Jane's chocolate bar is 51% cocoa. If the weight of the chocolate bar is 76 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.

The answers to the questions on linear combination have been solved below

1. We can start by multiplying both sides by -2 to eliminate the x-term:

2x + 4y = 0

-2(2x + 4y) = -2(0)

-4x - 8y = 0

Now, we have:

-4x - 8y = 0

9x + 4y = 28

We can now use linear combination by adding these two equations to eliminate the y-term:

(-4x - 8y) + (9x + 4y) = 0 + 28

5x = 28

Dividing both sides by 5, we get:

x = 28/5

Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the second equation:

2x + 4y = 0

2(28/5) + 4y = 0

56/5 + 4y = 0

4y = -56/5

y = -14/5

Therefore, the solution to the system of equations is:

x = 28/5

y = -14/5

We can check that these values satisfy both equations:

9x4y = 28

9(28/5)(-14/5) = 28

-352/25 = 28/25 (true)

2x + 4y = 0

2(28/5) + 4(-14/5) = 0

56/5 - 56/5 = 0 (true)

Therefore, the solution is verified.

2. The system of equations is:

5x + 3y = 41

3x - 6y = 9

We can simplify the second equation by dividing both sides by 3:

3x - 6y = 9

x - 2y = 3

Now we can use linear combination by multiplying the first equation by 2 to eliminate the y-term:

2(5x + 3y) = 2(41)

10x + 6y = 82

(x - 2y) + (10x + 6y) = 3 + 82

11x = 85

Dividing both sides by 11, we get:

x = 85/11

Now we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:

5x + 3y = 41

5(85/11) + 3y = 41

425/11 + 3y = 41

3y = 41 - 425/11

3y = (451 - 425)/11

y = 26/33

Therefore, the solution to the system of equations is:

x = 85/11

y = 26/33

We can check that these values satisfy both equations:

5x + 3y = 41

5(85/11) + 3(26/33) = 41

425/11 + 26/11 = 41

451/11 = 41 (true)

3x - 6y = 9

3(85/11) - 6(26/33) = 9

255/11 - 52/11 = 9

203/11 = 9 (true)

Therefore, the solution is verified.

3.

3(x - 2y) = 3(-8)

3x - 6y = -24

3x - 6y = -12

3x - 6y = -24

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

0 = 12

This is a contradiction, since 0 cannot equal 12. Therefore, there is no solution that satisfies both equations.

This means that the system is inconsistent, and there are no solutions.

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Answer:

19

Step-by-step explanation:

If the number of skits is x we can write:

9x + 5 = 176

9x = 171

x = 19

After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.

To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.

Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.

The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.

To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.

Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.

To find the value of s, we take the square root of both sides. So, s = √(7√3).

Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

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If you are allocated 1 TB data to use on your phone, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.

1 Terabyte (TB) = 1,000 Gigabytes (GB

So, 1 TB = 1,000 GB

So, the total data available is 1,000 GB/month

Then, to find how many years it will take until you run out of your quota of 1 GB/month consumption, divide the total data available by the monthly consumption:

1,000 GB/month ÷ 1 GB/month = 1,000 months

To convert months to years, divide by 12:1,000 months ÷ 12 months/year ≈ 83.33 years

Therefore, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.

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Answer:

a) 58.24 square centimeters

b) 5cm

Step-by-step explanation:

a) Area of a parallelogram

The formula for the Area of a parallelogram = Base × Height

Height : 5.2cm

Base : 11.2cm

Area = 5.2 cm × 11.2cm

= 58.24 square centimeters

b) Volume of a cuboid

The formula for the Volume of a cuboid = Length × Width × Height

7cm = Width

3cm = Length

y = Height

Volume = 105cm³

We are to find y

Hence,

105cm³ = 7cm × 3cm × y

y = 105cm³/7cm × 3cm

y = 5cm

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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Let's solve your inequality step-by-step.

h−(−2)≥10

Step 1: Simplify both sides of the inequality.

h+2≥10

Step 2: Subtract 2 from both sides.

h+2−2≥10−2

h≥8

Answer:

h≥8

(Pls mark brainliest)

The solution to the inequality h  -(-2)  ≥  10  is  h  ≥   8

The given inequality is:

h  -(-2)  ≥  10

Simplify the left hand side

h  +  2  ≥  10

Subtract 2 from both sides of the inequality

h  +  2  -  2  ≥  10  -  2

h    ≥   8

The solution to the inequality h  -(-2)  ≥  10  is  h  ≥   8

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If you eliminate your discretionary expenses, you can save $592.88 per month.

To calculate your total realized income, we can start by finding your gross income per week and then multiply it by the number of weeks in a month.

