A carton of apple juice displays the nutritional information shown below.
How many grams of sugar are there in a 200 ml glass of juice?
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I
Apple juice
250 ml contains
Carbohydrate
Sugar
Protein
1
29.5 g
25.5 g
| 0.3 g
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Answer >

\(8f+7-2f=16\\6f=16-7\\6f=9\\f=\frac{9}{6}\)

We know f, now we want the 12f+1

Therefore, Substitute f = 9/6 in 12f+1

\(12(\frac{9}{6})+1\\ = 2*9+1\\=18+1\\=19\)

If you are wondering where 2*9 comes from, it comes from the 12(9/6) and 12 is divided by 6 then we get 2 and multiply the 9 as we get 2*9.

Answer:

the answer is 10 +3x

Step-by-step explanation:

"the answer is not here" what do you mean

Answer:

q = -3/8

Step-by-step explanation:

Clearing out the fractions first simplifies this problem.  The LCD here is 8, so we multiply all three terms of 7/8 = q + 1/2 by 8 and simplify the result:

7 + 8q = 4.  

Combining the constants, we get:  8q = 4 - 7, or 8q = -3.

Finally, solve for q:

q = -3/8

Given the vertices of triangle ABC:

A(2, 5), B(-3, 3), C(2, -1)

Let's dilate the triangle ABC by a scale factor of 2 with a center of dilation of (2, 3)

Here, since we have a scale factor, k, of 2 and center of dilation (2, 3), apply the formula:

(x', y') = k(x - a)+a, k(y - b)+ b

Where:

(a, b) is the center of dilation: (2, 3)

(x, y) is the coordinate

(x' y') is the new coordinate

k is the sale factor = 2

Thus, we have the following:

A(2, 5) ==> 2(2 - 2)+2, 2(5 - 3)+3 ==> 2(0)+2, 2(2)+3 ==> (2, 9)

B(-3, 3) ==> 2(-3 - 2)+2, 2(3 - 3)+3 ==> 2(-5)+2, 2(0)+3 ==> (-8, 3)

C(2, -1) ==> 2(2 - 2)+2, 2(-1 - 3)+3 ==> 2(0)+2, 2(-4)+3 ==> (2, -5)

Therefore, the vertices of triangle ABC after the dilation are:

A'(2, 9), B'(-8, 3), C'(2, -5)

ANSWER:

A'(2, 9), B'(-8, 3), C'(2, -5)

The expected frequency of east campus and passed is C. 42 students

The table for expected frequency is ,

East Campus West Campus Total

Passed (84*100)/22=42 (84*100)/200 =42 84

Failed (116*100)/200=58 (116*100)/22=58 116

Total 100 100 200

Passed = 84×100/200

= 42

Therefore, the expected frequency of East Campus and Passed is 42 students.

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To find the points of horizontal and vertical tangency to a curve, we need to determine the locations where the slope of the curve is zero (horizontal tangency) or the derivative is undefined (vertical tangency).

To find the points of horizontal tangency, we need to find the x-values where the derivative of the function is zero. These points indicate where the slope of the curve is horizontal or flat. To find the points of vertical tangency, we look for the x-values where the derivative is undefined, which typically occurs at vertical asymptotes or sharp corners in the graph.

Using a graphing utility, we can plot the given curve and examine its behavior. The points where the curve appears to be flat horizontally or has a vertical slope can be identified as points of tangency. By analyzing the graph and using calculus techniques, we can determine the precise coordinates of these points.

It is important to note that without a specific equation or graph provided, it is challenging to provide specific points of tangency.

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Answer:

They will have the same amount of sugar in their canisters in 15 days

Step-by-step explanation:

Here in this question, we are concerned with knowing the number of days in which the amount of sugar in both canisters will be the same.

Since we do not know the number of days it will

take, we have to represent it using a variable.

Let the number of days be x days

Now, we are told Li uses 8.4 g per day.

So in x days, the amount user will be 8.4 * x = 8.4x g

Thus, the amount of sugar remaining in her canister after x days will be 128 - 8.4x

For Sue, she uses 12.6 grams each day. So in x days, the amount of sugar used will be 12.6 * x = 12.6x g

So the amount of sugar left in her canister will be 191-12.6x

Since on the xth day , the amount of sugar remaining is same, we can equate the amount of sugar remaining in both canisters. That would be;

128-8.4x =191-12.6x

Collect like terms;

12.6x-8.4x = 191-128

4.2x = 63

x = 63/4.2

x = 15 days

The probability that it will rain both days is \(\frac{1}{4}\).

