Joe and Janna leave home at the same time, traveling in opposite directions. Joe
drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will
they be 510 miles apart?
O a) 7 hours
Ob) 6 hours
Oc) 4 hours
Od) 5 hours​

Answer:

Step-by-step explanation:

x + 3y = 1

-3x - 3y = -15

-2x = -14

x = 7

7 + 3y = 1

3y = -6

y = -2

(7, -2)

Answer:

x =7 , y= -2

Step-by-step explanation:

x + 3y = 1

-3x - 3y = -15

Add the equations together to eliminate y

x + 3y = 1

-3x - 3y = -15

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

-2x = -14

Divide by -2

-2x/-2 = -14/-2

x = 7

Now we can find y

x+3y = 1

7 + 3y = 1

Subtract 7 from each side

7+3y-7 = 1-7

3y = -6

Divide by 3

3y/3 = -6/3

y = -2

Answer:

The first coal mine worker is 650 feet below, so they're -650 ft.

The second coal mine worker is 7 feet above, so they're +7 ft.

| -650 | = 650 ft

| 7 | = 7 ft

650 > 7, so the first worker is farther from the surface.

Answer:

5 dimes and 18 nickels

Step-by-step explanation:

5D + 18 N =

5 x 10 + 18 x 5 =

5 x.10 + 18 x 0.05=

.50 + .90=

$1.40

Answer:

23/26 = 0.8846=0.88 [ to the nearest hundredth]

Step-by-step explanation:

4 sec a-5 = 0; seca=1/cos a

Therefore;

4 sec a-5 = 0=>4/cos a - 5 = 0

Multiplying through by cos a, we have;

4-5cosa= 0=>4= 5cosa

4/5 = cosa

a = cos^{-1}0.8

=36.88

Alternatively Cos a =4/5

Sina = 3/5; {note Cos a = adjacent / hypothesis and from Pythagoras rule we can derive the value of the opposite side which is;

5^2 -4^2 = 25-16 = 9; hence the opposite side is √9 = 3;sin a = opposite/ hypothenus = 3/5}

Substituting the value of Cosa and Sina into the expression below;

2 cos a + 5 sin a ÷ 2 sin a + 5 cos a​

We have ;

[2×4/5 + 5× 3/5 ]/ [2 × 3/5 + 5× 4/5]

[8/5 + 15/5 ]/ [6/5 + 20/5]

[23/5]/[26/5] = 23/5 × 5/26 = 23/26

=

Answer:

A, B, D and E.

Step-by-step explanation:

From the diagram

[tex]ED \cong DB\\FA \cong AC[/tex]

The correct options are A, B, D and E.

Answer:

1, 2, 4, 5

Step-by-step explanation:

Line segment E B  is bisected by Line segment D F .

A is the midpoint of Line segment F C .

Line segment E B  is a segment bisector.

FA = One-halfFC.

Answer:

[tex]A=1500-1450e^{-\dfrac{t}{250}}[/tex]

Step-by-step explanation:

The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.

Volume = 500 gallons

Initial Amount of Salt, A(0)=50 pounds

Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min

[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of brine)

[tex]=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}[/tex]

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

Concentration c(t) of the salt in the tank at time t

Concentration, [tex]C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}[/tex]

[tex]R_{out}[/tex]=(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}[/tex]

Now, the rate of change of the amount of salt in the tank

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]

[tex]\dfrac{dA}{dt}=6-\dfrac{A}{250}[/tex]

We solve the resulting differential equation by separation of variables.  

[tex]\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}[/tex]

Taking the integral of both sides

[tex]\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}[/tex]

Recall that when t=0, A(t)=50 (our initial condition)

[tex]50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}[/tex]

Answer:

Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.

Step-by-step explanation:

We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.

A random sample of 39 steel bolts is selected.

Let [tex]\bar X[/tex] = sample mean diameter

The z score probability distribution for sample mean is given by;

                            Z  =  [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean diameter = 141 millimetres

           [tex]\sigma[/tex] = standard deviation = 7 millimetres

           n = sample of steel bolts = 39

Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P([tex]\bar X[/tex] > 141.4 millimetres)

      P([tex]\bar X[/tex] > 141.4) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex] > [tex]\frac{141.4-141}{\frac{7}{\sqrt{39} } } }[/tex] ) = P(Z > 0.36) = 1 - P(Z [tex]\leq[/tex] 0.36)

                                                            = 1 - 0.6406 = 0.3594

The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.