Gross income per week:

$11.75/hr * 40 hr/wk = $470/week

Gross income per month:

$470/week * 4 weeks = $1,880/month

Now, let's calculate your deductions:

FICA (7.65%):

$1,880/month * 7.65% = $143.82/month

Federal tax withholding (10.75%):

$1,880/month * 10.75% = $202.30/month

State tax withholding (7.5%):

$1,880/month * 7.5% = $141/month

Total deductions:

$143.82/month + $202.30/month + $141/month = $487.12/month

To find your total realized income, subtract the total deductions from your gross income:

Total realized income:

$1,880/month - $487.12/month = $1,392.88/month

Next, let's calculate your fixed expenses. Fixed expenses typically include essential costs such as rent, utilities, insurance, and loan payments. Since we don't have specific values for your fixed expenses, let's assume they amount to $800/month.

Fixed expenses:

$800/month

Finally, to calculate your discretionary expenses, we'll subtract your fixed expenses from your total realized income:

Discretionary expenses:

$1,392.88/month - $800/month = $592.88/month

If you eliminate your discretionary expenses, you can put the entire discretionary expenses amount towards savings each month:

Savings per month:

$592.88/month

Therefore, if you eliminate your discretionary expenses, you can save $592.88 per month.

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Answer:

functions: first one, third one, fifth one, seventh one, eigth one

the rest are not function

Step-by-step explanation:

if it is a function it either passes the line test or it doesnt have two outputs

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer:

Number of people in each car = x = 8

Number of people in each van = y = 22

Step-by-step explanation:

Let

Number of people in each car = x

Number of people in each van = y

8x + 8y = 240 (1)

4x + y = 54 (2)

From (2)

4x + y = 54 (2)

y = 54 - 4x

Substitute y = 54 - 4x into (1)

8x + 8y = 240 (1)

8x + 8(54 - 4x) = 240

8x + 432 - 32x = 240

8x - 32x = 240 - 432

-24x = -192

x = -192/-24

x = 8

Substitute x = 8 into (2)

4x + y = 54 (2)

4(8) + y = 54

32 + y = 54

y = 54 - 32

y = 22

Number of people in each car = x = 8

Number of people in each van = y = 22

Answer:

D....because its the odd one out and makes since :)

Answer:

0

Step-by-step explanation:

\(m=\frac{-21-(-21)}{-14-36}\)

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

As we know, opposite sides of a cyclic quadrilateral add up to 180°, let's use this property to find Angle L

\(\qquad \tt \dashrightarrow \: \angle L + 68 = 180\)

\(\qquad \tt \dashrightarrow \: \angle L = 180 - 68\)

\(\qquad \tt \dashrightarrow \: \angle L = 112 \degree\)

So, measure of Angle L is 112°

Answer:

The dolphin is -8 feet below sea level

Step-by-step explanation:

Start a -3 feet below sea level. Then subtract the -9 from when the dolphin dives. Then add the +4 feet. And you'll get -8. Hope this helps:)

The dolphin’s final elevation relative to sea level will be -8 feet.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a dolphin is swimming 3 feet below sea level. It dives down 9 feet to catch some fish. Then the dolphin swims 4 feet up toward the surface with its catch.

The elevation of the Dolphin is:-

Elevation = -3 - 9 + 4

Elevation  = -8 feet

Therefore, the dolphin’s final elevation relative to sea level will be -8 feet.

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Based on the description given by Cristina, the shape she is describing is an equilateral triangle. Equilateral triangles are triangles where all three sides are of equal length. In this case, each side is 4 centimeters long.

To draw this triangle, start by drawing a straight line with a ruler. Then, using a protractor or by estimating, draw two lines that intersect with the first line to form a triangle. Make sure that all three angles are not right angles, as Cristina stated.

Next, label each side with its corresponding length of 4 centimeters. You can do this by using a ruler and measuring each side carefully, or by estimating if you don't have a ruler handy. Label each side with the number "4" to indicate its length.

It is important to note that equilateral triangles are a type of regular polygon, meaning that all angles and sides are equal. In the case of an equilateral triangle, all angles are also 60 degrees. This information is not necessary for drawing the shape and labeling the sides, but it is interesting to know nonetheless.

In conclusion, Cristina's shape is an equilateral triangle with each side measuring 4 centimeters.

