back row. After choosing the tallest cheerleader in the back row, there are 9 choices for the second tallest cheerleader, 8 choices for the third tallest cheerleader, and so on, until there are 6 choices for the shortest cheerleader in the back row.

Once we have arranged the back row, there are 5 cheerleaders left to be arranged in the front row. Since the heights of the cheerleaders in the front row are smaller than the heights of the cheerleaders in the back row, we can simply arrange them in any order. There are 5! (5 factorial) ways to arrange the cheerleaders in the front row.

Therefore, the total number of ways to line up the cheerleaders is: 10 x 9 x 8 x 7 x 6 x 5! = 10! = 3,628,800 ways.

Answers: 1h, 2e, 3d, 4a, 5f, 6b, 7c, 8g

 Statement                                             Reason

1. JKLM is a rectangle                         1. Given

2. ∠K and ∠L are right angles            2. Definition of rectangle

3. ΔJKM and ΔMLJ are right angles   3. Definition of right triangles

4. [tex]\overline{JM}[/tex] ≅ [tex]\overline{JM}[/tex]                                         4. Reflexive Property

5. [tex]\overline{JK}[/tex]  ≅ [tex]\overline{LM}[/tex]                                        5. Definition of rectangle

6. ΔJKM ≅ Δ MLJ                                 6. HL congruency theorem

Answer: (C) 1

Step-by-step explanation:

The question is asking which y-value are not represented in the graph.  IN other words, they are asking for which values are not included in the range.

You can do this by graphing the equations:

y = x + 2    for x ≥ 0     has a y-intercept of +2 with y-values increasing

y = x - 2     for x < 0     has a y-intercept of -2 with y-values decreasing

Therefore, there are no y-values between +2 and -2 (including -2). The only option provided between these values is 1, which is option C.

Step-by-step explanation:

The given function is an increasing piecewise function with a jump at x=0 from

f(0-) = -2 to f(0)=+2.

Hence values of f(x) in the interval (-2,+2] cannot be achieved, since

for all x<0, f(x)<-2, and

for all x>=0, f(x)>= +2.

See attached graph for visual explanation.

To find the inverse of the function f(x) = 2x - 5/3x + 4, swap x and y and solve for y. The inverse function is f-1(x) = (x - 4) / (2 - 5/3).

To find the inverse of a function, we need to swap the variables x and y and solve for y. Let's start:

f(x) = 2x - 5/3x + 4

Replace f(x) with y:

y = 2x - 5/3x + 4

To find the inverse, solve for x:

x = (y - 4) / (2 - 5/3)

Now, swap x and y to find the inverse function:

y = (x - 4) / (2 - 5/3)

Therefore, the inverse of f(x) = 2x - 5/3x + 4 is f-1(x) = (x - 4) / (2 - 5/3).

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