Four times a number is equal to the number increased by 12. Find the number

Answer:

7x ( - x + 5 )

Step-by-step explanation:

- 7x² = 7x × - x

35x = 7x × 5

- 7x² + 35x = 7x ( - x + 5 )

The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

Given is the expression as follows -

f(x) = 4/(x - 3)

[A] -

{x - 3/x + 2} • {x + 2/4} = {x - 3/4}

[B] -

{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}

[C] -

{x + 2/x - 3} • {4/x + 2} = {4/x - 3}

[D] -

{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}

Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

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Answer:

10°

Step-by-step explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.

x + 3x + 4x + 5x + 6x + 8x + 9x = 360

36x = 360

x = 10

In a polygon, an exterior angle is supplementary to its adjacent interior angle.

The smallest exterior angle is x, and x = 10.

Answer: 10°

The distances that represent the percentages are given as follows:

A proportion is a fraction of a total amount, used along with the unit measures and basic arithmetic operations to obtain the desired measures in the context of a problem.

28m is 80% of the distance, hence 100% of the distance is obtained applying the proportion as follows:

0.8x = 28

x = 28/0.8

x = 35.

Then the distance that represents 20% of a rotation is calculated as follows:

0.2 x 35 = 7 meters.

The complete problem is given by the image shown at the end of the answer.

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The equation in slope intercept for the given line is  y = -2/3x - 28/3.

What is Slope ?

The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.

Given,  the line crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6.

We know that two parallel lines always have the same slope.

We can say that the line has coordinate as (14,0) and slope (m) as -2/3.

We know that the slope-intercept form of the line is,

                    y= mx + b

Now, We put x=14, y=0 and m=-2/3 in equation above,

We get, 0 = -2/3 × 14 + b

             b = -28/3

So, the slope intercept form will be :

               y = -2/3x - 28/3

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The area of the shape as shown in the diagram is 11.25 cm².

Area is the region occuppied by a plane shape.

To calculate the area of the shape, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these question into equation 1

Hence, the area of the shape is 11.25 cm².

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Answer: the first one is 7/9 and the second one is option 2

Step-by-step explanation:

4+7 = 11

< or> = open dot

Answer:

the mean (i.e. the average)

Step-by-step explanation:

There's no clear outlier or inconsistency therefore the mean should be used.

You can quickly calculate the radius of a cylinder using an online calculator.

What is the radius of a cylinder with a capacity of 100 cubic units and a height of 5 units?

Solution:

The radius of a cylinder (r) is equal to (V / h).

= √(100 / π × 5)

= 2.523 units

As a result, a cylinder's radius is 2.523 units.

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Answer:

Step-by-step explanation:

its a

Division followed by simplification of mentioned rational function gives:

(x + 1)/(x + 4)

Factoring an algebraic expression specifically means writing a given expression as the product of its factors. These factors may be numbers, variables, or algebraic expressions.

1, 2, 6, and 12 are all divisors of 12 because they divide 12 equally. This is an important algebraic operation, which is used to simplify expressions, simplify fractions, and solve equations. This is also called algebraic factorization.

Factorization of x² + 2x - 3

x² + 3x - x - 3

(x² + 3x) - (x + 3)

x(x + 3) - 1(x + 3)

(x + 3)(x - 1)

Factorization of x² + 3x - 4

x² + 4x - x - 4

(x² + 4x) - (x + 4)

x(x + 4) - 1(x + 4)

(x + 4)(x - 1)

Factorization of x² - 2x - 3

x² - 3x + x - 3

(x² - 3x) + (x - 3)

x(x - 3) + 1(x - 3)

(x - 3)(x + 1)

Using identity, a² - b² = (a + b)(a - b)

x² - 9 = x² - 3²

x² - 3² = (x + 3)(x - 3)

Now, for the division:

(x² + 2x - 3)/(x² - 9) ÷ (x² + 3x - 4)/(x² - 2x - 3)

[(x + 3)(x - 1)/(x + 3)(x - 3)] ÷ [(x + 4)(x - 1)/(x - 3)(x + 1)]

By reciprocal of (x + 4)(x - 1)/(x - 3)(x + 1)

[(x + 3)(x - 1)/(x + 3)(x - 3)] × [(x - 3)(x + 1)/(x + 4)(x - 1)]

= (x + 1)/(x + 4)

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The line segment of length 3 1/2 is sketched with mid pint at -1 and attached

A line segment in geometry has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

The endpoints is important before a line can be defined as a line segment, however the midpoint will be essential in calculating for the endpoints

The mid point of the line is given to be -1

the other ends will be 3 1/2 /2

1.75

from -1 add and subtract 1.75 to get the endpoint's

-1 + 1.75 = 0.75

-1 - 1.75 = 2.75

each unit on the number line is 0.3333

to get 0.75 from 0 count two units to give 0.6667 then a bit more to get to 0.75

to get 2.75 from 2 count two strokes to get to 2.6667, then add a little more to get 2.75

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Answer:

p = -8 6/35

Step-by-step explanation:

p/(1 6/7)=−4.4

To solve for p, multiply each side by 1 6/7

p/(1 6/7) * ( 1 6/7)=−4.4 *  (1 6/7)

p = - 4.4 * ( 1 6/7)

Change each number to fractions

p = -44/10 * 13/7

p = -286/35

Change to a mixed number

p = -8 6/35

The critical value is -2.70

What is a null hypothesis?

