Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 8 miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.

Answer:

q=4

p=2

Step-by-step explanation:

3p+2q=14

10p+6q=44

10(3p+2q=14)

3(10p+6q=44)

30p+20q=140-

30p+18q=132

2q=8

2q/2=8/2

q=4

3p+2*4=14

3p+8=14

3p=14-8

3p/3=6/3

p=2

hope this helps

Answer:

[tex]p=2\\q=4[/tex]

Step-by-step explanation:

One is given the following system of equations,

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

The fastest method to solve a system of equations is the method of elimination. This process is manipulating one of the equations, by multiplying or diving it by a value, such that one of the coefficients variables in the equation is the additive inverse of the like term in the other equation. That way, when one adds the equations, one of the variables cancels out. Then one can solve for the other term. Finally, one can back sovle by substituting the value of the solved variable into one of the equations and simplifying to find the value of the other variable.

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

Manipulate the first equation so that the variable (q) cancels

[tex](3p + 4q = 22) *(-3)\\\\10p + 12q = 68[/tex]

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

Add the equations,

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

Simplify,

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

[tex]p=2[/tex]

Backsovle for the variable (p). Substitute the values of (p) into one of the original equations. Then simplify and use inverse operations to solve for the variable (q).

[tex]3p+4q=22[/tex]

Substitute,

[tex]3(2)+4q=22[/tex]

Simplify,

[tex]3(2)+4q=22[/tex]

[tex]6+4q=22[/tex]

Inverse operations,

[tex]6+4q=22[/tex]

[tex]4q=16\\q=4[/tex]

Answer:

m - 11 = 44

Step-by-step explanation:

Breaking the phrase down...

"The difference of Malik's height and 11" - this indicates subtraction.

m - 11

"is 44" - this indicates that the value of the diffrence would be '44'.

'= 44'

The equation should be:

m - 11 = 44

Hope this helps.

Answer:

B is the answer

Step-by-step explanation:

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other

Answer:

y = 2x - 5

Step-by-step explanation:

We can use trial and error to solve this.

4 = x and 3 = y

y = x + 3: 4 + 3 = 7 ≠ 3 (not what we want)

y = 3x + 4: (3 x 4) - 4 = 8 ≠ 3 (not what we want)

y = 2x - 5: (2 x 4) - 5 = 3 (what we want)

y = 2x - 1: (2 x 4) - 1 = 7 ≠ 3 (not what we want)

The answer is y = 2x - 5

The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66  professors.

Given,

A small college has 1200 students and 80 professors.

The college is planning to increase enrollment to 1450 students next year.

We need to find how many new professors should be hired to keep the

ratio of students to professors the same.

If the two ratios are the same then we called it that they are in proportion.

Example:

4/6 = 10/15

2/3 = 2/3

Find the ratio between the students and professors before the increase in enrollment.

= Number of students / Number of professors

= 1200 / 80

Dividing by 8

= 150 / 10

= 15 / 1

This means one professor for 15 students.

Find the number of students after the increase in enrollment.

= 1450

Find the number of new students enrolled.

= 1450 - 1200

= 250

Since the ratio between the students and professor is 15 students for one professor.

For 250 new students, the number of new professors we need is:

= 250 ÷ 15

= 16.66

This means we need around 16.66 new professors.

Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.

Learn more about finding the number of students in a college with students and professors relation is given here:

https://brainly.com/question/4773301

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Answer:

922.868

Step-by-step explanation:

[tex]942.600-19.732=922.868[/tex]

Answer:

[tex]\frac{257357187500}{19683}[/tex]

Step-by-step explanation:

We can convert these mixed fractions to ordinary fractions.

[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]

[tex]3(1/3)=\frac{10}{3}[/tex]

[tex]3(1/2)=\frac{7}{2}[/tex]

[tex]9(3/4)=\frac{39}{4}[/tex]

Then we have:

[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]

[tex]\frac{257357187500}{19683}[/tex]

I hope it helps you!

Answer:

8ft

Step-by-step explanation:

We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,

[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]

Answer:

No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine

Hope This Helps!!!

Answer:

1 : 5000

0.02%

Step-by-step explanation:

A solution = solute + solvent

A 2 Litre solution = (2 * 1000) = 2000 mg

Having, 400 mg of solute ;

Recall ;

1 mg = 0.001 ml

400 mg = (0.001 * 400) = 0.4 ml

The strength of the solution :

Amount of solute / Amount of solution

0.4 / 2000

As a ratio :

0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)

0.4 / 2000

= 0.0002

(0.0002 * 100%) = 0.02% (As a percentage)

Answer:

sorry dko alm hahahahahahahahajshaja

Answer:

d

Step-by-step explanation:

because u did the math for you

Square both sides:

x^2+2sqrt3+3=0

x^2=-2sqrt(3)-3

x=sqrt(2sqrt(3)+3)i

or

x=-sqrt(2sqrt(3)+3)i

Answer:

Bottom left

Step-by-step explanation:

Mark brainliest please

Yes, Lara is correct.

