What number when multiplied by 1 1/4 has a product of 1

The value of x=20, according to the given question.

What is meant by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to the given data in the question,

We know that y varies directly with x like that,

y=kx..................(1)

y=12 when x=15.

Now, we have to find the value of x when y=16.

Then, putting the given values of x & y in the eq. (1), and determine the value of k.

12=k(15)

[tex]k=12/15\\k=4/5\\[/tex]

Now, putting the value of k in the second statement in eq.(1), where only y's value is given.

[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]

Hence, the value of x=20.

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The equation of a line u perpendicular to line t and passes through (3, -3) is  y = -2x + 3

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Line t has equation as y + 3 = 1 / 2 (x - 7).

Line u is perpendicular to line t and it passes through (3, -3).

The products of the slope of perpendicular lines is equals to negative 1.

Therefore,

m₁ m₂ = -1

1 / 2 m₂ = -1

m₂ = -2

Therefore,  the equation of the line have a slope of -2.

let's find the y-intercept using (3, -3)

-3 = -2(3) + b

b = -3 + 6

b = 3

Therefore, the equation in slope intercept form is y = -2x + 3.

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Answer: 1/6

Step-by-step explanation:

To subtract fractions, you must have a common denominator. To do this, the common multiple of 3 and 2 is 6. So 2/3 is multiplied by 2/2 and 1/2 is multiplied by 3/3. The multiplication is valid since we multiplied by one, it didn't alter the value but rather it put it into an alternate, equivalent form.

Answer:

IT IS A FUNCTION

It is specifically a Surjective/ onto Mapping/function

Step-by-step explanation:

surjective or onto function is when y has an image in x

Answer:

The graph is a function

Step-by-step explanation:

-For every input (x) there is only one output value (y)

Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.

Ex.

X: 2, 4, 7 , 2, 5         This is not a function. More than one input for each output.

Y: 1, 2, 4, -3, 7

Ex.

X: 5, 6, -5, 8  this is a function. Exactly one input for every output.

Y: 1, 4, 5, 9

The value of dy/dx is ( v du/dx - u dv/dx)/v²

From the question, we have

y = (1+x)u/(1+x)v

y = u/v

dy/dx = d/dx(u/v)

d/dx(u/v) = ( v du/dx - u dv/dx)/v²

Derivatives:

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.

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Answer:

1: D

2: B

3: A

D: C

Step-by-step explanation:

Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

What is the differentiation of the function?

A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.

We have,

                                     [tex]f(x) = (-x^{2} - 4)x^{5}[/tex]

By simplifying the given function, we get

                                      [tex]f(x) = -x^{7} - 4x^{5}[/tex]

Now, we will differentiate the given function with respect to [tex]x[/tex].

                                    [tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]

                                    [tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]

                                     [tex]f'(x) = -7x^{6} - 20x^{4}[/tex]

Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

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The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.

As given in the question,

Given expression is equal to :

f(x) = 4 ( 7x )

Calculate the value of the given function for x = -2 is given by :

Substitute value of x = -2 we get.

f(-2)

= 4 ( 7 ( -2) )

Seven is positive and 2 is negative , multiplication of positive to negative is always negative.

So, 7 ( -2 ) is -14 Substitute in above equation we get,

= 4 ( -14 )

= -56

Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to

f( -2 ) = -56.

The complete question is  :

If f(x) = 4 (7x) , what is the value of f(-2)?

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Answer:

I believe that the answer is $2.04, per gallon.

Step-by-step explanation:

I added the $25 he paid with the gift card, and the $26, which was $51 that Corey paid in total. Corey had gotten 25 gallons and they want to figure out how much he paid for each gallon. So we take the total he spent divided by the number of gallons he had gotten. So 51/25=2.04

Hope this helps!!!!

The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)

In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.

Horizontal translation

g(x) = f(x - k), where k > 0 for a translation in + x direction.

Vertical translation

g(x) = f(x) + k, where k > 0 for a translation in + y direction.

After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down.  Then, we find the following transformation formula:

g(z) = f(z) - 2

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Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

What is an leading coefficient?

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.