Answer:

Hello There Again. The correct answer is D.

Explanation: Because it shows that you need to subtract 2.75 - 3.50 which that will be 75. So the correct answer will be D.

Hope It Helps! :)

Sixth graders paid a total of $508.50 for all their meals on Monday.

Answer:

Step-by-step explanation:

a) The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of group 1

x2 = sample mean of group 2

s1 = sample standard deviation for data 1

s2 = sample standard deviation for data 2

For a 90% confidence interval, the z score is 1.645

From the information given,

x1 = 24.5

s1 = 4.3

n1 = 200

x2 = 16.3

s2 = 3.1

n2 = 200

x1 - x2 = 24.5 - 16.3 = 8.2

z√(s1²/n1 + s2²/n2) = 1.645√(4.3²/200 + 3.1²/200) = 1.645√0.1405

z = 0.62

Therefore, the 90% confidence interval is 8.2 ± 0.62

Interpretation:

B.The researchers are 90% confident that the difference of the means is in the interval.

b) B.Since the 90% confidence interval does not contain​ zero, the results suggest that priming does have an effect on scores.

Answer:

8(3)=24

3(8) =24

Step-by-step explanation:

Step-by-step explanation:

i want brainliest please

Answer:

8 sets of 3 positive tiles.

Which of the following multiplication expressions can be modeled by the tiles shown? Check all that apply.

yes 8(3) = 24

no 6(4) = 24

no (3)(12) = 36

no 24(3) = 72

yes 3(8) = 24

no 2(12) = 24

yah welcome

Answer:

The estimated standard error is SM=1.1547 . The t statistic is 1.4722.

Step-by-step explanation:

We have to esimate the standard error and test statistic for a sample.

The sample has a size n=27.

The sample mean is M=17.7.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√36=6.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{27}}=1.1547[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.7-16}{1.1547}=\dfrac{1.7}{1.1547}=1.4722[/tex]

Answer:

6/8

Step-by-step explanation:

6/8

Answer:

Step-by-step explanation:

Given SinP + SinQ = 7/5...1 and

∠P + ∠Q = 90°... 2

From compound angle; SinP +SinQ = [tex]2sin(\frac{P+Q}{2} )cos(\frac{P-Q}{2} )[/tex]... 3

Substituting equation 2 into 3 we will have;

SinP +SinQ = [tex]2sin(\frac{90}{2} )cos(\frac{P-Q}{2} )[/tex] = 7/5

[tex]2sin45^{0} cos\frac{P-Q}{2}=7/5[/tex]

since P = 90-Q from equation 1, then;

[tex]2sin45^{0} cos\frac{90-Q-Q}{2}=7/5\\2sin45^{0} cos\frac{90-2Q}{2}=7/5\\2(\frac{1}{\sqrt{2} } ) cos\frac{90-2Q}{2}=7/5\\cos\frac{90-2Q}{2} = 7/5* \frac{\sqrt{2} }{2} \\cos\frac{90-2Q}{2} = \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = cos^{-1} \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = 8.15\\90-2Q = 16.30\\2Q = 90-16.3\\2Q = 73.7\\Q = 36.85^{0} \\\\P = 90-36.85\\P = 53.15^{0}[/tex]

To get sin2P; Accoding to the trig identity;

Sin2P = 2SinPCosP

Sin2P = 2Sin53.15cos53.15

sin2P = 0.9598

sin2P ≈ 1

Answer:

−4(x^2+9)

Step-by-step explanation:

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Answer:

C. 0.1515

Step-by-step explanation:

The main objective here is to find the P-value for the test of [tex]H_0[/tex]

Given that ;

the mean value = 2.2

the standard deviation = 1.4

number of recorded accident per week = 52

The null  hypothesis is : [tex]H_o: \mu =2[/tex]

The alternative hypothesis is : [tex]H_A = \mu < 2[/tex]

The Z- value can be calculated as:

[tex]z = \dfrac{x- \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]z = \dfrac{2- 2.2}{\dfrac{1.4 }{\sqrt{52}}}[/tex]