The steps are as follow:

So Lara is correct

Learn more about Congruent triangle here:

https://brainly.com/question/1675117

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Answer:

Hello good evening friend

Answer:

Speed of the river = [tex]\frac{4}{3}[/tex] km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]

                                           = [tex]\frac{6}{4-v}[/tex] hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = [tex]\frac{12}{4+v}[/tex] hours

Since, time taken by the boat in both the cases is same,

[tex]\frac{6}{4-v}= \frac{12}{4+v}[/tex]

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = [tex]\frac{24}{18}[/tex]

v = [tex]\frac{4}{3}[/tex] km per hour

Answer:

Area of a trapezoid= (big base+small base)/2 x height

A=(67+54)/2 x 18

A=60.5 x 18

A=1089  

Integrate:

[tex]\displaystyle\int_{-2}^3((x+6)-x^2)\,\mathrm dx = \int_{-2}^3(6+x-x^2)\,\mathrm dx[/tex]

[tex]=\left(6x+\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{-2}^3[/tex]

[tex]=\left(18+\dfrac92-9\right) - \left(-12+2+\dfrac83\right)[/tex]

[tex]=\boxed{\dfrac{125}6}[/tex]

Answer:

a) The 60th percentile of the diameters is of 25.0177 millimeters.

b) The 67th percentile of the diameters is of 25.0308 millimeters.

c) The diameter of the hole should be of 24.8562 millimeters.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter.

This means that [tex]\mu = 25, \sigma = 0.07[/tex]

(a) Find the 60th percentile of the diameters.

This is X when Z has a p-value of 0.6, so X when Z = 0.253.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.253 = \frac{X - 25}{0.07}[/tex]

[tex]X - 25 = 0.253*0.07[/tex]

[tex]X = 25.0177[/tex]

The 60th percentile of the diameters is of 25.0177 millimeters.

(b) Find the 67th percentile of the diameters.

This is X when Z has a p-value of 0.67, so X when Z = 0.44.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.44 = \frac{X - 25}{0.07}[/tex]

[tex]X - 25 = 0.44*0.07[/tex]

[tex]X = 25.0308[/tex]

The 67th percentile of the diameters is of 25.0308 millimeters.

(c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be.

This is the 2nd percentile, which is X when Z has a p-value of 0.08, so X when Z = -2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.054 = \frac{X - 25}{0.07}[/tex]

[tex]X - 25 = -2.054*0.07[/tex]

[tex]X = 24.8562[/tex]

The diameter of the hole should be of 24.8562 millimeters.

9514 1404 393

Answer:

  (c)  x = 12.5

Step-by-step explanation:

  -0.2(x -4) = -1.7

  -0.2x +0.8 = -1.7 . . . eliminate parentheses using the distributive property

  -0.2x = -2.5 . . . . . . subtract 0.8

 x = 12.5 . . . . . . . . divide by -0.2

Answer:

16. false

17. True

18. True

19. True

20. false

Step-by-step explanation:

16. all terms are expressions of weather - except for cold snow. "snowfall" would be the weather condition. "snow" itself is the accumulated mass of snowflakes on the ground.

17. that is simply true. there is nothing really to explain.

18. the same as 17. that is the definition of weather.

19. yes, that is part of the explanation of the difference between weather and climate.

20. South North is NOT a direction. it kind of contradicts itself. and what is between South and North ? East and West. so, even from that perspective it is not clear.

overall, what kind of math question is that ? that is more for geography, Earth science, or meteorology or something like this.

Hello!

(6x⁵z)³/4x⁴z² =

= 216x¹⁵z³/4x⁴z² =

= 54x¹¹z

Good luck! :)

Answer:

-∞ <y<5

Step-by-step explanation:

The range of the graph is the values that y can take.  The graph can go from negative infinity to 5

-∞ <y<5

Answer:

-37 subtract -53

-53 subtract -37 = -16

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

-37-(-53) = -37 + 53

You can flip it to 53 - 37 which equals 16.

Hope this helps! :)

*Heads up you can also search this up* ^^

Answer:

125x=(62.50+(62.50)×0

⭕ 17.3

#CARRYONLEARNING

[tex]{hope it helps}}[/tex]

Answer:

A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 6.13 centimeters and a standard deviation of 0.06 centimeters.

This means that [tex]\mu = 6.13, \sigma = 0.06[/tex]

Value that separated the top 7%:

The 100 - 7 = 93rd percentile, which is X when Z has a p-value of 0.93, so X when Z = 1.475.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.475 = \frac{X - 6.13}{0.06}[/tex]

[tex]X - 6.13 = 1.475*0.06[/tex]

[tex]X = 6.2185[/tex]

Value that separates the bottom 7%:

The 7th percentile, which is X when Z has a p-value of 0.07, so X when Z = -1.475.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.475 = \frac{X - 6.13}{0.06}[/tex]

[tex]X - 6.13 = -1.475*0.06[/tex]

[tex]X = 6.0415[/tex]

A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.