PLEASE HELP ME

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the expressions with their simplified forms.

Answer:

Step-by-step explanation:

integrate with respect to x

Area is symmetric so will be twice the integral from zero to 1

( I cannot seem to figure out how to make the lower limit negative in this editor)

\(A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx\))

\(A = 2\int\limits^1_0 {-3x^2 + 3} \, dx\)

\(A = 6\int\limits^1_0 {-x^2 + 1} \, dx\)

A = 6(-⅓x³ + x)\(\left \| {{x=1} \atop {x=0}} \right.\)

A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))

A = 6(⅔)

A = 4 units²

Answer:

\(3.4x\le 100\)

Step-by-step explanation:

Given that,

Michael is cutting a 100-yard ribbon into pieces 3.4 yards long.

Michael says that an inequality that represents his project is 3.4x 100.

Let Michael cuts the ribbon in x no of variables. It is given as :

3.4x is the total length of all the pieces together

i.e.

3.4x is less than or equal to 100.

The required equation that represents the given scanario is :

\(3.4x\le 100\)

Answer:

Step-by-step explanation:

Sample Response: The variable, x, is the number of pieces of ribbon Michael cuts. Since each piece is 3.4 yards long, 3.4x is the total length of all the pieces together. This total length cannot be more than the 100 yards of ribbon he has, so 3.4x must be less than or equal to 100.

Answer:

Equation: y = -4x + 1

Slope: -4

Y-intercept: y = 1

Step-by-step explanation:

To find the equation of the line you need the gradient and the y-intercept

To find the gradient we need to divide the change in y by the change in x:

As the graph has a negative correlation the gradient would have a minus which is why it would be -4!

To find the y-intercept we need to find the number on the y-axis that the line crosses which in this case would be y = 1!!

Hope this helps, have a great day!!

Answer:

equation:y=4x+1

y-intercept:1

slope:4/1 or 4

Step-by-step explanation

the equation has to be in slope intercept form which is \(y=mx+b\) where m is the slope and b is the y-intercept. the y-intercept is when x is 0 in this case when x is 0 y is 1 (0,1) so the y-intercept is 1. the slope is rise/run so pick two points that cross the grid perfectly and count the units rise and run. this line rises 4 and runs 1 so the slope is 4/1 so 4 hence the equation \(y=4x+1\)

In summary a) sine(0°) = 0, cosine(0°) = 1, tangent(0°) = 0/1 = 0, b) sine(360°) = 0, cosine(360°) = 1, tangent(360°) = 0/1 = 0, c) sine(450°) = 1, cosine(450°) = 0, tangent(450°) is undefined

Why is it?

In the unit circle, a 0° angle lies on the positive x-axis, while a 360° angle completes one full revolution and returns to the same point on the unit circle as 0°. Similarly, a 450° angle completes 1 full revolution and moves an additional 90° counterclockwise.

Here are the sine, cosine, and tangent values for these angles:

For 0° and 360°, the values are the same since they lie on the positive x-axis:

sine(0°) = 0

cosine(0°) = 1

tangent(0°) = 0/1 = 0

For 450°, we can subtract 360° to get an equivalent angle:

sine(450°) = sine(450° - 360°) = sine(90°) = 1

cosine(450°) = cosine(450° - 360°) = cosine(90°) = 0

tangent(450°) = tangent(450° - 360°) = tangent(90°) is undefined (since cosine(90°) = 0)

Therefore, the values for the sine, cosine, and tangent functions of the angles a) 0°, b) 360°, and c) 450° are:

a) sine(0°) = 0, cosine(0°) = 1, tangent(0°) = 0/1 = 0

b) sine(360°) = 0, cosine(360°) = 1, tangent(360°) = 0/1 = 0

c) sine(450°) = 1, cosine(450°) = 0, tangent(450°) is undefined

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The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.

To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:

30% of $86 = 0.3 x $86 = $25.80

Therefore, Pedro will need to pay $25.80 for shipping and handling.

