Mary works for a company that pays time and a half for hours over 40 in a week and double time for holidays. This week she worked 8 hours on Monday (which was a holiday), 10 hours on Tuesday, 10 hours on Wednesday, 9 hours on Thursday, and 8 hours on Friday. If Mary earns $8 per hour, what is the total of Mary’s earnings for the week?

If you buy three hamburgers, the cost of each hamburger is $2.50.

One hamburger costs $2.50.

To determine the price of one hamburger, first take the total cost of all three hamburgers, which is $7.50.

Then, divide the total cost of all three hamburgers by the number of hamburgers, which is three.

This yields $2.50, which is the price of one hamburger.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

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A cylinder has volume of 45 and radius 3, the height of the cylinder is 5 units.

The formula for the volume of a cylinder is given by V =

[tex]\pi r^2 h,[/tex]

where V is the volume, r is the radius, and h is the height.

In this case, we know that the volume is 45

[tex]\pi[/tex]

and the radius is 3. We can plug these values into the formula and solve for the height:

[tex]45 \pi = \pi (3)^2 h[/tex]

Simplifying the right-hand side of the equation:

Dividing both sides by 9

[tex]h = \frac{45 \pi}{9 \pi} = 5[/tex]

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Therefore , the solution of the given problem of unitary comes out to be the school supply business may distribute 500 chalkboards.

By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.

Here,

Assuming each chalkboard costs the company $5 and they can spend up to $2,500 on the chalkboards:

Number of chalkboards Equals Total allowable spending / Chalkboard cost

=> Chalkboard count =  $2,500 / $5

=> 500 chalkboards are present.

Consequently, the school supply business may distribute 500 chalkboards.

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Therefore, the other two zeros of the function are approximately -1.802 and -0.198.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.

by the question.

To find the zeros of the function, we need to solve the equation F(x) = 0. Since the given function has one known zero, which is 2 under the root, we can use this to simplify the expression.

Let's start by factoring out (x - 2^(1/2)) from the expression:

[tex]F(x) = (x - 2^(1/2))(6x^2 + 12x + 2^(1/2) - 4\sqrt{2})[/tex]

Now we need to find the zeros of the quadratic factor:

[tex]6x^2 + 12x + 2^(1/2) - 4\sqrt{2} = 0[/tex]

Using the quadratic formula, we get:

[tex]x = [-12±\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2}))]/(2(6))[/tex]

Simplifying the expression under the square root gives:

[tex]\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2})) = \sqrt(144 - 24\sqrt{2} - 96) = sqrt(48 - 24\sqrt{2})[/tex]

So, the zeros of the function are:

[tex]x = 2^(1/2), (-1 -\sqrt{6 + 3\sqrt{2}})/3, (-1 + \sqrt{6 + 3\sqrt{2}})/3[/tex]

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Answer:

3.87 miles

Step-by-step explanation:

The attached figure gives the relative locations of the courthouse, the library and the pool.

The three locations represent a right triangle with the distance between courthouse - pool as the hypotenuse and the distance between courthouse - library as the vertical leg

By the Pythagorean theorem if c is the hypotenuse and a, b the other two legs

[tex]c^2 = a^2 + b^2[/tex]

a = distance between courthouse and library = 7 miles
c = distance between courthouse  and pool = 8 miles
and we have to find b

So plugging in known values
[tex]8^2 = 7^2 + b^2\\\\b^2 = 8^2 - 7^2\\\\b^2 = 64 - 49\\\\b^2 = 15\\\\b= \sqrt{15} = 3.87298 \approx 3.87 \;miles[/tex]

The angle that has the sine ratio, 4/5, is: A. Angle P.

Sine Ratio:

The sine ratio is the ratio of the side opposite the hypotenuse of a right triangle to a given reference angle. When the ratio is found using the opposite and the hypotenuse, we call it the sine ratio rather than the tangent ratio.