[tex]z = \dfrac{- 0.2}{\dfrac{1.4 }{7.211}}[/tex]

z = -1.03

From the normal distribution table for probability;

P(z< -1.03 ) = 0.1515

Answer:

The first book can be chosen from ANY of the 6 books,

the second book can be chosen from the OTHER 5 books and continuing in this way, we get:

6 * 5 * 4 * 3 * 2 * 1 = 720 ways

Step-by-step explanation:

Answer:

a) 240 ways

b) 12 ways

c) 108 ways

d) 132 ways

e) i) 0.55

ii) 0.4125

Step-by-step explanation:

Given the components:

Receiver, compound disk player, speakers, turntable.

Then a purcahser is offered a choice of manufacturer for each component:

Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers

Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers

Speakers: Boston, Infinity, Polk => 3 offers

Turntable: Onkyo, Sony, Teac, Technics => 4 offers

a) The number of ways one component of each type can be selected =

[tex] \left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]

[tex] = 5 * 4 * 3 * 4 = 240 ways [/tex]

b) If both the receiver and compact disk are to be sony.

In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.

Thus, the number of ways components can be selected if both receiver and player are to be Sony is:

[tex] \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]

[tex] = 1 * 1 * 3 * 4 = 12 ways [/tex]

c) If none is to be Sony.

Let's exclude Sony from each component.

Receiver has 1 sony = 5 - 1 = 4

CD player has 1 Sony = 4 - 1 = 3

Speakers had 0 sony = 3 - 0 = 3

Turntable has 1 sony = 4 - 1 = 3

Therefore, the number of ways can be selected if none is to be sony:

[tex] \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) [/tex]

[tex] = 4 * 3 * 3 * 3 = 108 ways [/tex]

d) If at least one sony is to be included.

Number of ways can a selection be made if at least one Sony component is to be included =

Total possible selections - possible selections without Sony

= 240 - 108

= 132 ways

e) If someone flips switches on the selection in a completely random fashion.

i) Probability of selecting at least one Sony component=

Possible selections with at least one sony / Total number of possible selections

[tex] \frac{132}{240} = 0.55 [/tex]

ii) Probability of selecting exactly one sony component =

Possible selections with exactly one sony / Total number of possible selections.

[tex] \frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240} [/tex]

[tex] = \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240} [/tex]

[tex] \frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125 [/tex]

Answer:

      x = 32

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5/8*x+4-(3/8*x+12)=0

Step by step solution :

Step  1  :

           3

Simplify   —

           8

Equation at the end of step  1  :

   5         3

 ((—•x)+4)-((—•x)+12)  = 0

   8         8

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  8  as the denominator :

         12     12 • 8

   12 =  ——  =  ——————

         1        8  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x + 12 • 8     3x + 96

———————————  =  ———————

     8             8  

Equation at the end of step  2  :

   5               (3x + 96)

 ((— • x) +  4) -  —————————  = 0

   8                   8    

Step  3  :

           5

Simplify   —

           8

Equation at the end of step  3  :

   5               (3x + 96)

 ((— • x) +  4) -  —————————  = 0

   8                   8    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  8  as the denominator :

        4     4 • 8

   4 =  —  =  —————

        1       8  

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

5x + 4 • 8     5x + 32

——————————  =  ———————

    8             8  

Equation at the end of step  4  :

 (5x + 32)    (3x + 96)

 ————————— -  —————————  = 0

     8            8    

Step  5  :

Step  6  :

Pulling out like terms :

6.1     Pull out like factors :

  3x + 96  =   3 • (x + 32)

Adding fractions which have a common denominator :

6.2       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(5x+32) - (3 • (x+32))     2x - 64

——————————————————————  =  ———————

          8                   8  

Step  7  :

Pulling out like terms :

7.1     Pull out like factors :

  2x - 64  =   2 • (x - 32)

Equation at the end of step  7  :

 2 • (x - 32)

 ————————————  = 0

      8      

Step  8  :

When a fraction equals zero :

8.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 2•(x-32)

 ———————— • 8 = 0 • 8

    8    

Now, on the left hand side, the  8  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2  •  (x-32)  = 0

Equations which are never true :

8.2      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

8.3      Solve  :    x-32 = 0

Add  32  to both sides of the equation :

                     x = 32

One solution was found :

                  x = 32

Step-by-step explanation:

Answer:

  4.1 cm

Step-by-step explanation:

The segment marked x bisects the chord, so the triangle shown has legs x and 7.8, and hypotenuse 8.8.