According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero

Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i

and f(x) be a polynomial with real coefficients.

therefore by fundamental theorem of algebra

+i and -3-i are also zeros of f(x)

so zeros of f(x) are 7, -i, -3 + i, i, -3 -i

Degree is 5, so there is at most 5 zeros therefore the required polynomial will be

f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)

= a[(x +7)(x² + 1)(x² +6x + 10)]

[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]

[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

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The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:

0.3214 = 32.14%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

The probabilities that compose the formula are listed as follows:

The events in this problem are given as follows:

The probabilities are given as follows:

P(A) = 0.28, P(A and B) = 0.09.

Hence the conditional probability is obtained as follows:

P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.

The probability asked is that a camper entering the Luray Caverns has Canadian license Plates.

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The number of minutes is 195 minutes when the customer spends $267.00. The correct option is B.

From the information, the total cost of a plane ride, C, is given as a function

C = $33.00 + $1.20m

where n = number of minute

Since the customer spends $267.00 on a plane ride, this will be:

C = = 33.00 + $1.20m

33 + 1.2m = 267

Collect like terms

1.2m = 267 - 33

1.2m = 234

Divide

m = 234 / 1.2

m = 195

Minutes used is 195 minutes

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The greatest common factor of 160, 320 and 480 will be 160.

The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.

In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)

Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.

Factorize number 160

160 = 2×2×2×2×2×5

Factorize number 320

320 = 2×2×2×2×2×2×5

Factorize number 480

480 = 2×2×2×2×2×3×5

The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.

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Answer The answer is 96 but as a fraction 96 8/13

Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.

Answer:  7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6

Answer Overall : 38/5

Step-by-step explanation:  Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10

To find a new numerator:

a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10

b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74

c) Write a previous answer (new numerator 74) over the denominator 10.

Seven and four tenths is seventy-four tenths

Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5

The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.

In other words - seventy-four tenths plus two tenths is thirty-eight fifths.

First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4

add them together but DONT add the denominators

These numbers can be simplified by 2 so the final answer is:

The image after a 270 rotation is (4, -3)

If the point of rotation is not the origin, the steps are as follows:

1. Subtract the point of rotation off each vertex point of

the shape

2. Rotate as you would around the origin

3. Add the point of rotation back to each vertex point of

the shape

Given: R(1, 2) after a 270 rotation about (0, - 2)

step1: (1-0, 2-(-2)) = (1, 4)

step 2: For rotation about the origin through 270°, the image is (y, -x). Thus, (1, 4) => (4, -1)

step 3: (4, -1) => (4+0, -1+(-2) ) = (4, -3)

Therefore, the image of R(1, 2) after a 270 rotation about (0, - 2) is (4, -3)

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Answer:

-5/7, 10/7

Step-by-step explanation:

The slope of an equation in standard form is -a/b

so -5/7

Set x to 0 to find the vertical intercept

5(0)+7y=10

7y=10

y=10/7

The z-score of a person who scored 128 on the exam is equal to 2.9

A z-score is also referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (128 - 70)/(20)

Z-score, z = 58/20

Z-score, z = 2.9

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The Sales of the electronic store in 1 year is 66,776.88    

Applications of Compound interest:

Compound interest is an interest that is calculated on the principal and the interest accumulated over the previous period. The concept of compound interest can be used in different types of situations like an Increase in population or a decrease in population, Depreciation, or increasing the value of an item, etc.

The formula for compound interest is given by

Total amount, A = P(1 + r/n)^nt  

where  P = initial amount

r = rate of increase              

n = number of compounds in year

t = time period in years

Here we have,

The rate of increase in sales r = 2.7% (per monthly)  

=> r = 2.7/100 = 0.027

Here sales are increased monthly

then the number of compounds per year = 12

Sales in this month, P = 65000  

From above formula

Sales in 1 year, A = 65000(1 + 0.027/12)¹²

= 65,000(1 + 0.00225)¹²

= 66,776.88    

Therefore,

Sales of the electronic store in 1 year =  66,776.88      

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Answer:

Step-by-step explanation:

4x(power of 5) divided by x(power of 2)

5y(po7) div by y(po2)

not 100% sure as i havent learnt this before lol

Step-by-step explanation:

the list of your answer options has a different sequence than the picture.

I assume the picture shows us the correct sequence.

the correct answer is

D : the y-values are all greater than our equal to 2

why ?

because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.

so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.