Example:

Then we say that the sine of 45 degrees is equal to 0.707. In short, we can use the notation sin instead of sine and write sin(45 degrees) = 0.707

In general, the sine of angle A = leg length of opposite angle A / hypocenter

sin(A ) = opposite / hypotenuse

Given:

sine ratio of 4/5, then it means:

Opposite side (side directly opposite to the reference angle) = 4

Hypotenuse (longest side) = 5.

Thus, in the image given, using P as the reference angle, the sine ratio of P is:

QR/PQ

= 16/20 = 4/5

Therefore, the angle with the sine ratio of 4/5 is: A (P)

Complete Question:

Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?

A. P

B. Q

C. T

D. U

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The evaluation of the statements and the values of the side lengths and angles of the quadrilateral are;

A. 1.) [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False

2.) [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]; True

3. ∠BDA ≅ ∠BDC; False

4. ∠BOA ≅ ∠CBD; False

5.) m∠BAD + m∠ADC = 180°; True

6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]; True

7.) ∠BCD = 90°; False

8.) ∠BOA = 90°; True

9.) ∠ABD = 45°; False'

10. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]; True

B. I. ∠NAL = 124°

∠CNL = 28°

∠CLN = 28°

∠NLA = 28°

II. 5.) ∠1 = 45°

∠2 = 90°

III 7.) [tex]\overline{OP}[/tex] = 7 cm

8.) [tex]\overline{OE}[/tex] = 12 cm

9.) [tex]\overline{EO}[/tex] = 13 cm

10. ∠5 = 60°

A quadrilateral is a four sided polygon.

The evaluation of the quadrilaterals are presented as follows;

1. [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]

[tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] are the diagonals of the rhombus, and the properties of a rhombus indicates that the diagonals of a rhombus are not congruent, the statement,  [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex] is therefore false

[tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False

2.  [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]

[tex]\overline{BO}[/tex] and [tex]\overline{CO}[/tex] are segments on the two diagonals of the rhombus which are perpendicular. The statement, [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex] is therefore; True

3. ∠BDA ≅ ∠BDC

∠ADC = ∠BDA + ∠BDC

The diagonals of a rhombus do not bisect the vertex angles, therefore;

m∠BDA ≠ m∠BDC

∠BDA [tex]\ncong[/tex] ∠BDC

The statement, ∠BDA ≅ ∠BDC, therefore is; False

4.) ∠BOA ≅ ∠CBD

The diagonals of a rhombus are perpendicular, therefore angle ∠BOA = 90°

∠CBD is an interior angle of the rhombus, and ∠CBD = 90° if the rhombus is a square.

The specified rhombus is not shaped like a square. The statement, ∠BOA ≅ ∠CBD, is therefore; False

5.) m∠BAD + m∠ADC = 180°

The angles, ∠BAD and ∠ADC are adjacent interior angles, therefore, according to the properties of a rhombus, m∠BAD + m∠ADC = 180°. The statement is therefore; True

6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]

The segments [tex]\overline{CO}[/tex] and [tex]\overline{AO}[/tex] are formed by the intersection of the diagonal [tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] at O. The diagonals of a rhombus bisect each other. The statement, [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex] is therefore; True

7.) ∠BCD = 90°

∠BCD = 90° when the rhombus is a square, the statement is therefore False

8.) ∠BOA = 90°

∠BOA is formed by the intersection of the diagonals of a rhombus, which are perpendicular to each other. Therefore, ∠BOA = 90°, the statement is therefore; True

9) ∠ABO = 45°

∠ABO = 45° if the rhombus is a square, the statement is therefore; False or more information required

10) [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]

[tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are side lengths of the rhombus and are therefore, congruent. The statement, [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is; True

B. I. ∠NAL and ∠CNA are supplementary, therefore;

∠NAL + ∠CNA = 180°

∠NAL= 180° - ∠CNA

∠CNA = 56°

∠NAL= 180° - 56° = 124°

2.) Whereby the diagonal of the rhombus bisects the angle ∠CNA, we get;

∠CNL = ∠ANL = 56°/2 = 28°

3.) ∠CLN = ∠CNL = 28°

4.) ∠NLA = ∠CNL = 28°

II. The properties of a square indicates that we get;

The diagonals of a square bisect the vertex angles, therefore;

