A salad dressing is made by mixing lemon juice and vinegar in the ratio of 4:3. 700ml is taker for salad dressing . how much lemon juice is used?

Answer: -7

Step-by-step explanation:

Here we will show you step-by-step with detailed explanation how to calculate 98 divided by 14 using long division.

Instead of saying 98 divided by 14 equals 7, you could just use the division symbol, which is a slash, as we did above.

Also note that all answers in our division calculations are rounded to three decimals if necessary.

Here are some other ways to display or communicate that 98 divided by 14 equals 7:

98 ÷ 14 = 7

98 over 14 = 7

98⁄14 = 7

The easiest way we found to answer the question "what 98 divided by 14 means", is to answer the question with a question: How many times does 14 go into 98?

Answer:

-10+4=-x

-x_=-6_

x=6

if you don't understand

negative x over negative x and negative x over 6 the negative will cancle the negative you will get x to be 6

The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.

The equation that can be used to determine the total cost of renting shoes at both locations is:

total cost = fixed cost + variable cost

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

Where

x = number of games played

In order to determine the number of games that would make the cost

equal in both locations, the following steps would be taken:

$5 + $1.1x = $3 + $1.50x

Combine similar terms

$5 - $3 = $1.50x - $1.1x

$2 = $0.40x

Divide both sides of the equation by $0.4

x = 2 / 0.4

x = 5 games

Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50

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Answer: f = 14h (f is total fee, h is the hour luke worked)

Step-by-step explanation:

A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.

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Answer:

m = 5/4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, -3) (4,2)

We see the y increase by 5 and the x increase by 4, so the slope is

m = 5/4

Given quadratic equation has same solution set as -x=x²+12x+36 i.e. C.

A second-degree algebraic equation in x is a quadratic equation. Ax2 + bx + c = 0 is the quadratic equation in its standard form, with a and b acting as coefficients, x acting as the variable, and c acting as the constant term.

The coefficient of x2 must not be zero (a 0) for an equation to qualify as a quadratic equation. The x2 term comes first, followed by the x term, and finally the constant term when stating a quadratic equation in standard form. Instead of being written as fractions or decimals, the numerical values a, b, and c are frequently expressed as integral values.

Now,

Given equation is √-x=x+6

-x = (x+6)²

-x = x² +36+12x

x² + 11x + 36 = 0

As it is same quadratic equation as given in option C.

Hence,

         Given quadratic equation has same solution set as

-x = x² + 12x + 36.

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Dont worry I gotchu

Answer: 33.7°

By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.

When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.

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The number of unique committees is 240 / 4 = 60. So the answer is d. 60.

What is the combination?

The permutation is to select an object and then arrange it and it cares about the orders while Combination is about only selecting an object without caring about the orders.

To form a committee with 2 women and 2 men, we have 4 choices for the first woman, 3 choices for the second woman, 5 choices for the first man, and 4 choices for the second man.

Therefore, the number of ways to form a committee is 4 * 3 * 5 * 4 = 240. This is the total number of combinations, and to find the number of unique committees,

we need to divide by the number of ways to arrange the members within each committee.

As the members are distinguishable, the number of arrangements is simply 2! * 2! = 4.

Therefore, the number of unique committees is 240 / 4 = 60. So the answer is d. 60.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is illustrated in the figure below.

b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.

b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:

∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy

Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:

∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

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Answer:

Step-by-step explanation:

An inequality that best represents this situation is: x - 1300 > 2500.

a) Let x be the amount of money Sara has in savings. We know that the amount she wants to spend on vacation is $1300, so we have x - 1300 > 2500.

b) To solve for x, we can add 1300 to both sides: x > 3800.

c) The value of x in this situation represents the amount of money Sara has in savings.

The inequality x > 3800 means that Sara must have more than $3800 in savings in order to spend $1300 on a vacation while following the financial planner's suggestion to spend less than $2500.

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The measure of the angle ∠DBC, m∠DBC, found by writing an equation based on the angle addition postulate is m∠DBC = 30°

An equation consists of two expressions that are specified as being equivalent, by joining them by an equals to '=' sign.

The specified information are;

m∠ABD = (3·x+ 15)° and m∠DBC = (2·x)°, m∠ABC = 90°

The angle addition postulate indicates that we get;

m∠ABC = m∠ABD + m∠DBC

m∠ABC = 90° = (3·x+ 15)°  + (2·x)° (substitution property)

90° = (3·x+ 15)°  + (2·x)°  = (5·x+ 15)°

(5·x + 15)° = 90°

5·x = 90° - 15° = 75°

5·x = 75°

x = 75°/5 = 15°

x = 15°

m∠DBC = 2·x

Therefore, m∠DBC = 2 × 15° = 30°

m∠DBC = 30°

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Step-by-step explanation:

to solve an equation with a variable we want to transform the equation, so that in the end we have the variable alone on one side of the equation, and everything else on the other side.

so, when we look at

(n + 8)/2 - 4 = 16

what blocks us from reading the value of n ?

several things on the left side.

