1. Bennet is getting in shape for football season. He runs 400 yards 3 times a day for 5 days. How many feet did he run in 5 days?

2. The Russel family is keeping track of the milk they drink each week:

- The first week they drank 2 gallons, 1 quart and 1 cup of milk
- the second week they drank 3 gallons of milk

which week did they drink more milk?

Answer:

Math = 97

English = 66

Step-by-step explanation:

Let the score of the Math test be x, and the score of the English text be y

Then we have the two equations

[tex]x+y = 163\\x-y = 31[/tex]

To solve for x and y there are multiple ways, one of the easy ways is just to add the two equations together because that would cancel out the y:

[tex]x + x + y -y = 163 +31\\2x = 194\\x = 97\\[/tex]

Then using the  x, we can find y by doing

[tex]x+y = 163\\97 + y = 163\\(97 + y) - 97 = (163) - 97\\y = 66[/tex]

Therefore, we have a math score of 97, and an English score of 66.

Answer:

180 - 92 - 41 = 47

There are not two similar congruent angle in the triangles.

Hope this helps!

Answer:

96 is the number of original women investors.

Step-by-step explanation:

Let X be the number of young women in the initial group.  They raised 480000, so the average payment per person was (480000/X).  

When 4 pull out, the new average is (480000/(X-4)).  We are told that this new average required the remaining women (X-4) to add another 20000.

The four women therefore had contributed 20000 in total, making their average 20000/4 = 5000 each.  

This would have been the same amount contributed by all X women.  Thus, we can set the average (480000/X) equal to 5000

(480000/X) = 5000

(480000) = 5000X

(480000)/5000 = X

X = 96

The original number of women was 96.

===

Check

(96 Women)(5000/Woman) = 480000  CHECKS

(4 Women pull out)*(5000) = 20000 that needs to be added to stay at 480000.  CHECKS

I'm guessing the equation should read something like

[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]

or possibly with minus signs in place of +.

Multiply both sides by [tex]\frac1{x^2}[/tex] to get

[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]

Now substitute

[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]

to transform the equation to

[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]

which simplifies to

[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]

The ODE is now separable.

[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]

Integrate both sides. On the left, substitute

[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]

[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]

[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]

[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex].

[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]

[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]

[tex]w^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]v[/tex].

[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]y[/tex].

[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]

Solve for [tex]y[/tex].

[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]

[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]

[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]

[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]

Answer: D. 2x + 4x = 150

Step-by-step explanation:

We know that the section of 2x and 4x together equal 150 degrees because they are vertical angles.  The 150 degrees is vertical to the section with 2x and 4x.  So you would use equation D to solve for x.

In order to create the reverse of the 150 angle, when two angles meet, 2x and 4x are combined.

Thus, the angles formed by 2x, 4x, and 150 are vertical. We know that vertical angles are equivalent, .Therefore, the labeled angles are equivalent.

Answer :-

[tex]\bf D. \: 2 {x}^{o} + 4 {x}^{o} = 15 {0}^{o} [/tex]

Answer:

26

Step-by-step explanation:

You want to know the value of x that makes y=1000. You can plug the equation in to your calculator or desmos. Look at the table for when y=1000. X is 26.

To check, plug in 26 for x. 26^2 + 20(26) - 196 = 1000.

Answer: 26 sales

Step-by-step explanation:

The probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].

To find the probability of picking a card with an even number:

Therefore, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].

Know more about probability here:

https://brainly.com/question/24756209

#SPJ4

COMPLETE QUESTION:

The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down. The probability of picking a card with an even number is _____.

The angle m∠MLP in the rhombus is 56 degrees.

A rhombus has all its sides equal to each other.  The diagonals of a rhombus are angle bisectors.

Therefore,

m∠MLP = m∠MLO / 2

m∠MLO = 112°

m∠MLP = 112 / 2

Therefore,

m∠MLP = 56 degrees.

learn more on rhombus here: https://brainly.com/question/18651035

#SPJ1

Answer:

B. 56

Step-by-step explanation:

trust

Answer:

37/70

Step-by-step explanation:

5/8 + 3/10 = (5 × 5)/ (8 × 5) + (3 × 4)/ (10 × 4) =

25/40 + 12/40 = 37/40

By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.

In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:

Since PQ ǁ RS, PT = 16

PT/RP = QT/SQ

16/4 = 20/SQ

Cross-multiplying, we have:

16SQ = 20 × 4

SQ = 80/16

SQ = 5 cm.