∠1 which is the angle formed by the the diagonal [tex]\overline{AT}[/tex] that bisects the angle ∠CAR = 90° is; ∠1 = 90°/2 = 45°

6.) The diagonals of a square are perpendicular, therefore;

∠2 = 90°

III. 7.) The facing sides of a rectangle are congruent, therefore;

[tex]\overline{HE}[/tex] ≅ [tex]\overline{OP}[/tex]

[tex]\overline{OP}[/tex] = [tex]\overline{HE}[/tex] = 7 cm

8.) The diagonals of a square have the same length, therefore;

The length of [tex]\overline{OE}[/tex] = The length of [tex]\overline{HP}[/tex] = 12 cm

9.) Pythagorean Theorem indicates, that we get;

[tex]\overline{EO}[/tex] = √([tex]\overline{OP}[/tex]² + [tex]\overline{EP}[/tex]²)

Therefore;  [tex]\overline{EO}[/tex] = √(5² + 12²) = 13

[tex]\overline{EO}[/tex] = 13 cm

10.) ∠2 and ∠5 are vertical angles, therefore;

∠2 ≅ ∠5

∠5 ≅ ∠2 (Symmetric property)

m∠5 = m∠2 = 60° (Definition of congruency)

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Answer:

The maximum number of possible extreme values for a fourth-degree polynomial function like f(x) = x^4 + x^3 - 7x^2 - x + 6 is 3.

To determine the number of extreme values, we can find the derivative of the function f(x) and set it equal to zero to solve for critical points.

f(x) = x^4 + x^3 - 7x^2 - x + 6

f'(x) = 4x^3 + 3x^2 - 14x - 1

Setting f'(x) = 0, we can solve for critical points:

4x^3 + 3x^2 - 14x - 1 = 0

Using numerical methods like the cubic formula or numerical approximation techniques, we can find that there are three real roots for this equation, which correspond to the critical points of f(x).

Since f(x) is a fourth-degree polynomial, we know that it has at most four critical points. Therefore, the maximum number of extreme values for f(x) is three, which can be achieved if the function has two local maxima and one local minimum or one local maximum and two local minima.

Answer: 412.5 ml

Step-by-step explanation:

500 ( 1 - 25%) ( 1 + 10%)

= 412.5 ml

Answer:

412.5 ml

Step-by-step explanation:

To decrease 500 ml by 25%, you would need to multiply 500 by 0.25 to find the amount of decrease:

Subtract that amount from the original value:

Therefore decreasing 500 ml by 25% would give us 375 ml.

To then increase this value by 10%, you would multiply it by 0.10 to find the amount of increase:

Now, add that amount to the previous value:

Therefore, if you decrease 500 ml by 25% and then increase it by 10%, the final result is 412.5 ml.

Answer:If the bridge is divided into four equal parts, then the length of each part can be found by dividing the total length of the bridge by 4. Therefore:

Length of each part = Total length of the bridge / Number of parts

Length of each part = 440 m / 4

Length of each part = 110 m

Therefore, each part of the bridge is 110 metres long.

Step-by-step explanation:

Answer:78.9

Step-by-step explanation:

78.9x 0896968

It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The area of the shop can be found by multiplying its length by its width:

Area = Length x Width

        = 8 meters x 12 meters

        = 96 square meters

To recarpet the entire shop, we need to purchase 96 square meters of carpet.

If the carpet costs = $3.00 per square meter.

The total cost can be found by multiplying the area by the cost per square meter:

Total cost = Area x Cost per square meter

Total cost = 96 square meters x $3.00 per square meter

Total cost = $288.00

Therefore,

It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.

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The final result of the subtraction is: -4 ÷ (1 - 5[tex]x^{2}[/tex])

What is Algebraic expression ?

A cοmbinatiοn οf variables and cοnstants is an algebraic expressiοn.