I would start with the "- 4".

to get rid of that from the side of the variable we need to add 4. and to keep the equality true, we need to add this on both sides :

(n + 8)/2 - 4 + 4 = 16 + 4

and we get

(n + 8)/2 = 20

what blocks us now ?

I would say the fraction, this division by 2.

how do we get rid of that ?

by multiplying everything by 2 :

2×(n + 8)/2 = 2×20

and we get

n + 8 = 40

still, something is blocking us from reading the value of n : the "+ 8".

how do we get rid of that ?

by subtracting 8 from both sides :

n + 8 - 8 = 40 - 8

and we get

n = 32

that's it. we are finished. goal achieved.

The perimeter ratio of the figures is given as follows:

9:16.

Considering the side length ratio of a:b, the perimeter ratio has the proportion given as follows:

a:b.

This is because both the side lengths and the perimeter are measured in units, hence the perimeter ratio is the same as the side length ratio.

Considering that the area is measured in square units and the volume in cubic units, their ratios would be given as follows:

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The rational functions with the given asymptotes are presented as follows:

1. y = 1/(x³ + x² - 6x).

2. y = 1.5x²/(x² + 0.5x - 0.5).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

For item 1, due to the vertical asymptotes, the denominator is given as follows:

x(x + 3)(x - 2) = x(x² + x - 6) = x³ + x² - 6x.

As the horizontal asymptote is of zero, the numerator has a lower degree than the denominator, hence it can be constant, and the function is given as follows:

y = 1/(x³ + x² - 6x).

For item 2, the denominator is given as follows:

(x + 1)(x - 0.5) = x² + 0.5x - 0.5.

Due to the horizontal asymptote of 3/2, the degree of the numerator must be the same as the denomiator, with a coefficient 3/2 that of the denominator, hence the numerator is given as follows:

3x²/2 = 1.5x².

Meaning that the function is:

y = 1.5x²/(x² + 0.5x - 0.5).

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Answer:

s= 19/-9

s≈-2.111

Step-by-step explanation:

s is being multiplied by -9

so, to get s by itself we divide both sides by -9

s= [tex]\frac{19}{-9}[/tex]

if you need it in decimal form, s≈-2.111

Answer:

is 2

because it's below for and two is the closest answer to the function variable answer to this question that you have here

The value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [tex][1,4][/tex] is -5.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4].

Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.

Using the method of integrating by parts, we have:

∫[tex]x????"(x)????(x) dx= x????(x)[/tex] ×[tex]\frac{x}{2} -[/tex]∫[tex](\frac{x^{2} }{2} )????'(x) dx[/tex]

We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let [tex]u=\frac{x^{2} }{2}[/tex] and [tex]dv=????'(x) dx[/tex]. Then [tex]du=x dx[/tex] and [tex]v=????(x)[/tex].

So we have:

∫[tex]x????"(x)????(x) dx = x????(x)[/tex]× [tex]\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c[/tex]

Where C is an arbitrary constant of integration.

We can use the given values of ????(1) and ????(4) to evaluate the definite integral:

∫[tex]x????"(x)????(x) dx[/tex] = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)

= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.

Therefore, the value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4] is -5.

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Answer: c

Step-by-step explanation:

quite easy because y=mx+b (y=3x-1)

the -1 is the y-intercept. (Where the line meets the y line. c is the only one where the y-intercept is -1

Answer:

2347

2347 * 2347 = 5508409

Step-by-step explanation:

Hope it helps! =D

The greatest common factor of 12 and 80 is 12, so we can use the distributive property to factor that out.

Identify the greatest common factor (GCF). In this case, it's 12.

Rewrite the expression so the GCF is outside of the parentheses. 12 + 80 = 12(1 + 80/12).

Simplify the expression inside the parentheses. 1 + 80/12 = 7.

Substitute the simplified expression back into the original equation. 12 + 80 = 12(7).

Simplify the expression. 12 + 80 = 84.

Therefore, 12 + 80 = 84 after applying the distributive property to factor out the greatest common factor of 12.

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The range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -

(ax + b) > (cx + d)    

kx < 6

Given is the inequality statement as -

"The area of a circle is more than 2 square units but less than 4 square units".

The area of a circle is -

{A} = πr²

Mathematically, we can write the inequality statement as -

2 < {A} < 4

2 < πr² < 4

(2/π) < r² < (4/π)

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  

Therefore, the range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

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The value that 50% of the data, is 50 the median.

An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.

Given Data: 42, 44, 50, 54, and 56

The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.

The median value shows that 50% of the data set is above it while 50% is below it also.

So, 50 is the median, and this means that 50% of the data lie above 50.

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When 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

Dividend/Divisor is the quotient.

Divide the dividend by the divisor to obtain the quotient.

Here, Dividend = 1/4

Divisor = 3

Divisor/Dividend =(1/4)/3 = 1/12

So, when 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

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