The Pythagorean theorem can be used to find x:

  8.8² = x² +7.8²

  x² = 8.8² -7.8² = 77.44 -60.84 = 16.60

  x = √16.6

  x ≈ 4.1 . . . cm

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean score of in-state applicants

x2 = sample mean score of out -of-state applicants

s1 = sample standard deviation for in-state applicants

s2 = sample standard deviation for out-of-state applicants

n1 = number of in-state applicants

n1 = number of out-of-state applicants

For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (17 - 1) + (10 - 1) = 25

z = 1.708

x1 - x2 = 1046 - 1118 = - 72

Margin of error = z√(s1²/n1 + s2²/n2) = 1.708√(37²/17 + 50²/10) = 31.052239

Confidence interval is - 72 ± 31.052239

Answer:

  see below

Step-by-step explanation:

There are a few relevant relations involved:

AB is a diameter, so arcs AB are 180°.

a) BC is the supplement to arc AC: 180° -140° = 40°

b) BG is the supplement to AG: 180° -64° -38° = 78°

c) ∠1 has the measure of BC: 40°

d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°

e) ∠3 is half the measure of arc AE: 64°/2 = 32°

f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°

g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°

h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°

i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°

j) ∠8 is the measure of arc AC: 140°

k) ∠9 is the supplement to arc AC: 180° -140° = 40°

l) ∠10 is the complement of angle 7: 90° -31° = 59°

Answer:

2 cups

Step-by-step explanation:

to find the extra cup of coffee

[tex]3\frac{1}{2}-1\frac{1}{2}=\frac{7}{2}-\frac{3}{2}=\frac{4}{2}=2 cups[/tex]

Answer:

40*40 =1600

Step-by-step explanation:

Answer:

43.96

Step-by-step explanation:

you do 6 divided by 2 to find the radius

then u find the volume

v= [tex]\pi[/tex]r^2h/3

v=3.14(3 to the power of 2)7/3

hope this helps

correct me if this is wrong

Answer:

It is about 1.41421356. (square root of 2)

Step-by-step explanation:

You can use a calculator to figure it out! Just enter the value (-45) and press the sec button! Hope this helps :)

sec (-45) = 1/ cos (-45) .

and cos (-45) = (sqrt 2)/2 is the answer to the question

What is the value of sec(-45°)? there was no photo given or answer choices... sorry guys. thats why i asked on here lol

Answer:

D. Logical Fallacies

Step-by-step explanation:

Let's break this down:

fallacy: A false or mistaken idea.

By this definition, we can see that "false" would go with the word "faulty". A logical Fallacy is is a false or mistaken idea that's intended to sound logical. I hope this helps you!!

Answer:

b. less than evens

Step-by-step explanation:

the probability that the next roll is 6 is

[tex] \frac{1}{6} [/tex]

B. less than evens should be the answer

By the ratio test, the series converges if

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(x-2)^{n+1}}{(n+1)!2^{n+1}}}{\frac{(x-2)^n}{n!2^n}}\right|=|x-2|\lim_{n\to\infty}\frac{n!2^n}{(n+1)!2^{n+1}}[/tex]

[tex]=\displaystyle\frac{|x-2|}2\lim_{n\to\infty}\frac1{n+1}[/tex]

is less than 1. The limit itself is 0 < 1, so the series converges everywhere, i.e. on the entire real line [tex](-\infty,\infty)[/tex].

Answer:

H(24) = 70,000

Step-by-step explanation:

If the growth equation is

H(35020) = 12

Then we are told to find H(70,000)

35020 = 12

70,000 = x

35020x = 12 × 70,000

x = 12 × 70,000/35020

= 23.99

≈ 24.

H(24) = 70,000

Answer:

-15

Step-by-step explanation:

g(x) = -4x + 5, find g(5)

Let x = 5

g(5) = -4*5 +5

      = -20 +5

     = -15