2-7, please help BRAINLEST

Answer:

4

Step-by-step explanation:

(10-x)/x=3/2

so 2*(10-x)=3x

20-2x=3x

+2x        +2x

20=5x

x=20/5

x=4

verify

(10-4)/4=3/2

6/4=3/2

TRUE

Answer:

x=7

Step-by-step explanation:

took the test

The required solution of the equation is x = 7.

Given that,
Solution of the equation,
x / 3 + x / 6 = 7 / 2 is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The equation is the relationship between variables and represented as y = ax + b   is example of a polynomial equation.

Here,
x  / 3 + x / 6 = 7 / 2
Taking LCM on the left side
[2x + x] /6 = 7 / 2
3x / 6 = 7 / 2
x / 2 = 7 / 2
x = 7

Thus,  the required solution of the equation is x = 7.

Learn more about arithmetic here:

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Answer:

A) P_n = 1.06(P_(n-1)) - 80

B) 887 fishes

Step-by-step explanation:

A) We are told that the lake initially contains 1000 fishes.

Thus, P_o = 1000

Now, the number of fishes increases by 6% each month

Thus, after n months, we have;

P_n = P_(n-1) + 0.06P_(n-1)

P_n = 1.06P_(n-1)

Where P_(n-1) is the population of fish in the previous month.

We are told that 80 fishes are lost each month.

Thus;

P_n = 1.06(P_(n-1)) - 80

B) We want to find out how many fishes we have after 5 months.

Thus;

P_5 = 1.06(P_(5-1)) - 80

P_5 = 1.06(P_4) - 80

We don't know P_4,thus;

P_o = 1000

P_1 = 1.06(1000) - 80 = 980

P_2 = 1.06(980) - 80 = 958.8

P_3 = 1.06(958.8) - 80 = 936.328

P_4 = 1.06(936.328) - 80 = 912.50768

Thus,

P_5 = 1.06(912.50768) - 80 = 887.2581408 ≈ 887

Answer:

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

[tex]\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}[/tex]

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=[tex]\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0[/tex]

[tex]-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0[/tex]

[tex]\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}[/tex]

squaring both sides; we get

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}[/tex]

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}[/tex]

By cross multiplying; we get

[tex]49x^2 = 25(54^2+x^2)[/tex]

[tex]49x^2 = 25 \times 54^2+ 25x^2[/tex]

[tex]49x^2-25x^2 = 25 \times 54^2[/tex]

[tex]24x^2 = 25 \times 54^2[/tex]

[tex]x^2 = \dfrac{25 \times 54^2}{24}[/tex]

[tex]x =\sqrt{ \dfrac{25 \times 54^2}{24}}[/tex]

[tex]x =\dfrac{5 \times 54}{\sqrt{24}}[/tex]

[tex]x =\dfrac{270}{\sqrt{4 \times 6}}[/tex]

[tex]x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}[/tex]

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Answer:

the expression of the information in terms of function f is:

13 = f(40)

The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.

Step-by-step explanation:

suppose G and p are the  two unknowns variables.

where;

G is measured in tons per week and:

p is measured in thousands of people.

∴

The relation between the amount of garbage produced by a city with population p can be expressed as:

G = f(p)

However;

The town of Tola has a population of 40,000 and produces 13 tons of garbage each week.

The objective is to express the information in terms of the function f.

So, if there is a population of 40,000 person in the town,

since p is measured in person per thousand and the value of garbage produced is 13 tons per week.

∴ the expression of the information in terms of function f is:

13 = f(40)

Explain the meaning of the statement f(5) = 2.

The given statement implies that

P which is measured in thousand people = 5

and the value of the garbage produced is 2.

SO , we can say that;

The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.

Answer:

the answer is going to be A. -6x - 14 x+ 6

Solve using PEMDAS for the numerator and denominator.

24-11^4/24+11^4

24-14641/24+14641

-14617/14665

Best of Luck!