Read more on basic proportionality theorem here: https://brainly.com/question/8160153

#SPJ1

Complete Question:

In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?

Answer:

2061.9[tex]mm^{3}[/tex]

Step-by-step explanation:

We can see the original shape of the gold block is a cuboid.

Volume of Cuboid = Length x Width x Height

Volume of Original Gold Block = 27mm x 8mm x 12mm = [tex]2592mm^{3}[/tex]

Next, we can see the shape of the cut-out hole is a cylinder.

Volume of Cylinder = [tex]\pi r^{2} h[/tex]

We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm

Volume of cut-out hole = [tex]\pi (2.5)^{2} (27)\\[/tex] = [tex]168.75\pi mm^{3}[/tex]

Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole

= [tex]2592mm^{3} -168.75\pi mm^{3}[/tex]

= 2061.9[tex]mm^{3}[/tex]

Answer:

Step-by-step explanation:

g(x) = [tan( 4x-1)]2

The expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

The given parameters are:

Initial value, a = 33741  

Rate, r = 2.8%

The cost of tuition each year since 2015 is represented as

B(x) = a * (1 + r)^x

This gives

B(x) = 33741 * (1 + 2.8%)^x

Evaluate

b(x) = 33741 * (1.028)^x

Hence, the expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

Read more about exponential functions at:

https://brainly.com/question/12636638

#SPJ1

Complete question

A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.

Find the expression that completes the function b(x)​

The equation of directrix is D. y=± 432/13.

Definition of hyperbola -

1. The vertex i at (0, 36) and a focus at (0, 39), then you have:

  a=36

a²=1296

2. The equation of directrix is:

y =  a² =c

c  =  39

y =  1296/39

y  =  432/13

Therefore, the answer is the option D, which is: D. y=± 432/13

Learn more about hyperbola

brainly.com/question/27799190

#SPJ4

The complete question is -

A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)

Which are the equations of the directrices ?

A. x= ±12/13

B. y=±12/13

C. x=±432/13

D. y=± 432/13

Answer: Correct

Step-by-step explanation:

Answer:53 mph

Step-by-step explanation:106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.

Answer:

Step-by-step explanation:

Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive?

106 miles is 2 hours = 53 miles in 1 hour (106 : 2)

so your answer is 53 mph

Answer:

$127.50

Step-by-step explanation:

The average profit is found by adding up the profits from both scenarios.

39(4.5) + 1(-48)

= $127.50

Brainliest, please :)

The statement (inequality) which best describes all possible values of m is: -12 < m < 4.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

The table indicates two local extremes or potential turning points at x = 1 and x = -1. Thus, the value of m can't exceed f(-3) = -12.

In conclusion, the statement (inequality) which best describes all possible values of m is: -12 < m < 4.

Read more on inequalities here: brainly.com/question/24372553

#SPJ1

The table that shows a function that is decreasing only over the interval (–1, ∞) is:

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.

A function is decreasing if when we increase the value of x, we decrease the value of y, and vice versa.

Decreasing on the (–1, ∞) means that as x increases on the interval, i.e. x = -100, then x = -10, then x = -2, the value of y decreases. The function that follows this pattern only on this interval is:

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.

More can be learned about decreasing functions at https://brainly.com/question/2649645

#SPJ1

Answer:

A

Step-by-step explanation:

The circumference of the circle and round to the nearest tenth is 25.1 yds

The formula for calculating the circumference of a circle is expressed as:

C = 2πr

Given the following

radius r = 4yds

Substitute

C = 2(3.14)(4)

C = 25.12 yds

Hence the circumference of the circle and round to the nearest tenth is 25.1 yds

Learn more on circumference here: https://brainly.com/question/27447563
#SPJ1

The discriminant of the quadratic equation is -20 and there are two non real solutions.

The discriminant of a quadratic equation uses the equation:

[tex]b^{2} -4ac[/tex]

Where the value of this calculation can tell you what solutions there are, plug known values in:

[tex]x^{2} +6x+14[/tex]

a=1

b=6

c=14

[tex]b^{2} -4ac[/tex]

which is equal to -20 on putting the values of a,b and c in the equation

As -20 < 0, this means that there is not a real solution, resulting in the first option being correct.

For more information about discriminant, visit https://brainly.com/question/2507588

#SPJ1

Taking into account the change of units, the total distance that he biked in his first month of training is 55.8 miles.

In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

In his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month.

So you can apply the following rule of three: if for each workout Landon biked 3.1 miles, in 18 workouts he biked how far?

