This morning, Ravi's car had 15.04 gallons of fuel. Now, 4.9 gallons are left. How much fuel did Ravi use?
gallons

Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ

The given logarithmic equation is :

log ₁₀y + log ₁₀x = 2

Now we know that: 1 = log₁₀10

∴log ₁₀y + log ₁₀x = 2× log₁₀10

or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)

or,  log ₁₀y + log ₁₀x = log₁₀100

we know that log p+ log q = log pq

or, log ₁₀xy =  log₁₀100

Now we take antilog on both sides of the equation:

or, xy = 100

or, y = 100 / x

or, y = 100x⁻¹

Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.

A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.

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Answer: 15/14

Step-by-step explanation:

Use the slope formula: y2-y1/x2-x1

Apply that:

-15-0/-11-3 = -15/-14 = 15/14

Answer: Let the number = x

5x+10 = 120

Or, 5x = 120 - 10

Or, 5x = 110

Or, x = 110/5

Or, x = 2

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{2}x[/tex]

Step-by-step explanation:

I don’t know exact what is being asked but I got this

slope intercept form is y=mx+b

m=slope

b=y intercept

[tex]y=\frac{1}{2}x+0[/tex]

[tex]y=\frac{1}{2}x[/tex]

Hopes this helps please mark brainliest

Perimeter of the park = 10km

Part of the wall's construction completed =

[tex] \frac{4}{5}th \: of \: perimeter [/tex]

=

[tex] \frac{4}{5} \times 10[/tex]

(cancel 5 and 10)

=

[tex] \frac{4}{1} \times 2[/tex]

= 8km

•.• Part of the wall left (to be constructed) = 10km - 8km = 2km

HOPE THIS HELPS YOU

The correct answer is Men continue to earn more than women.

The average yearly wages of men and women are different from one another. Men make more money than women do.

What is the annual salary?

Annual earnings may also be referred to as annual income or yearly income. It displays a person's earnings over a specific time period.

The yearly earning of a person or a corporation is calculated by dividing the monthly earnings by the number of months in a year.

Men continue to earn more than women under the situation mentioned above, hence their wages are higher. The red line is always above the blue line.

As a result, choice A is accurate which is men continue to earn more than women.

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Answer: C. women's earnings have increased in relation to men's earnings

Step-by-step explanation:

The chart shows that

As per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:

a. Amount of almonds sold on Friday as per given condition is equal to

13 kg.

b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.

As given in the question,

Amount of almonds sold by Tariq from Monday to Thursday are as follow:

Monday  = 2 kg

Tuesday = 4kg

Wednesday = 3 kg

Thursday = 4kg

a. Condition given:

Amount of almonds sold on Friday is equal to total sold quantity of previous four days that is Monday to Thursday

= (2 + 4 + 3 + 4) kg

= 13kg

b. Amount of almonds Tariq sell from Monday to Thursday is

= (2 + 4 + 3 + 4) kg

= 13kg

Therefore, as per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:

a. Amount of almonds sold on Friday as per given condition is equal to

13 kg.

b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.

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The value of E[X Y] is 44.25.

According to the question,

E[X] = ∑ x × P(X=x)

=0×P(x=0) + 5×P(x=1) + 10×P(x=2)

= 0+5×(0.49)+10×(0.31)

= 5.55

E[Y] = ∑ y × P(Y=y)

=0×P(x=0) + 5×P(x=5) + 10×P(x=10) + 15×P(x=15)

= 0+5×(0.49)+10×(0.31)+15×(0.21)

= 8.55

Now,

E [X²] =  ∑ x² × P(X=x)

= 0²×P(x=0) + 5²×P(x=1) + 10²×P(x=2)

= 0 + 25×0.49 + 100×0.31

= 43.25

E[Y²] = ∑ y² × P(Y=y)

= 0²×P(x=0) + 5²×P(x=5) + 10²×P(x=10) + 15²×P(x=15)

= 0 + 25×0.49 + 100×0.31 + 225×0.21

= 92.25

Therefore , V[X] = E[X²] - {E[X]} = 43.25 - 30.8025 =12.4475

V[Y] = E[Y²] - {E[Y]}² = 92.25 - 73.1025 = 19.1475

E[X Y] = ∑xy P(X=x, Y=y)

= {0×0×P(X=0,Y=0)} + {0×5×P(X=0,Y=5)} + {0×10×P(X=0,Y=0)} + {0×15×P(X=0, Y =15)} + {5×0×P(X=5,Y=0)} + {5×10×P(x=5,Y=10)} +  {5×5×P(x=5,Y=5)} +  {5×15×P(x=5,Y=15)} + {10×0×P(x=10,Y=0)} + {10×5×P(x=10,Y=5)} + {10×10×P(x=10,Y=10)} + {10×15×P(x=10,Y=15)}

= 0+0+0+0+0 + {50×0.20} +{25×0.15} + {75×0.10} + 0 + {50×0.15} + {100×0.14} + {150×0.01}

= 10 + 3.75 + 7.5 + 7.5 + 14 + 1.5

Hence the final answer is = 41.25

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For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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The amount in the account after the daily deposit for 5 days is $5

The given parameters i the question are represented as follows

Initial balance = -$30

Daily deposit = $7

Number of days of deposit = 5

The equation that represents the amount in the account is represented as

Amount = Initial balance + Daily deposit * Number of days

Substitute the known values in the above equation So, we have the following equation

Amount = -30 + 7 * 5

Evaluate

Amount = 5

Hence, the amount is $5

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The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

Given that

sinx = [tex]\frac{3}{5}[/tex]

sinx = [tex]\frac{opp}{hyp}[/tex]

Using the Pythagoras' theorem

[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]

adj = 4.