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.

Here, we have

The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.

So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.

Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:

X₁: Braking distance of an SUV equipped with tires made with compound one.

Its sample mean is X[bar]₁= 41 feet

And the Standard deviation S₁= 12.1 feet

X₂: Braking distance of an SUV equipped with tires made with compound two.

Its sample mean is X[bar]₂= 46 feet

And the Standard deviation S₂= 9.0 feet

We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.

The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂

The statistical hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

α: 0.05

The statistic to use to compare these two populations is a pooled Z test

Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)

Z = {(41-46)-0}/√146.41/66+81/66

Z = -5/1.85

Z = -2.70

The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:

Z(α) = Z(0.05) = -1.645

Decision rule:

If Z(H₀) ≥  -1.645, then you do not reject the null hypothesis.

If Z(H₀) < -1.645, then you reject the null hypothesis.

Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.

At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.

Hence, the critical value is -2.70.

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By the Application of Prime factorization method the value of x is 48

what is Prime factorization method?

Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.

Solution:

HCF = ( X, 54 ) = 6

LCM = ( X, 54 ) = 432

a = x  b = 54

using property

a * b = LCM * HCF

54a = 6 * 432

   a  = (6 * 432) / 54

   a = 48

Hence the value of x is 48.

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The solution is Option A.

The exponential growth model for the number of bacteria in the sample after x hours is    [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the equation for the number of bacteria in the sample after x hours = P

The value of the equation P ( x ) is given by

After 4 hours , the sample contained 400 bacteria

So ,

when x = 4

[tex]P ( 4 ) = ae ^{4b }=400[/tex]   be equation (1)

After 12 hours , the sample contained 1600 bacteria

And , when x = 12

[tex]P ( 12 ) = ae ^{12b }=1600[/tex]   be equation (2)

Divide equation (2) by equation (1) , we get

[tex]\frac{P ( 12 )}{P ( 4 )} = \frac{ae ^{12b }}{ae ^{4b }} = \frac{1600}{400}[/tex]

On simplifying the equation , we get

e¹²ᵇ⁻⁴ᵇ = 4

e⁸ᵇ = 4

Taking logarithm on both sides of the equation , we get

8b = ln (4)

Divide by 8 on both sides , we get

b = ln (4) / 8

Substituting the value for b in equation (1) , we get

[tex]ae ^{4*ln (4) / 8 }=400[/tex]

[tex]ae ^{ln (4) / 2}=400[/tex]

On simplifying the equation , we get

a x 2 = 400

Divide by 2 on both sides of the equation , we get

a = 200

Therefore , the exponential growth equation is given by

Substitute the values of a and b in the equation , we get

[tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

Hence , The exponential growth model for the number of bacteria in the sample after x hours is    [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]

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Answer:

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

If the amount of sales for current week is x, Jamie's earning is:

Solve it for x:

Answer:

To solve a problem involving a whole number and a fraction, you can first convert the whole number to a fraction by writing it as a fraction with a denominator of 1. For example, if the whole number is 4, you can write it as the fraction 4/1.

Then, you can add or subtract the fractions as you would normally, making sure to find a common denominator if necessary. For example, suppose you want to add the whole number 4 and the fraction 3/5. You can first write 4 as the fraction 4/1, giving you:

4/1 + 3/5

To add these fractions, you need to find a common denominator. A common denominator for 1 and 5 is 5, so you can rewrite the fractions with denominators of 5:

4/1 = 20/5

3/5 = 3/5

Now you can add the fractions:

20/5 + 3/5 = 23/5

So the solution to the problem is 23/5.

If you need to multiply or divide the whole number and fraction, you can treat the whole number as a fraction with a denominator of 1 and then perform the multiplication or division as you would normally with fractions.

Step-by-step explanation:

Answer:

$16,000

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Let investment 1 be the bond that pays 5.75% simple interest.

Let investment 2 be the bond that pays 7.25% simple interest.

Given:

Create two equations for the interest from both investments.

Interest from Investment 1

[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]

[tex]\implies \sf I_1=0.0575\:P_1[/tex]

Interest from Investment 2

[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]

[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]

[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]

Given that the sum of the interest from both investments is $1,790:

[tex]\implies \sf I_1+I_2=1790[/tex]

[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]

[tex]\implies \sf -0.015\:P_1=-240[/tex]

[tex]\implies \sf P_1=16000[/tex]

Therefore, $16,000 should be invested in the 5.75% bond.

