(4b) If you know that you can drive 230 miles withthat much gas, how many miles per gallon doesyour bus get?Round your answer to the nearest tenth of a mile.The bus gets miles per gallon,

Explanation:

For the given equation

For Erika to resolve the question

Step 1: We will take the logarithm of both sides

Step 2: Simplify the expression

Thus

Step 3: Solve for x

A percent discount of 30%

Explanation:

Since $129 represent 100% of the price, then the new price $90.30 represent 70 %

129 * 100 / 90.30 = 70 %

Since from the 100% of the price, it went to 70% of it, there was a discount of 30%

100 - 70 = 30%

Using percentages, the answer to both the subparts are:

So, since the interest is annual 6.5%:

(A) Interest that will be owed after 178 days:

Now, 3.25% of 4200:

(B) Interest after 178 days if sop doesn't repay:

Now, 6.5% of 4200:

Therefore, using percentages, the answer to both the subparts are:

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Answer:

See below.

Step-by-step explanation:

Given multiplication:

[tex]3 \dfrac{1}{5} \times 2 \dfrac{5}{8}[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]\implies \dfrac{3 \times 5+1}{5} \times \dfrac{2 \times 8+5}{8}[/tex]

[tex]\implies \dfrac{15+1}{5} \times \dfrac{16+5}{8}[/tex]

[tex]\implies \dfrac{16}{5} \times \dfrac{21}{8}[/tex]

[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]

[tex]\implies \dfrac{16 \times 21}{5 \times 8}[/tex]

[tex]\implies \dfrac{336}{40}[/tex]

Reduce the fraction by dividing the numerator and denominator by the common factor of 8:

[tex]\implies \dfrac{336 \div 8}{40 \div 8}[/tex]

[tex]\implies \dfrac{42}{5}[/tex]

Divide the numerator by the denominator:

[tex]\implies 42 \div 5=8\;\textsf{remainder}\;2[/tex]

The mixed number answer is the whole number and the remainder divided by the denominator:

[tex]\implies 8 \dfrac{2}{5}[/tex]

Step-by-step explanation:

when you want to start solving it you will do 16 over 5 * 21/8equals 8 whole number 2/5

it will give you 336 all over 40 if you divide by 8 you will get 42/5 which is 8 whole number 2/5

Answer:

maya is able to make 47 bracelets

Step-by-step explanation:

The number of horses on the harm will be 24.

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

A local farm raises horses and goats.

The total number of horses and goats on the farm is 96.

Let number of horses = x

Since, The number of goats is 3 times the number of horses.

Then, Number of goats = 3x

The total number of horses and goats on the farm is 96.

Hence, we can formulate;

x + 3x = 96

4x = 96

x = 24

Thus, The number of horses on the harm will be 24.

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The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.

The four lines that are skew to line EF are AB, GB, CH, and DC.

The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.

We have,

A line EF on the given square figure.

We have the following lines on the given figure.

DG, CB, HA, FA, FG, GB, AB, EH, ED, DC,CH,

We see that,

FG, FA, EH, and ED are perpendicular and intersecting to line EF.

DG, CB, and HA are parallel to line EF.

So the remaining lines will be skew to line EF

i.e AB, GB, CH, and DC

Thus,

The four lines that are skew to line EF are AB, GB, CH, and DC.

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The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0

The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be

(x - 2) (x - √5) (x + √5) = 0

(x - 2) (x² - 5) = 0

x³ - 5x - 2x² + 10 = 0

=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.

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We have to use the slope formula

Let's replace the points (9,-24) and (13,-21). Where

2x² + 5x - 3 = 0

Multiply the coeeficient of x² and the constant (-3)

That is 2 ( - 3) = -6

Find the numbers whose sum is 5 and whose product is -6

The number is 6 and -1

Replace 5x by the numbers

2x² + 6x - x - 3 = 0

2x( x + 3) - 1 ( x + 3) = 0

(2x - 1 ) ( x + 3) = 0

Either 2x -1 = 0 or x + 3 = 0

2x = 1

x = 1/2 or x = -3

Answer:

x+8 - 6/x+3

Step-by-step explanation:

The area of the smaller rectangle is 108 inches².

The area of a rectangle is calculated to determine the area occupied by the rectangle within its boundary. A rectangle's area (A) is the product of its length 'a' and width or breadth 'b'. As a result, the Area of the Rectangle = (a × b) square units.

Given the dimensions of the smaller rectangle:

Length = 12 inches

Width = x inches

Given the dimensions of the larger rectangle:

Length = 20 inches

Width = 15 inches

To find the value of x we use proportion,

[tex]\frac{12}{x} = \frac{20}{15}[/tex]

Cross-multiplying, we get

12 × 15 = 20x

x = 180/20 = 9

Hence, the width of the smaller rectangle is 9 inches.

Area of the smaller rectangle = length × width

                                                = 12 × 9

                                                = 108 inches²

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harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend​

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$800

r=9%=9/100=0.09

n=12

t=2 years

substitute in the expression above

Answer:

66

Explanation:

By the Thales theorem, if we have the following figure:

Then, the following equation applies:

So, in this case, we can formulate the following equation:

Then, solving for x, we get:

Therefore, the value of x is 66.

Answer:

  B, C

Step-by-step explanation:

You want to find the equivalent expressions among ...

The relevant rule of exponents is ...

  a^b = (1/a)^-b

Expressions with the same base and different exponents will not be equivalent. (A≠B).

Expressions with different bases and the same exponent will not be equivalent. (A≠C).

A variable in the base cannot replace a variable in the exponent. (A≠D).

The rule of exponents tells us replacing the base by its reciprocal and negating the exponent will result in an equivalent expression. (B=C).