Answer:

BAP=12

ABP=32.5

BCP=45.5

Answer:

arithmetic sequence

is my answer

Hey there!

“3(a+b)+15-a+2b”

First DISTRIBUTE

3(a) + 3(b) + 15 - a + 2b

3(a) = 3a

3(b) = 3b

New EQUATION

3a + 3b + 15 - a + 2b

COMBINE your LIKE TERMS

(3a - a) + (3b + 2b) + (15)

~NOTE: “a” is understood as an invisible 1!~

(3a - 1a) = 2a

(3b + 2b) = 5b

(15) = 15

Therefore, your answer is: 2a + 5b + 15 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

The given data exists 46, 34, 25, 31, 15, 50, 37, 42

Mean, μ = 35

Variance, σ² = 114.5

Standard deviation, σ = 10.7004

A standard deviation (or σ) exists as a measure of how dispersed the data exists concerning the mean. Low standard deviation indicates data exist clustered about the mean, and high standard deviation suggests data exist better spread out.

Given data 46, 34, 25, 31, 15, 50, 37, 42

The number of elements exists n = 8 (8 numbers in the set)

To calculate the mean,

(46+34+25+31+15+50+37+42)/8 = 280/8 = 35

μ = 35

To calculate the variance,

Sum of the squared difference between each number of the set and the mean divided by the number of elements of the sample minus one.

Variance = [(46-35)² + (34-35)² + (25-35)² + (31-35)² + (15-35)²+ (50-35)² + (37-35)² + (42-35)²]/8

= 916/8

= 114.5

σ² = 114.5

Standard deviation exists as the square root of the variance.

σ² = 114.5

√σ² = √114.5

σ = 10.7004

Therefore, the standard deviation exists at 10.70.

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Answer:

The marked price of the watch is $2,702.27.

Step-by-step explanation:

Since allowing 20% discount on the marked price of a watch, the value of the watch will be Rs. 2378, to determine, if the VAT of 10% is added, it's marked price, the following calculation must be performed:

1 - 0.2 = 0.8

0.8 x 1.1 = 2378

0.88 = 2378

0.88 = 2378

0.8 = X

0.8 x 2378 / 0.88 = X

1,902.4 / 0.88 = X

2,161.81 = X

0.8 = 2,161.81

1 = X

2,161.81 / 0.8 = X

2,702.27 = X

Therefore, the marked price of the watch is 2,702.27.

Answer:

hdisiejehe

Step-by-step explanation:

step sister

Answer: 17/24

Step-by-step explanation:

let x be the fertilizer used in the flower bed

to find how much he has left

1 3/8 - x = 2/3

the fraction 1 3/8 we can write as 11/8

11/8 - x = 2/3

11/8 -2/3= x

we need the common denominator between 8 and 3, which is 24

33/24-16/24=17/24

Solution

For this case we can do the following:

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS  is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.

Here,

Given:

we have to solve the system of equations given. .Each equation is added together to remove the variable Y.

2x + y = 4  

+

3x - y = 6

________

=> 5x =10

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

x =10 / 5 = 2

⇒ x=2

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Answer:

Haley completed 11/12 and has yet to finish 1/12 of her homework.

Step-by-step explanation:

\(\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}\)

Haley completed 11/12 of her homework.  To find how much she has left is simple subtraction:

\(\frac{12}{12} - \frac{11}{12} = \frac{1}{12}\)

So Haley has 1/12 of her homework left to complete.

For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8

Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.

To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.

According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:

4 lemons / 5 cups = 0.8 lemons per cup of lemonade

This means that for every cup of lemonade, 0.8 lemons are used.

Alternatively, we can also express this rate as a fraction, which gives us:

0.8 lemons / 1 cup of lemonade

Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.

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Answer:

Morgan.

Step-by-step explanation:

The applicant who has the highest z-score would be the one who performs best.

z-score = (s - m)/ d       where  s = score, m = mean and d = the standard deviation.

Morgan's z-score = (81.7 - 60.9) / 13

= 1.6

Frankie's = (314.8 - 294) / 26

= 0.8.