To subtract the expression:

(-10 ÷ (2 - 10[tex]x^{2}[/tex])) - (-2 ÷ (2 - 10[tex]x^{2}[/tex])))

we need to first simplify the denominator by factoring out a common factor of 2:

2 - 10[tex]x^{2}[/tex]= 2(1 - 5[tex]x^{2}[/tex])

Now we can write the expression as:

(-10 ÷ [2(1 - 5[tex]x^{2}[/tex])]) - (-2 ÷ [2(1 - 5[tex]x^{2}[/tex])])

which simplifies to:

(-5 ÷ [1 - 5[tex]x^{2}[/tex]]) - (-1 ÷ [1 - 5[tex]x^{2}[/tex]])

Using the fact that subtracting a negative is the same as adding a positive, we can rewrite this as:

(-5 + 1) ÷ [1 - 5[tex]x^{2}[/tex]]

which equals:

-4 ÷ [1 - 5[tex]x^{2}[/tex]]

Therefore, the final result of the subtraction is: -4 ÷(1 - 5[tex]x^{2}[/tex])

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Complete Answer:

Subtract the expression [tex]$(-10\div(2-10x^{2}))-(-2\div(2-10x^{2}))$[/tex]

Option B is the true statement based on the given information by solving the method of average.

In mathematics, the average (also called the arithmetic mean) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of values in the set.

Since both tests had a median score of 78, we know that there were nine scores below 78 and nine scores above 78 on each test.

If the original test had a range of 20, that means the highest score was 20 points above the lowest score. Therefore, the lowest score on the original test was 78 - 10 = 68, and the highest score was 68 + 20 = 88.

If the retest had a range of 2, that means the highest score was only 1 point above the lowest score. Therefore, the lowest score on the retest was 78 - 1 = 77, and the highest score was 77 + 2 = 79.

We don't know the mean score for either test, so we cannot determine if option A is true or false. We also don't know if any student scored exactly 78 on the retest, so we cannot determine if option C is true or false. Finally, we know that the highest score on the retest is 79, so option D is false.

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Answer:

Step-by-step explanation:

If the ratio of cows to sheep is 3:7, then there are 210 sheep on the farm if there are 90 cows.

The first step is to write out the parameters:

Now, the number of sheep on the farm can be calculated as follows:

Hence there are 210 sheep on the farm

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The intermediate step in the form (x+a)²=b as a result of completing the square is: (x + 7)² = -4. We can calculate it in the following manner.

To complete the square for the equation x² + 22x = 8x - 53, we need to move the constant term to the right side and the linear term to the left side, and then add a constant value to both sides so that the left side becomes a perfect square trinomial. The steps are as follows:

x² + 22x = 8x - 53 (original equation)

x² + 14x = -53 (subtract 8x from both sides)

x² + 14x + (14/2)² = -53 + (14/2)² (add (14/2)² to both sides)

x² + 14x + 49 = -53 + 49 (simplify)

(x + 7)² = -4 (factor the left side and simplify the right side)

So the intermediate step in the form (x+a)²=b as a result of completing the square is:

(x + 7)² = -4

Note that this equation has no real solutions, since the square of any real number is always nonnegative, whereas the right side of this equation is negative.

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Answer:

Below

Step-by-step explanation:

2x + 3y =3       since  x = 6y+24  put that in for 'x'

2 ( 6y+24) + 3y = 3

12 y + 48 + 3y = 3

15 y + 48 = 3

15 y = -45

y = -3     <======use this value of 'y' in one of the equations to calculate the corresponding 'x' value :

 x = 6y + 24

 x = 6(-3) + 24

 x = 6

The number of hazardous waste sites in State Y in the year 2000 was 21.

Let n be the number of hazardous waste sites in State Y.

Based on the problem statement, we have

2n - 8 = 34

So, we have

2n = 42

Divide

n = 21

Hence, the waste sites in State Y in the year 2000 was 21.

Given that

6x + 1.6 = 58

Apply the subtraction property

6x = 56.4

Apply the division property

x = 9.4

Here, we have the bar diagram

Adding the terms in the bar, we have

n + n + n + 8 = 53

3n + 8 = 53

Apply the subtraction property

3n = 45

Apply the division property

n = 15

Hence, the bar equation is 3n + 8 = 53

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The estimated depth of the Grand Canyon would be approximately 467 feet.