Answer:

56 different ways

Step-by-step explanation:

This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.

nCr = n!/(n-r)!r!

According to the question, If the police have 8 ​suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5

8C5 = 8!/(8-5)!5!

8C5 = 8!/(3!)!5!

8C5 = 8*7*6*5!/3*2*5!

8C5 = 8*7*6/3*2

8C5 = 8*7

8C5 = 56 different ways

Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.

Answer:

We conclude that there is no difference between the two classes.

Step-by-step explanation:

We are given that two statistics teachers both believe that each has a smarter class.

A summary of the class sizes, class means, and standard deviations is given below:n1 = 47, x-bar1 = 84.4, s1 = 18n2 = 50, x-bar2 = 82.9, s2 = 17

Let [tex]\mu_1[/tex] = mean age of student cars.

 [tex]\mu_2[/tex] = mean age of faculty cars.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that there is no difference in the two classes}  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that there is a difference in the two classes}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;

                         T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~  [tex]t_n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years

[tex]\bar X_2[/tex]  = sample mean age of faculty cars = 5.3 years  

[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years  

[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years  

[tex]n_1[/tex] = sample of student cars = 110  

[tex]n_2[/tex] = sample of faculty cars = 75  

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(47-1)\times 18^{2}+(50-1)\times 17^{2} }{47+50-2} }[/tex]  = 17.491

So, the test statistics =  [tex]\frac{(84.4-82.9)-(0)}{17.491 \times \sqrt{\frac{1}{47}+\frac{1}{50} } }[/tex]  ~  [tex]t_9_5[/tex]

                                     =  0.422    

The value of t-test statistics is 0.422.

Now, the P-value of the test statistics is given by;

P-value = P([tex]t_9_5[/tex] > 0.422) = From the t table it is clear that the P-value will lie somewhere between 40% and 30%.

Since the P-value of our test statistics is way more than the level of significance of 0.04, so we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.

Therefore, we conclude that there is no difference between the two classes.

Answer:

0.0075

Step-by-step explanation:

According to the given situation, the calculation of the probability that the TPMS will trigger a warning is shown below:-

The tire pressure which is 26% below the target pressure is

[tex]= 26\% \times 28[/tex]

= 7.28

Therefore, Tire pressure monitoring systems warn at below is

= 28 - 7.28

= 20.72

Now we will assume tire pressure be x

So,

[tex]P(X<20.72) = P(\frac{X-\mu}{\sigma}<\frac{20.72-28}{3} )[/tex]

After solving the above equation we will get

= [tex]P(X<20.72) = P(Z<-2.43)[/tex]

we will get

= 0.0075

Answer:

98

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

Answer:

A - the arrow on the right points to the point -2. the arrow on the left moves 7 places to the left to the point -9.

this is what the expression is stating: -2 - 7 = -9

Answer:

D

Step-by-step explanation:

3x - 4 < 8

Add 4:

3x - 4 + 4 < 8 + 4

3x < 12

Divide by 3:

3x / 3 < 12 / 3

x < 4

Answer:

D. x<4

Step-by-step explanation:

3x-4<8

3x<8+4

3x<12

x<4

Hope this helps ;) ❤❤❤

Steps to solve:

-k^2 - (3k - 6n) + 2n; k = -3, n = -5

~Substitute ans simplify

-(-3)^2 - (3(-3) - 6(-5)) + 2(-5)

3^2 - (-9 + 30) - 10

~Use PEMDAS and solve the rest

9 - 21 - 10

-13 - 10

-23

Best of Luck!