Answer:

In the first one you should write: 6, because the test tells you that in 6 minutes she runs 3/4miles.

So in 12 minutes she runs (3/4miles)*2. (basically 3/4 miles in the first 6 minutes, and other 3/4 miles in the remaining 6munutes).

So in the second space you can write 12, and on the right 2*(3/4), which is... (3/2).

To find the equation:

3/4 = 6

(3/4)*2= 6*2

so we know that in 1 minute we do 1/8miles, and now we have our formula. (1/8)*6=1*6

the formula is: y(miles) =(1/8)*x

in fact is x=6 minutes, y= (1/8)*6, so y=3/4.

Answer:

x ≥ 6

Step-by-step explanation:

|-3x| - 7 ≥ 11     The absolute value of -3x is 3x

3x - 7 ≥ 11        Cancel the 7 by adding it on both sides

3x ≥ 18            To get x by itself divide 3 on both sides

x ≥ 6

Answer:

7 hours.

Step-by-step explanation:

Use a clock and count forward.

The  mean height of the low tides is 1.21 ft

The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft

The mean of a sample is given by the formula =

summation of all observation / number of observation

mean = (x₁ + x₂ + x₃ + x₄)/ 4

mean = -0.22 + 2.64 - 0.22 + 2.64 / 4

mean = 4.48 / 4 = 1.21

Therefore, the  mean height of the low tides is 1.21 ft

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The probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute is; 0.012676.

This z-score is used to tell us the number of standard errors that exists between the sample mean and the population mean.

The formula for z-score here is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 97

Population mean; μ = 91

Standard deviation; σ = 10

Sample size; n = 20

Thus;

z = (x' - μ)/(σ/√n)

z = (97 - 91)/(10/√20)

z = 2.236

From online p-value from z-score calculator, we have;

p = 0.012676

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Complete question is;

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

The probability that the student will pass the test, using the binomial distribution, is of:

0.172 = 17.2%.

The formula that gives the probability of x successes is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

The probability of passing is given by:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.5)^{7}.(0.5)^{3} = 0.1172[/tex]

[tex]P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0440[/tex]

[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]

[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.0010[/tex]

Then:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1172 + 0.0440 + 0.0098 + 0.0010 = 0.172 = 17.2%.

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The price that yields maximum revenue is equal to $99. Also, the maximum revenue is equal to $490,050.

In order to determine the price that would yield the maximum revenue, we have to find the derivative of the revenue function R(p) by applying the Power Rule.

Mathematically, the revenue function, R(p) is given by this mathematical expression:

Revenue function, R(p) = NP

Where:

Let the variable n represent the number of reductions in the price. Therefore, we have:

N = 3,400 + 50n    ....equation 1.

P = 130 - n

n = 130 - P

From equation 1, we have:

N = 3,400 + 50(130 - P)

N = 3,400 + 6,500 - 50P

Next, we would re-write the revenue function R(p) as follows:

Revenue function, R(p) = (3,400 + 6,500 - 50P)P

Revenue function, R(p) = 3,400P + 6,500P - 50P²

Revenue function, R(p) = 9,900P - 50P²

Taking the derivative of R(p), we have:

R'(p) = 9,900 - 100P

100P = 9,900

Price, P = 9,900/100

Price, P = $99

For the the maximum revenue, we have:

Maximum revenue, R(p) = 9,900P - 50P²

Maximum revenue, R(p) = 9,900(99) - 50(99)²

Maximum revenue, R(p) = 980,100 - 490,050

Maximum revenue, R(p) = $490,050.

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Complete Question:

A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.

Measure of largest. smallest and middle angle of a triangle under given conditions is 145°, 15° and 20° respectively.

What is angle sum property of a triangle?

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

According to the given question:

Let the measure of middle angle = x

The measure of the smallest angle is three-quarters the measure of the middle angle.

∴ Smallest angle = (3/4)x

The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles.

∴ Largest angle = 110° + x + (3/4)x

Now, by Angle sum property of a triangle

x + (3/4)x + 110° + x + (3/4)x = 180°

On solving for the value of x we get

2x + (3/2)x = 70°

7x = 140°

x = 20°

Therefore,

measure of middle angle x = 20°

measure of smallest angle (3/4)x = 15°

measure of the largest angle 110° + x + (3/4)x = 145°

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