First we need to calculate the height of the girl in inches. Since a foot is equal to 12 inches, the girl's height would be 5 x 12 = 60 inches. If the girl's shadow is 9 inches, then the ratio between the girl's height and her shadow is 60/9 or 6.6667 (rounded to 4 decimal places).Now, if the girl's shadow is 9 inches long, and she takes 280 steps to reach the end of it, and each step is approximately 3 feet long, then the total distance she has covered would be 280 x 3 = 840 feet.

The distance from the girl to the canyon is the height of the canyon. If we multiply the distance covered by the girl, which was 840 feet, by the ratio between the girl's height and her shadow length, which was 6.6667, we will get the height of the canyon. Therefore, the height of the Grand Canyon can be estimated to be 840 x 6.6667 = 5600 inches (rounded to the nearest whole number), which is equivalent to approximately 467 feet. Answer: The estimated depth of the Grand Canyon would be approximately 467 feet.

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The number of different pizzas that can be made with 5 toppings each, without repeating the toppings, after counting the combinations, is 3003.

To find the number of different pizzas that can be made with 5 toppings each, without repeating the toppings, we can use the combination formula:
C(n , r) = n! / (r! * (n-r)!)

Where:
n = the total number of toppings available (15)
r = the number of toppings on each pizza (5)
So, substituting the values into the formula, we get:
C(15,5) = 15! / (5! * (15-5)!)
C(15,5) = 15! / (5! * 10!)
C(15,5) = 3003
Therefore, the number of different pizzas that can be made with 5 toppings each, without repeating the toppings is 3003.

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Simulation shows Luke's quiz score in 50 trials with a minimum passing score of 6. Probability of passing is about 0.1. Strong evidence that Luke understands some material as getting a score of 8 by guessing is highly unlikely.

Step 1: The teacher plans to give a multiple-choice test consisting of 10 questions with four answer options each. To conduct one trial of the simulation, a random number generator will be used. To pass the test, the student needs to answer at least six questions correctly. Since each question has four options, the probability of guessing the correct answer is one out of four. To simulate guessing, ten numbers will be generated between one and four, where one represents a correct answer and 2, 3, 4 represent incorrect answers.

Step 2: The dot plot provided illustrates the simulated quiz score of Luke through 50 trials. Each dot on the plot corresponds to a single trial. One dot, specifically the one located at 1, represents a simulated quiz score of one. This implies that in one of the simulation trials, Luke answered only one out of ten questions correctly.

Step 3: We must determine the likelihood of Luke passing the quiz, which contains 10 multiple-choice questions with four answer choices each, requiring a minimum of 6 correct answers to pass. In the dot plot depicting 50 trials of the simulation, the dots represent the quiz score, and 5 of the 50 trials resulted in a score of 6 or more. Thus, the probability of Luke passing the quiz is approximately 0.1 or 1/10.

Step 4: We need to determine whether there is sufficient evidence to support the claim that Doug has an understanding of some of the material.

Step 5: The dot plot displays the simulated quiz score over 50 trials when a person is guessing the answers to the questions. We can infer that it is highly improbable to obtain a quiz score of at least 8 by randomly guessing, as there are no dots above or to the right of 8 on the plot. This suggests that there is compelling evidence that the person understands some of the subject matter, as it is unlikely that they guessed correctly on all questions.

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The missing figure is in the image attached below

Charlotte, North Carolina had an approximate population of  531,145 in 2000.

To approximate Charlotte's population in 2000, we can use the formula for exponential growth:

P(t) = [tex]P0 \times e^{(rt)[/tex]

where P(t) is the population at time t, P0 is the initial population, r is the annual rate of growth as a decimal, and e is the mathematical constant e (approximately 2.71828).