Answer:

-2

Step-by-step explanation:

-(-3)∧2-(-9+30)+10= 9+9-30+10= -2

Answer:

9,962

Step-by-step explanation:

3,489+8,617+1,240=13,346

564*6=3,384

13,346-3,384=9,962

Answer:

D

Step-by-step explanation:

Given

f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x

     = 3(x² - 8x) + 10

Using the method of completing the square

add/ subtract ( half the coefficient of the x- term )² to x² - 8x

f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10

      = 3(x - 4)² - 48 + 10

      = 3(x - 4)² - 38 ← in vertex form → D

Answer:

d

Step-by-step explanation:

Answer: This is what i can do . i hope it helps:)

The angle between the longitude of the Galapagos Islands and that of Nauru is 90.30°+166.56°=256.86°.

We find the sum since these places have different longitude directions, but this is the major arc, and the minor arc will be 360°−256.86°=103.14°.

Angle between Galapagos Islands and 180°E/W = 180° - 90.30° = 89.70°

Angel between Nauru island and 180°E/W = 180° - 166.56° = 13.44°

Total angle between Galapagos Islands and Nauru = 89.70 ° + 13.44° = 103.14°.

Step-by-step explanation:

[tex]let \:\alpha \:be\:our\:teetah \\l = \frac{r \pi}{180 \°} \times \alpha \\\\= \frac{6400\pi}{180 \°} \times 103.14\\\\= 11520.848\\\\= 11521 km[/tex]

Answer:

0.16%

Step-by-step explanation:

From the statement of the question;

Number of Laryngeal cancer due to smoking = 160

Population of smokers = 100,000

Hence the percentage of smokers liable to have Laryngeal cancer = 160/100000 ×100/1

=0.16%

Hence 0.16% of smokers are liable to Laryngeal cancer

Answer: [tex]x^4-x^3-16x^2+16x[/tex]

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = [tex](x-(-4)), (x-0), (x-1) and (x-4)[/tex]   [By factor theorem ]

[tex]=(x+4), (x-0), (x-1) and (x-4)[/tex]

Multiplying these factors to get polynomial in standard form.

[tex](x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x[/tex]

Hence, B is the correct option.

Answer:

A).Amount = $218250

B). Amount = $88700

Step-by-step explanation:

A) .$5000 in an account at age 23, and withdraw it 42 years

Number of years t= 42 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 42

A= p(1+r/n)^(nt)

A= 5000(1+0.09/42)^(42*42)

A= 5000(1+0.002143)^(1764)

A= 5000(1.002143)^1764

A= 5000(43.65)

A= 218250

Amount = $218250

B).waits 10 years before making the deposit, so that it stays in the account for only 32 years

Number of years t= 32 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 32

A= p(1+r/n)^(nt)

A= 5000(1+0.09/32)^(32*32)

A= A= 5000(1+0.0028125)^(1024)

A= 5000(1.0028125)^1024

A= 5000(17.74)

A= 88700

Amount = $88700

Answer:

4times tall

Step-by-step explanation:

Volume of the boxes = Base area × height

Volume of the first box V1 = A1h1

Given the base of the first box to be 5cm, the base area:

A1 = 5cm×5cm = 25cm²

Volume of the first box V1 = 25h1... 1

Similarly, volume of the second box

V2 = A2h2

Given the base of the second box to be 10cm, the base area:

A2= 10cm×10cm = 100cm²

Volume of the second box

V2 = 100h2... 2

If the two boxes have the same volume, then V1 = V2

25h1 = 100h2

divide both sides by 25

25h1/25 = 100h2/25

h1 = 4h2

Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.

Answer:

4times tall

Step-by-step explanation:

Volume of the boxes = Base area × height

Volume of the first box V1 = A1h1

Given the base of the first box to be 5cm, the base area:

A1 = 5cm×5cm = 25cm²

Volume of the first box V1 = 25h1... 1

Similarly, volume of the second box

V2 = A2h2

Given the base of the second box to be 10cm, the base area:

A2= 10cm×10cm = 100cm²

Volume of the second box

V2 = 100h2... 2

If the two boxes have the same volume, then V1 = V2

25h1 = 100h2

divide both sides by 25

25h1/25 = 100h2/25

h1 = 4h2

Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.

Answer:

The first car used 30 gallons and the second one 20 gallons of gas during the trip.