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1/4

Hence,

The probability that it will rain both days is \(\frac{1}{4}\).

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Answer:

455 red roses

Step-by-step explanation:

Given parameters:

Number of roses sold by florist  = 715

Unknown:

Number of red roses she sold  = ?

Solution:

From the problem statement, we know that;

       7 out of every 11 roses were red.

Let us divide the roses sold into group of 11s;

          In 715 we 65 groups of 11;

if;

            7 out of every 11 roses were red;

  In a group of 65, we will have 65 x 7 red roses  = 455 red roses

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

The radius of convergence of the given series is infinity.

To find the radius of convergence, we use the ratio test, which involves computing the limit of the ratio of successive terms. Applying the ratio test to the given series, we get:

limit as n approaches infinity of [((n+1)!)^k/(k(n+1))!][k!/(n!)^k][x^(n+1)][(kn)!/k!][n!/(kn)!]*[x^n]

Simplifying the expression, we get:

limit as n approaches infinity of [(n+1)/(kx)]*|x|

Since the limit is infinity, the radius of convergence is infinity. This means that the series converges for all values of x.

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Answer:

A = $ 9,257.50

A = P + I where

P (principal) = $ 7,000.00

I (interest) = $ 2,257.50

Step-by-step explanation:

The value of X from the similar triangles above would be = 4. That is option B.

To determine the value of X from the missing part of the similar triangles, the formula that should be used is given below as follows:

VR/VU = VQ/VT

Where;

VR = 33

VU = 44

VQ = 8x-2

VT = 40

That is;

33/44 = 8x-2/40

33×40 = 44(8x-2);

1320 = 352x-88

1320+88 = 352x

1408 = 352x

X = 1408/352

= 4.

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The arc angle x in the circle is 38 degrees.

An inscribed angle in a circle is formed by two chords that have a common end point on the circle.

The inscribed angle A is half of the arc angle x of the circle.

Therefore,

51 + 53 + ∠A = 180

∠A = 180 - 51 - 53

∠A = 76 degrees

Therefore,

x = 1 / 2∠A

Hence,

x = 1 / 2 × 76

x = 38 degrees

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The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

Given: Function f(x) is (x - 5)3(x + 2)2

If a curve touches the x-axis then f(x) = 0

⇒ (x - 5)3(x + 2)2 = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ (x - 5)3 = 0 and (x + 2)2 = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

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Answer:

here's the answer to your question

Answer:

The two digit number is 83

Step-by-step explanation:

Hi

Assume the 2 digit number as xy. Here x is the tens digit and y is the units/ones digit.

Now apply the given information,

x + y = 11    (i)

x - y = 5     (ii)

Lets add both the equations to create a unified equation.

x + y + x - y = 11 + 5

[as there is a positive y and negative y, adding it will lead to its cancellation]

Thus, x + x = 16

2x = 16

x = 16/2

x = 8

To find y, you have to substitute the value of x to either equation (i) or (ii).

x + y = 11    (i)

8 + y = 11

y = 11 - 8

y = 3

[Even if you apply these to the equation (ii)

x - y = 5

8 - y = 5

y = 8 - 5

y = 3

The answer is same ]

Tens digit = 8

Units digit = 3

Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

\(f(x)=x^3\)

If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.

\(f(x)=(x-8)^3\)

graph shifted toward right by \(8\) units right

\(f(x)=(x-8)^3+3\)

graph shifted toward right by \(3\) units up

Thus the new function is:

\(g(x)=(x-8)^3+3\)

If an asset purchased for $46,200 with a useful life of four years and an expected residual value of $6,300 is sold for $32,600 exactly two years after its purchase, the company will record a loss of $3,300.

The straight-line method is used to allocate the cost of an asset evenly over its useful life. In this case, the asset's initial cost is $46,200, and it has a useful life of four years.

The annual depreciation expense is calculated as the difference between the initial cost and the expected residual value, divided by the useful life:

($46,200 - $6,300) / 4 = $9,225 per year

After two years, the accumulated depreciation would be

2 years x $9,225 = $18,450.