Now we have to find out tanx and cosx

[tex]tanx = \frac{opp}{adj}[/tex]

[tex]= \frac{3}{4}[/tex]

[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]

Now we have to find out the given equation (tanx+2cox)

[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]

Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

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Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

In 3 - box system:

There are two tensions and two strings, let T1 and T2 be the tensions.

Let mass of boxes be m1,m2,m3

total mass m = m1+m2+m3

Acceleration a = force / m

a = f/m1+m2+m3

T1 = m2 * f/m

T2 = m3 * f/m.

Therefore Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

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Answer:

$455.75

Step-by-step explanation:

End amount = 200.00(1 + 0.04)^(21) = $455.75

Answer: I believe this is True!

Step-by-step explanation:

I know what associative property and that seems like a example.

And if its false then answer should be false.

Try True, if not True then False!

The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .

In the question ,

it is given that ,

the bottom of the box is =  square ,

let the side of the square bottom be = "s" ,

so , the base area [tex]=[/tex] s²

let the height of the box [tex]=[/tex] h ,

Volume of the box = height × (base area)

So , the Volume of the box [tex]=[/tex] s²h

given that the volume of the box is 252 m³ , that means

s²h = 252

h = 252/s²

given that the Cost of bottom = $40 per m²

and the Cost of sides = $30 per m²

So , the total cost = 40s² + 30×(4sh)

substituting the value of h= 252/s² , we get

C = 40s² + 120s×252/s²

C = 40s² + 30240/s

to minimize the cost we differentiate with respect to s , and equating it  to 0 ,

we get ,

80s - 30240/s² = 0

s³ = 30240/80

s³ = 378

s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it  to 0 ,

we get ,

d²C/ds² = 80 + (30240*2)/s³

at s=7.23 , d²C/ds² > 0

So , the minimum is at s = 7.23 ,

we have h = 252/(7.23)²

h = 4.82 .

Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .  

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The Central Angle of the sector in radians is  0.3184 π  .

In the question ,

it is given that ,

the radius of the sector = 24 m

the area of the sector = 288 m²

we know that the Area of the sector of the circle is given by the formula

Area = πr²(θ/360)

Substituting the values , we get

288 = (3.14)*(24)²*(θ/360)

θ = (288*360)/((3.14)*(24)²)

θ = 1,03,680/1808.64

θ = 57.32°

converting the angle to radian ,

we get

θ = 57.32° ×  π/180 radian

= 0.3184 π

Therefore  , The Central Angle of the sector in radians is  0.3184 π  .

The given question is incomplete , the complete question is

A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .

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Step-by-step explanation:

d = number of dimes

n = number of nickels

one dime = $0.10

one nickel = $0.05

d = 3n

0.1×d + 0.05×n = 3.85

0.1×3n + 0.05×n = 3.85

0.3×n + 0.05×n = 3.85

0.35×n = 3.85

n = 3.85 / 0.35 = 11

d = 3n = 3×11 = 33

she has 33 dimes (and 11 nickels).

Answer:

Step-by-step explanation:

The goal for the fundraiser is to earn $50.00 each day

90%  of 50= $45

106%  of 50=$53

86%  of 50=$43

after the three days they earned:

45+53+43=$141

Members earn $141 from ticket sales on all three days.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

The members of a school club are selling tickets for a fundraiser.

The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day.

1).

On the first day, the members earned 90% of their daily goal.

90% of 50

= 90 x 50 / 100

= 4500/100

= $45

2).

On the second day, the members earned 6% more than their daily goal.

That means,

50 + 6% of 50

= 50 + 6 x 50 / 100

= $53

3).

On the third day, the members earned 14% less than their daily goal.

That means,

50 - 14% of 50

= 50 - 14 x 50 / 100

= $43

The total earning = $45 + $53 + $43

= $141

Therefore, $141 is the total earning.

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The length of the equator is 40192 km.

The radius of the earth is approximately 6400 km.  The equator is the circle around the earth dividing it into the northern and southern hemisphere.

Let's find the length of the equator as follows:

The length of the equator is the circumference.

Therefore,

L = 2πr

where

L = 2 × 3.14 × 6400

L = 6.28 × 6400

L = 40192 km

Therefore, the equator which is the circle around the earth has a length of 40192 km.

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The accuracy of the USA Today claim about the access the internet read the international news online by adults is 0.089.