Step-by-step explanation:

35x+40y = 1850     equation 1

x+y = 50        equation 2

x=car 1

y=car 2

Solve it

Answer:

The stock market increased 75 point: 75 or +75

Answer:

The stock market increased by 75 so your answer according to my understanding is +75 or 75.

Step-by-step explanation:

Hope it will help you :)

Answer:

Hi

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Answer:

B and C

Step-by-step explanation:

1/5 prefer apple juice

T = prefer orange juice

9/20 prefer apple or oranger juice

First, we can subtract 1/5 from 9/20 to get 1/4 (simplified)

Equation = 9/20  - 4/20 = 5/20 = 1/4

Plug it in:

A. 9/20 + 1/4 =1/5 (Incorrect)

B. 1/5 + 1/4 = 9/20 (Correct

C. 1/4 + 1/5 = 9/20 (Correct)

D. 1/4 - 1/5 = 9/20 (Incorrect)

Answer:

1/5 + t = 9/20

t + 1/5 = 9/20

Step-by-step explanation:

1/5 are apple + unknown for orange = apple + orange

1/5  + unknown = 9/20

Let t = unknown

1/5 + t = 9/20

order doesn't matter on the left side since we are adding

t+1/5 = 9/20

Answer:

[tex]x\geq -30[/tex]

Step-by-step explanation:

Work to isolate x on one side of the inequality:

[tex]3-\frac{x}{2} \leq 18\\3-18\leq \frac{x}{2} \\-15\leq \frac{x}{2}\\-30 \leq x[/tex]

Therefore the answer is all x values larger than or equal to -30

[tex]x\geq -30[/tex]

Answer:

66

Step-by-step explanation:

In statistics, the formula for RANGE is given as the difference between the Highest and the Lowest value.

In the above values we are given data consisting of the 7 games that Roger bowled.

155, 165, 138, 172, 127, 193 , 142.

Step 1

We arrange from the least to the highest.

127, 138, 142, 155, 165, 172, 193

Step 2

Lowest value = 127

Highest value = 193

Step 3

Range = 193 - 127

= 66

Therefore, the range of Roger's scores is 66

Answer:32

Step-by-step explanation:

768/24=32

The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.

A rent-to-own contract is a contract where the buyer pays for something as rent to the owner until the set period in the contract.

In the question, we are informed that a person decides to buy a new computer. He has two options to buy. Either he can pay the full cost of the computer = $768, or he can choose a rent-to-own option, in which he will pay $37 per week for 24 weeks.

We are asked to find the extra cost that the person will pay if he chooses the rent-to-own option, after completing all his payments.

The total amount that the person pays in the rent-to-own option = $37*24

or, the total amount that the person pays in the rent-to-own option = $888.

The actual cost of the computer = $768.

∴ Extra payment = Total Payment - Actual cost

or, Extra payment = $888 - $768 = $120.

∴ The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.

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Answer: Need more info. We need to know how many minutes over the 300 minutes were used in order to calculate the correct monthly fee.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \sf{ {x}^{2} - 4x - 21}[/tex]

Here, we have to find the two numbers that subtracts to 4 and multiplies to 21

⇒[tex] \sf{ {x}^{2} - (7 - 3)x - 21}[/tex]

⇒[tex] \sf{ {x}^{2} - 7x + 3x - 21}[/tex]

Factor out X from the expression

⇒[tex] \sf{ x(x - 7) + 3x - 21}[/tex]

Factor out 3 from the expression

⇒[tex] \sf{x(x - 7) + 3(x - 7)}[/tex]

Factor out x-7 from the expression

⇒[tex] \sf{(x - 7)(x + 3)}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{\boxed{\bold{(x - 7)(x + 3)}}}[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 4x - 21 \\ {x}^{2} - 7x + 3x - 21 \\ x(x - 7) + 3(x - 7) \\ (x - 7)(x + 3)[/tex]