Let's let t = 13 be the number of years between 2000 and 2013. We know that P(13) = 775,000, and r = 0.032. We can solve for P0 as follows:

775,000 = [tex]P0 \times e^{(0.03213)[/tex]

P0 = [tex]775,000 / e^{(0.03213)[/tex]

Using a calculator, we can approximate P0 as:

P0 ≈ 531,145

Therefore, an approximation of Charlotte's population in 2000 is  531,145.

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The answer fοr the imaginary expressiοn is 4i (οptiοn D)

Imaginary numbers are numbers that are nοt real. We knοw that the quadratic equatiοn is οf the fοrm ax² + bx + c= 0, where the discriminant is b²-4ac. In imaginary expressiοn οr number the discriminant becοmes negative οr less than 0.

Imaginary numbers are the numbers that give a negative number when squared. In οther wοrds, we can say that an imaginary number is basically the square rοοt οf a negative number which dοes nοt have a tangible value.

√-16

=√16i² [since i²= -1]

= 4i

Hence the value οf the imaginary number is 4i

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Answer: 4i and i√16

Step-by-step explanation: Just did it.

Answer:The answer is 7 pancakes, I think.

Step-by-step explanation:

28:20

?:5

Divide 28 by 20.

You get 1.4 because every person eats 1.4 .

Multiply 1.4 by 5. You give all of the five people 1.4 pancakes each.

The total will be 7 pancakes.

The number of hours it will take for them to plant the same number of vegetable rows is equals to one hour. Total twelve rows of vegitables they will each have completed.

We have, Malik and his mom are planting vegetables in their garden.

For Malik : he has finished planting 7 rows of carrots and his planting rate = 5 rows per hour.

For his mom : She has finished 10 rows of tomatoes and continue.

Her planting rate = 2 rows per hour.

Let they finish an equal number of carrot and tomato rows in "x hours". That is we can wright the provide information in equation form : Malik plants 5 rows of vegitable per hour, so he will plant 5x rows in x hours. Similarly, his mother will plant 2x rows of vegitables in x hours. Thus, after x hours, (Malik) 7 + 5x = 10 + 2x (mom)

Simplify the above equation,

=> 5x - 2x = 10 - 7

=> 3x = 3

=> x = 1

So, x = 1 be the hours it will take for them to plant the same number of vegetable rows. Now, total rows they will each have completed = 7 + 5×1 = 12 rows or 10 +2×1

= 12

Thus, total 12 rows they finally completed.

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On solving the question we have that Therefore, the center of the circle equation is (3/10, -7/10) and the radius is √(1/5).

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

The given equation is that of a circle in standard form:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where the center of the circle is (h, k) and the radius is r.

To convert the given equation to this form, we need to complete the square for both x and y terms. Let's start with the x terms:

[tex]5x^2 - 3x = 5(x^2 - (3/5)x)\\5(x^2 - (3/5)x + (3/10)^2 - (3/10)^2)\\5((x - 3/10)^2 - 9/100)\\5y^2 + 7y = 5(y^2 + (7/5)y)\\5(y^2 + (7/5)y + (7/10)^2 - (7/10)^2)\\5((y + 7/10)^2 - 49/100)\\5((x - 3/10)^2 - 9/100 + (y + 7/10)^2 - 49/100) - 1 = 0\\5(x - 3/10)^2 + 5(y + 7/10)^2 = 1\\[/tex]

Therefore, the center of the circle is (3/10, -7/10) and the radius is √(1/5).

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The estimated transistors count in a computer in 2023 is given as follows:

1,680,085,700,000

The standard definition of an exponential function is given as follows:

y = a(b)^(x/n).

In which:

The number of transistors doubles every 24 months = 2 years, hence the parameters b and n are given as follows:

b = 2, n = 2.

The amount in the reference year of 2020 was 59,400,000,000, hence the parameter a is given as follows:

a = 59,400,000,000.

Then the function estimating the amount in x years after 2020 is given as follows:

y = 59,400,000,000(2)^(x/2).

The amount in 3 years after 2020 is given as follows:

y(3) = 59,400,000,000(2)^(3/2)

y(3) = 1,680,085,700,000.

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