Rebecca's = (7.5 - 7.2) / 0.6

= 0.5.

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

Answer: 162°

Step-by-step explanation:

To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.

First, a percent divided by 100 becomes a decimal.

       45% / 100 = 0.45

Next, "of" means multiplication in mathematics.

       0.45 * 360 = 162

The central angle will be 162°.

Answer:

Step 4

Step-by-step explanation:

because 100/20=5

so 60/5=12

⟨a⟩.Given that

Radius of the circle (r) = 21 cm

We know that

Area of a circle whose radius is r units is

πr² sq.units

Area of the given circle

⇛A = (22/7)×21² cm²

⇛A = (22/7)×21×21 cm²

⇛A = 22×3×21 cm²

⇛A = 1386 cm²

Answer: Area of the circle = 1386 cm².

⟨b⟩.Given that

Diameter of the circle (d) = 35 cm

Radius = Diameter/2

⇛Radius = 35/2 cm

Area of a circle whose radius is r units is

πr² sq.units

Area of the given circle

⇛A = (22/7)×(35/2)² cm²

⇛A = (22/7)×(35/2)×(35/2) cm²

⇛A = (22×35×35)/(7×2×2) cm²

⇛A = 11×35×5/2 cm²

⇛A = 1925/2 cm²

⇛A = 962.5 cm²

Answer: Area of the circle = 962.5 cm².

(or)

Diameter of the circle (d) = 35 cm

We know that

Area of a circle whose diameter is d units is πd²/4 sq.units

Area of the given circle

⇛A = (22/7)×(35)²/4 cm²

⇛A = (22/7)×(1225/4) cm²

⇛A = (22×1225)/(4×7) cm²

⇛A = (11×175)/2 cm²

⇛A = 1925/2 cm²

⇛A = 962.5 cm²

Answer: Area of the circle = 962.5 cm²

⟨c⟩.Given that

Circumference of the circle (C) = 484 cm

We know that

Circumference of a circle whose radius is r units is 2πr units

⇛2πr = 484

⇛2×(22/7)×r = 484

⇛(44/7)×r = 484

⇛r = 484×(7/44)

⇛r = 11×7

⇛r = 77 cm

Area of a circle whose radius is r units is

πr² sq.units

Area of the given circle

⇛A = (22/7)×(77)² cm²

⇛A = (22/7)×77×77 cm²

⇛A = (22×77×77)/7 cm²

⇛A = 22×77×11 cm²

⇛A = 18634 cm²

Answer: Area of the circle = 18634 cm²

(or)

Circumference of the circle (C) = 484 cm

We know that

Area of a circle whose circumference is C units is C²/4π units

Area of the circle

⇛A = (484)²/{4×(22/7)}

⇛A = (484×484)/(88/7)

⇛A = (484×484)×(7/88)

⇛A = 1639792/88

⇛A = 18634 cm²

Answer: Area of the circle = 18634 cm²

Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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Answer:

As the givens set A contains 24 elements.

Therefore,

The Cardinality of the set A = 24

Step-by-step explanation:

Let the given set is A

A = {x: x is a positive counting number less 25}

The set of natural numbers is often termed as the Counting number set.

Thus,

Set A will be:

\(A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}\)

The Cardinality of the set

The Cardinality of the set represents the total number of elements in a given set.

As the givens set A contains 24 elements.

Therefore,

The Cardinality of the set A = 24

In this scenario, the old man's intention is to help the three sons by giving them his ailing cow, Cotty.

The sons initially protest and are not ready to accept the cow because it is old, pale, lame, and weak. However, the old man insists on them taking Cotty and pushes the cow to join their other cattle.

The sons might consider the possibility of nursing Cotty back to health. With proper care, medication, and attention, the cow's condition could improve over time. This would require additional effort and resources from the sons, but it could result in a healthier and more productive cow in the future.

In the end, the old man goes home with his own cow, Cotty, suggesting that he might have intended the sons to take care of her temporarily or with the understanding that they would eventually return her.

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