We have provided in question that,

adults who access the internet read the international news online is 44% i.e 0.44

this provides the interval ( .344, .522)

Using the estimation formula (E) or margin error

= Z-value √(p (1-p)/n

where, p --> Sample proportion of sucess

1-p = q ----> sample proportion of failure

n ---> sample size

Now, a random sample of 120 adults is considered for survay.

i.e., n= 120 and 52 adults out of 130 are responded "yes" for reading international news online.

so, p = 52/120 = 0.433 and 1-p = q = 1-0.433

= 0.567

Confidence interval to test the newspaper's claim is 95% . Thus, the Z-value for 95% confidence interval is 1.96..

putting the value in above formula we get,

E = 1.96 √0.433×0.567/120 = 1.96√0.2455/120

= 1.96√0.00204 = 1.96× 0.0452 = 0.0889 ~ 0.089

So, accuracy is 0.089 to support the claim of newspaper.

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From the equations , the company A is selling the phone for less money

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equations for Company A :

The smart phone price per month = $ 35.50

The smart phone price for 1 year = $ 35.50 x 12

                                                      = $ 426

The price for 1/12 th of a phone = $ 35.50

The price for the entire phone = ( Price for 1/12 th of a phone ) x 12

                                                   = $ 35.50 x 12

                                                   = $ 426

Now , The equations for Company B :

The smart phone price per month = $ 18.00

The smart phone price for 2 year = $ 18.00 x 24

                                                        = $ 432

The price for 1/24 th of a phone = $ 18.00

The price for the entire phone = ( Price for 1/24 th of a phone ) x 24

                                                   = $ 432

Therefore , we can clearly see that price of the smart phone offered by Company A is lesser than price of the phone offered by Company B

And , $ 426 < $ 432

Hence , from the equations , the company A is selling the phone for less money

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At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off

which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days

If the answer you asked is this:

48s+12p-18  the correct answer

A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

In the given question we have to find the total bill of the customer.

A retaurant cutomer left ​$1. 65 a a tip.

The tax was 6% and the tip was ​15% of the cost including tax.

The tip was 15%(0.15) of the cost including tax.

Thus 0.15*X= 1.65

Divide both sides of the equation by 0.15.

x = 11

Now 6%(0.06) tax on meal at 11 is

11* 0.06 = 0.66

So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal

The total bill cost = $1.65 + $11+0.66

The total bill cost = 13.31

A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

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Answer:

Step-by-step explanation:

13n=78        /13

n= 6

The algebraic expression to represent the given situation is 24/x where x is the number of students.

According to the question,

We have the following information:

Some students equally share 2 baskets of apples. Each basket has 12 apples.

Now, this situation can be presented to find the number of apples each student had.

Let's take the number to students to be x.

(x is the variable in this case.)

Number of apples one student had = total number of apples/number of students

Number of apples one student had = (2*12)/x

Number of apples one student had = 24/x

Hence, the algebraic expression to represent the given situation is 24/x where x is the number of students.

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Answer:

The smaller number must be 12

Step-by-step explanation:

Ignoring the second sentence we can make an expression from the question :

x is larger number

y is the smaller number

x = 2y + 12

Now we substitute 36 for x and solve for y :

36 = 2y + 12

Subtract 12 from both sides :

24 = 2y

Divide both sides by 2 :

12 = y

y = 12

The smaller number must be 12.

But let's check :

12 × 2 = 24

24 + 12 = 36

✅

Hope this helped and have a good day

Answer:

Exact answer 32[tex]\pi[/tex]

Estimate 100.48

Step-by-step explanation:

Circuference = [tex]\pi[/tex](diameter)  Diameter is the distance across the cirlce going throught the middle

c = 32[tex]\pi[/tex]

Estimate

c = 3.14(32)

100.48

The standard error of the mean is 2.63.

The standard error simply means the statistical term that's used to measure the accuracy through which the sample distribution illustrates a population by using the standard deviation.

In this case, the effect of using standing height desks on the energy expended by nine elementary school students was studied.

The standard error will be:

= s /✓n

where

s = standard deviation

n = number of students = 9

= 7.9 / ✓9

= 7.9 / 3

= 2.63

The standard error is 2.63.

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The area of the composed rectangle and the semicircle is 92.56 square units.

Area of rectangle and semicircle

The formula for the Area of a Rectangle.

A = l × w.

where l refers length and w refers width of the rectangle

The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.

Given,

Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.

Here we know the following values,

Length of the rectangle = 10

Width of the rectangle = 8

Diameter of the circle = 8

Through the given diameter we have identified the radius as 4.

Now, the area of the rectangle is calculated as,

A = 10 x 8

A = 80 square units.

Similarly, the area of the semicircle is

A = 1/2 (π x 4²)

A = 1/2 x π x 8

A = π x 4

We know the value of π = 3.14, then the area of the semicircle is,

A = 3.14 x 4

A = 12.56 square units.

Therefore, the are of the figure is,

Total area = area of rectangle + area of semicircle

Total area = 80 + 12.56

Therefore, the total area of the figure is 92.56 square units.

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