The equivalent expressions are 4^(-3x^2) and (1/4)^(3x^2).

The domain of the function is [1, ∞) and the range of the function is [0,∞).

Domain and range:

The domain and range of a function are  refers the set of all the inputs and outputs a function can give respectively.

Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.

Given,

Here we have the function

y = √x - 1

Now, here we need to find the domain and range of the function.

The given function is rewritten as,

√x - 1 > 0

Square both sides then we get,

x - 1 > 0

Add 1 on both sides then we get,

x > 1

Therefore, the domain is [1, ∞).

Similarly, let us consider, y ≥ 0

Therefore, the range is [0,∞).

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Answer:

Step-by-step explanation:

Reduce the following expressions:

Operate like terms:

The time taken by Town A to Town B will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance traveled by time. The unit of speed in miles per hour.

Given that at 30 mph a trip from Town A to Town B takes 6 hours.

The time taken will be calculated as,

Total distance = 30 x 6 = 180 meters

Speed = 30 x 2 = 60 mph

The time,

T = 180 / 60= 3 hours

Therefore, the time taken by Town A to Town B will be 3 hours.

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If the cost to park in garage can be modeled by the equation P = 3+ch

Part A

The equation to find the number of hours a person parked h = (P-3) / c

Part B

If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5

Part C

If P = $25.50, the person parked 10 hours if the cost per hour is $2.25

The flat fee of parking = $3

The cost to park in garage can be modeled by the equation

P = 3+ch

Where c is the hourly rate to park

h is the number of hours parked in the garage

Part A

The equation to find the number of hours a person parked is

P = 3+ch

c × h = P-3

h = (P-3) / c

Part B

c = $2.25

h = 6 hours

P = 3 + 2.25×6

= 3 + 13.5

= $16.5

Part C

P = $25.50

c = 2.25

h = (P-3)/c

= (25.50-3)/2.25

= 10 hours

Hence, if the cost to park in garage can be modeled by the equation P = 3+ch

Part A

The equation to find the number of hours a person parked h = (P-3) / c

Part B

If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5

Part C

If P = $25.50, the person parked 10 hours if the cost per hour is $2.25

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The value of x is 10 and the length of SU is 50.

Here SU is the line and T is the mid-point of the line

So from this we have

SU = ST + TU

ST = TU

SU = 2ST = 2TU

ST = 3x - 5 and TU = 2x + 5

As ST = TU

3x - 5 = 2x + 5

x = 10

SU = 2ST

     = 2( 3x - 5)

     = 2( 3 × 10 - 5)

     = 2( 30 - 5)

     = 2× 25

     = 50

Therefore the value of x is 10 and the length of SU is 50.

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Given: Given the function: f(x) = (x − 3)(x + 7)(x − 1)

Required: its f-intercept and its x-intercepts.

Explanation:

For f-intercept, put x = 0

So the f-intercept is (0,21).

For x-intercepts, put f(x) = 0

So x-intercepts are (3,0),(-7,0) and (1,0).

Final Answer:

f-intercept: (0,21)

x-intercept: (3,0),(-7,0),(1,0).

SOLUTION:

Case: Distance time graph

Method:

a) the students speed from the 3rd to 5th minute

b) the times during the bike ride did the student come to a stop

d and h

8 minutes and 23 minutes

c) the students speed increase during.

b to c. 1 and 3 minutes

e to f. 11 and 15 minutes

f to g. 15 and 17 minutes

The number of people that can attend Jordan's party is 50 people.

The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.

The form of the linear equation would be:

Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)

$800 = $400 + ($50 x 4) + ($4 x p)

$800 = $400 + $200 + $4p

$800 = $600 + $4p

$800 - $600 = $4p

$200 = $4p

p = $200 / $4

p = 50 people

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You have one box that is 2 and 5/11

feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for

2 and 5/11. If you stack the​ boxes, about how tall will the stack​ be​

we have that

If you stack the​ boxes,

we have

2.45+2.45=4.90 ft

After throughfall calculating the multiplication 4505 x 219 in standard algorithm, we have come to find that product is 986595

In elementary math, a standard algorithm or method is a particular computation technique that is typically taught for resolving particular mathematical issues. In general, these techniques include exchanging, regrouping, long division, long multiplication using a standard notation, and standard formulas for average, area, and volume.

These techniques can vary somewhat by country and time, but they typically include these techniques. Similar techniques are also available for more complex functions like square roots, but they are no longer taught in general mathematics classes because calculators are more convenient.

4505 x 219 in standard algorithm is as follows:

⇒        4 5 0 5

         ×    2 1 9              

        4 0 5 4 5    

    +  4 5 0 5        

  + 9 0 1 0        

     9 8 6 5 9 5

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The division of the two numbers in scientific notation is equal to 1.91*10^15

To solve this problem, we have to divide the two numbers in scientific notation and to do this, we can simply apply division law of indices here;

We can first divide 6.1 by 3.2.

This will give us 1.90625 which is approximately 1.91.

Then applying the law of indices and subtract the power from one another. This becomes 20 - 5 = 15

The final value will be 1.91 * 10^15

The division of 6.1*10^20 by 3.2*10^5 is equal 1.91 *10^15

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Since BCE is an inscribed angle, it measures half the measure of the inscribed arc.

Angle BCE inscribes the arc BE of 180°, we have:

Therefore the correct option is 1)

We got the linear equation:

The slope of this line will be -8/5 and the y-intercept will be -4.

To graph it, first find the intercept with x - axis.

We can find it if we equal the equation to zero.

Now, we got two points:

To graph the function, we only join these points:

So that's the graph for the function.