1 workout ⇒ 3.1 miles

18 workouts ⇒ total distance

So: [tex]total distance=\frac{18 workoutsx3.1 miles}{1 workout}[/tex]

Solving:

total distance= 55.8 miles

In summary, the total distance that he biked in his first month of training is 55.8 miles.

Learn more with this example:

brainly.com/question/25200463

#SPJ1

m<1 =163 degrees

163,17,163,17 (all in degrees)

163,17,163,17  (all in degrees)

I have reproduced and attached a diagram (in figure 1) of the problem.

For ease of understanding, I have attached a second diagram which is labelled.

On line a

17+<CBE=180 (Linear Pair Postulate)

m<2=<CBE=180-17=163 degrees

<ABG=<CBE=163 degrees (Vertically Opposite Angles)

<ABE=<GBC= 17 degrees(Vertically Opposite Angles)

On line b

m<1=<DEB=<ABG=163 degrees (Corresponding Angles)

<BEF=<GBC= 17 degrees (Corresponding Angles)

<HEF=<DEB=163 degrees  (Vertically Opposite Angles)

<DEH=<BEF=17 degrees (Vertically Opposite Angles)

Therefore:

m<1 =163 degrees

Clockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.

Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.

Learn more about Transversal here

https://brainly.com/question/24607467

#SPJ4

Answer:

Θ ≈ 37° , x ≈ 13 cm

Step-by-step explanation:

(a)

using the cosine ratio in the right triangle

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ([tex]\frac{8}{10}[/tex] ) ≈ 37° ( to the nearest whole number )

(b)

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

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{15}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 15[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 7.5[tex]\sqrt{3}[/tex] ≈ 13 cm ( to the nearest whole number )

The probability that emission of both CO and hydrocarbon is in excess is 0.8.

The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.

Let, A be the event in which cars are emitting excess CO:

P(A) = 0.12

Let, B be the event in which cars are emitting excess hydrocarbons:

P(B) = 0.15

The cars which emit both CO and Hydrocarbons in:

P(A∩B) = 0.8

The probability that emission of both CO and hydrocarbon is in excess is 0.8.

Learn more about probability on:

https://brainly.com/question/25870256

#SPJ4

The expected value for the given Five possibilities is $6.

We have,

Payoffs of $2, $4, $6, $8, and $10.

Now,

We know that,

The expected value  [tex]=\Sigma (x*P(x))[/tex]

i.e. The sum of product of possible outcome and each outcome.

Here, x = Each outcome

And

P(x) = Possible outcomes

So,

Probability of x (Px) [tex]=\frac{1}{5}[/tex],

Now,

According to the above mentioned formula,

i.e.

The expected value  [tex]=\Sigma (x*P(x))[/tex]

We get,

[tex]=\Sigma\ (\frac{1}{5} * 2) + (\frac{1}{5} * 4) + (\frac{1}{5} * 6) +(\frac{1}{5} * 8) +(\frac{1}{5} * 10)[/tex]

On solving we get,

[tex]=\Sigma\ (0.4 + 0.8 + 1.2 + 1.6 + 2)[/tex]

i.e.

The expected value = $6

So,

The expected value for given possibilities is $6.

Hence we can say that the expected value for the given Five possibilities is $6.

Learn more about expected value here

https://brainly.com/question/17324165

#SPJ4

Answer: 18

Step-by-step explanation:

Opposite angles of a rhombus are congruent, so

[tex]5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18[/tex]

The function that describes the fund that was raised is 0.05³ - 30x - 12425

The revenue is  R (z) = 0.05x³ + 75

the cost = C(z) = 30x + 12,500.

Please note that the equation for revenue missed a sign in the question so I made use of the plus sign

We would have revenue - cost

Hence ( 0.05x³ + 75) - (30x + 12,500)

We would open the bracket

0.05x³ + 75 -30x -12500

We would take the like term to

0.05³ - 30x -12500 + 75

0.05³ - 30x - 12425

The function that describes the fund that was raised is 0.05³ - 30x - 12425

Read more on cost function here

https://brainly.com/question/2292799

#SPJ1

Answer: F(x)=0.05x^3-30x-12,575

Step-by-step explanation:

Correct on test.

Hello,

2x² - 8x = 0

2x × x - 2x × 4 = 0

2x(x - 4) = 0

2x = 0 or x - 4 = 0

x = 0 or x = 4

Answer:

α = αG − αZL

thos is the equation for the absoulute angle of attack