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Answer:

c

Step-by-step explanation:

just got it correct

The value of binomial expansion of expression (2x - 3)⁵ is,

⇒ (2x)⁵ – 15(2x)⁴ + 90(2x)³ – 270(2x)² + 405(2x) – 243

We have to given that;

The expression is,

⇒ (2x - 3)⁵

Now, We know that;

The formula of binomial expansion is,

⇒ (x + y)ⁿ = (ⁿ₀) xⁿy⁰ + (ⁿ₁) xⁿ⁻¹y¹ + (ⁿ₂) xⁿ⁻²y² + ...... + yⁿx⁰

Hence, The value of binomial expansion of (2x - 3)⁵ is,

⇒ (2x - 3)⁵

⇒ (2x + (- 3))⁵

⇒ (2x)⁵ – 15(2x)⁴ + 90(2x)³ – 270(2x)² + 405(2x) – 243

Thus, The value of binomial expansion of expression (2x - 3)⁵ is,

⇒ (2x)⁵ – 15(2x)⁴ + 90(2x)³ – 270(2x)² + 405(2x) – 243

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the only one i could figure out was that q= 24 and i think r=48

Remember that

the distance between two points is equal to

In this problem we have

d=6 units

A(-2,5)

B(x,y)

substitute the given values in the expression above

squared both sides

Find out three possible coordinates of point B

First and Second possibles coordinate

I will assume the x-coordinate

For x=-2

substitute in the expression above and solve for y

36=(y-5)^2

square root both sides

Values of y are

y=11 and y=-1

therefore

we have the coordinates of point B

(-2,11) and (-2,-1)

Find out the third possible coordinate of point B

I will assume the y-coordinate

For y=5

36=(x+2)^2

square root both sides

the values of x are

x=4 and x=-8

the possibles values of B are

(4,5) and (-8,5)

therefore

(-2,11)

(-2,-1)

(4,5)

(-8,5)

Part 2

Find out the midpoint of each of those possible segments

The formula to calculate the midpoint between two points is equal to

so

For A(-2,5) and B(-2,11)

substitute in the formula-------> M(-2,8)

For A(-2,5) and B(-2,-1) ------> M(-2,2)

For A(-2,5) and B(4,5) -------> M(1,5)

For A(-2,5) and B(-8,5) -----> M(-5,5)

Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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The only true statement is 2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4.

option A.

BODMAS is an acronym that stands for "Brackets, Orders, Division, Multiplication, Addition and Subtraction".

The rule of BODMAS states that when you have a mathematical expression that involves multiple arithmetic operations, you need to perform them in a certain order. You should start by evaluating anything inside brackets or parentheses first. Then, you should work out any exponents or square roots. After that, you should perform any division or multiplication from left to right, and finally, you should perform any addition or subtraction from left to right.

If we apply the rule of BODMAS to all the given options, we would notice that only option 1 is true.

2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4

L.H.S ⇒ 2 x (6) - 6

= 12 - 6

= 6

R.H.S ⇒ 14 ÷ (3.5 x 2 ) + 4

= 14 ÷ (7) + 4

= 2 + 4

= 6

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The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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.

Answer:

3 cup

Step-by-step explanation:

Answer:

Step-by-step explanation:

 From \(\frac{1}{8}\) cup of yoghurt  Arianys can   make  = 1  smoothie

From 2  cup of yoghurt  Arianys can  make  = \((\frac{1}{1/8} ) *2\)  smoothie  

From 2  cup of yoghurt  Arianys can  make  = 16 smoothie  

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θ is in quadrant I, so cos(θ) and sin(θ) and hence tan(θ) are all positive.

Recall that

sec²(θ) = 1 + tan²(θ)

We have

cos(θ) = 2/√14   ⇒   sec(θ) = √14/2 = √(7/2)

Then

tan(θ) = +√(sec²(θ) - 1) = √(5/2)

Also recall the identities

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

from which we get

tan(x + y) = (sin(x) cos(y) + cos(x) sin(y)) / (cos(x) cos(y) - sin(x) sin(y))

tan(x + y) = (tan(x) + tan(y)) / (1 - tan(x) tan(y))

so that

tan(2θ) = 2 tan(θ) / (1 - tan²(θ)) = -(2√10)/3

Answer: The first one 5/10 is 0.5 or 50% 5÷10. The second one 5/100 is 0.05 or 500%. The third one 5/1000 is 0.005 or 5000%.

Step-by-step explanation:

All you have to do is divide and you do that for all of them. Also did you know quotient means the answer to a division question. Wow! Also, if you see that all I did was add another zero in the middle of the decimals is because That is Decimal Place value. Here is a picture of that just in case.  The last answer for the very bottom one is what I just said about decimal place value so here is the reflection: When dividing by tens using decimals always be sure to use place value. Thank you I was happy to help!

we conclude the national average is greater than the alaska average  if the population standard deviation in each case is 3

Nationwide scores as  n1=1000, ` = 21.4 ,σ1 = 3

Carolina scores as n2=500,  ` = 21.2 ,σ2 = 3

So from here we can say

µ represents population mean.

represent population mean for nationwide scores.

represents population mean for Carolina scores.

is  =  and for   (claim)

Given Question is incomplete, Complete Question here,

a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?

use α=0.01 and  for the nationwide mean act score.

State the hypotheses and identify the claim.

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Answer: 200+300=500

Step-by-step explanation:

or 300+200=500