Check:

[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]

[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]

[tex]\implies \sf I_1+I_2=920+870=1790[/tex]

The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics.

Fill in blanks :

A point has no dimension. it is an abstract idea of a location in space.

A vertex is where two edges meet at a point

A line has edge dimension - length . An edge is a line segment where two faces meet.

A  flat plane figures has a 2 dimension - length and width

The 3 points of a 3D object is a plane.

Three dimensional objects have vertices, edges and faces unless they are the geometric solids like cylinders, cones and sphere.

when we talk about line we are looking at the measure of a one dimensional figure.

when we talk about area we are looking at the space inside of a two dimensional figure.

when we talk about volume we are looking at the total space enclosed by a three dimensional figure.

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The quadratic equations, or the equations that are quadratic in form, for this problem is given as follows:

The degree of a function is given by the highest exponent that appears in the definition of the function.

A quadratic function is a function that has a degree of 2.

The standard format of a quadratic function is given as follows:

y = ax² + bx + c.

(in which the coefficient a must assume a value different of zero).

The quadratic function in this problem is given as follows:

6(2x + 4)² = 2x + 4 + 2.

As (2x + 4)² = 4x² + 16x + 16, meaning that the highest exponent would be of 2.

However, equations of the fourth degree can also be quadratic in form, as long as the exponents go as follows: 4, 2 and 0.

Hence these following equations are also quadratic in form:

They are classified as quadratic in form because a transformation such as y = x² can make them quadratic.

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The plane touches the runway with a speed of 65 m/s then the acceleration of the plane during its landing will be equal to 65 m/s².

The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.

Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.

As per the given information in the question,

Velocity, v = 65 m/s

Time, t = 1 sec.

Use the equation of acceleration,

a = v/t

a = 65/1

a = 65 m/s²

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Answer:

I believe if I just believe that you can work this out then you can do it thank you You are intelligent you can do this

The probability that there were at most three successes in a trial is approximately 0.9.

It looks like the histogram shows the probability mass function (PMF) for the number of successes in a trial. The PMF for a random variable gives the probability of each possible value of the random variable.

To find the probability that there were at most three successes in a trial, we need to add up the probabilities of 0, 1, 2, and 3 successes. From the histogram, it looks like the probabilities of these values are approximately 0.2, 0.4, 0.2, and 0.1, respectively. Adding these up, we get an approximate probability of 0.2 + 0.4 + 0.2 + 0.1 = 0.9.

Therefore, the probability that there were at most three successes in a trial is approximate $\boxed{0.9}$.

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The cost of a 25-minute rental will be $92.00.

To find the amount a 25-minute rental would cost, we need to first determine the rate per minute and the flat fee. We can do this by setting up the following system of equations:

30 minutes x rate + flat fee = $110.50

40 minutes x rate + flat fee = $145

To solve this system of equations, we can multiply the first equation by 2 and subtract the second equation from it to eliminate the rate:

(30 minutes x 2) x rate + flat fee x 2 = 2 x $110.50

80 minutes x rate + flat fee x 2 = 2 x $110.50

Subtracting the second equation from the first equation, we get:

flat fee x 2 - flat fee x 2 = 2 x $110.50 - 2 x $145

flat fee x 2 - flat fee x 2 = -$34.50

Since the left side of the equation is equal to zero, we can divide both sides by 2 to solve for the flat fee:

flat fee - flat fee = -$34.50 / 2

flat fee - flat fee = -$17.25

Since the left side of the equation is also equal to zero, the flat fee must be zero.

We can now use either of the original equations to solve for the rate per minute. Using the first equation, we get:

30 minutes x rate + flat fee = $110.50

30 minutes x rate = $110.50

rate = $3.68

We can now use this rate to find the cost of a 25-minute rental:

25 minutes x $3.68 + flat fee = $92.00 (Since the flat fee is zero)

Thus, a rental of 25 minutes costs $92.00.

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Answer:

Step-by-step explanation:

40k

according to question,

given data.

h(x)=8x-3/4+5

then,

All the given three conditions are true for conducting a two proportion significance test.

To check the significance of two proportions, following conditions should be met

Hence, all the three conditions must be met to conduct a two-proportion significance test.

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bro this is middle school work not college

A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.

What is a logarithm function?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.

Given function are

f(x) = log x and g(x) = log₃ x.

The rate of raise of the graph g(x) is more than that of the graph f(x).

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Answer: 89

Step-by-step explanation:

1 hr of mowing = 8.20 dollars

1 hr of babysitting = 7.90 dollars

7 hrs of mowing = 8.20 x 7 = 57.4 dollars earned

4 hrs of babysitting = 7.90 x 4 = 31.6 dollars earned

Total amount she has earned = 57.4 + 31.6 + = 89 dollars