If the asset is sold for $32,600, the loss on the sale would be the difference between the selling price and the book value (initial cost - accumulated depreciation):

$32,600 - ($46,200 - $18,450) = $32,600 - $27,750 = $4,850

However, since the loss ($4,850) exceeds the expected residual value ($6,300), the loss recorded would be limited to the difference between the selling price and the expected residual value:

$32,600 - $6,300 = $26,300

Therefore, the company will record a loss of $3,300 ($26,300 - $23,000) when the asset is sold two years after its purchase.

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Answer:

$21,600

Step-by-step explanation:

h(x) = 5000 · (1.08)^4

5000 · 4.32

h(x)= 21,600

Answer:

$6802.44

Step-by-step explanation:

We will replace x with 4.

h(4) = 5000 · (1.08)^4

Use a calculator from here if you don't want stress.

1.08 x 1.08 x 1.08 x 1.08 = 1.36048896

1.36048896 x 5000 = 6802.4448

Since we are looking at the cost, we will approximate to the nearest hundredth.

6802.4448 ≈ 6802.44

The cost is $6802.44.

Answer:

\(x = 1.02 = \frac{51}{50} = 1 \frac{1}{50} \)

Step-by-step explanation:

6(2x - 2.1) = - x - (-8x + 7.5)

12x - 12.6 = - x + 8x - 7.5

12x - 12.6 = 7x - 7.5

12x - 7x = -7.5 + 12.6

5x = 5.1

x = 1,02 = 51/50 = 1 1/50

Answer:

$40

Step-by-step explanation:

The original price is the sale price divided by the difference of 1 minus the result of the discount divided by 100.

Yes, this is correct. An isometry is a transformation that preserves the sample size and shape of an object, meaning that the preimage and image are congruent.

An isometry is a transformation that preserves the size and shape of an object. This means that the preimage and image are congruent, meaning that they have the same size and shape. In order to determine if a transformation is an isometry, one must first identify the preimage and image. Once this has been done, the lengths of the corresponding sides must be compared in order to determine if they are congruent. If the lengths match, then the transformation is an isometry. Additionally, the angles of the preimage and image should also be compared to ensure that they are the same. If all the sides and angles match, then the transformation is an isometry.

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Answer:

3a + (5b + 7c)

Step-by-step explanation:

The answer cannot be 3a(5b +7c) because when the number is immediately before the brackets, it signifies multiplication. therefore the 3a(5b+7c) would be equivalent to 15ab+21ac

the answer cant be 7c(5b+3a) because of the same explanation as the one above, therefore 7c(5b+3a) would be equivalent to 35cb+21ca

the answer finally cant be 8ab+7c because it means that one added 3a and 5b giving you 8 but it cannot be ab because ab is equivalent to a×b, hence, one cant put a multiplied algebraic expression with an added number

The equation equivalent to the the expression (3a + 5b) + 7c is 3a + (5b+7c). Hence, the first option is the correct one.

In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.

For instance, the equation x + y has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.

The first option is correct because it does not affect the main equation rest are not the same as the equation.

For example, let's take the second equation :

3a (5b + 7C)

After solving this option we get 15ab + 21 ac so it is incorrect because it changed the main expression.

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Answer:

C

Step-by-step explanation:

In order to prove congruency using SSS, we need to prove that all three pairs of sides are congruent.

We are already given that EF ≅ HI and that FG ≅ IJ.

Therefore, the last bit of information we need to prove congruency using SSS is that EG ≅ HJ.

Hence, our answer is C.

In linear equation, x ≤ 2 is  the maximum number of outfits Nora can purchase while staying within her budget .

What is linear equation ?

$285.41 for the bike, $17.33 (times 4) for the reflectors, and $31.25 for the gloves.

Then you will subtract the costs ($73.43 each) of the outfits that he buys using a variable to solve for the maximum amount he can buy (x).

580 - 285.41 - (17.33 * 4) - 31.25 - 73.43x ≥ 0

1) Parentheses

580 - 285.41 -  69.32 - 31.25 -73.43x ≥ 0

2) Combine like terms

194.02 - 73.43x ≥ 0

3) Get the variable term alone

-73.43x ≥ - 194.02

4) Divide to solve

   x ≥ - 194.02/ -73.43

      x ≤ 2

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Answer:

Step-by-step explanation:

Image result for Identify the vertex of the following parabola. y = x2 - 4x +1

To find the vertex of a parabola, you first need to find x (or y, if your parabola is sideways) through the formula for the axis of symmetry. Then, you'll use that value to solve for y (or x if your parabola opens to the side) by using the quadratic equation. Those two coordinates are your parabola's vertex.

(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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