(30 de puncte) SUBIECTUL al III-lea. Scrieți rezolvările complete. 1. Denisa are cu 27 de ani mai puțin decât mama ei, care are cu un an mai puţin decât tatăl fetei. Denisa este de cinci ori mai tânără decât tatăl său. a) Cu câți ani este mai tânără Denisa decât tatăl ei? b) Determină vârsta fetei. (2p) (3p) (Sp)​

The statement that best describes the solution to the inequality in this problem is given as follows:

all real numbers except x = 1.

The inequality in the context of this problem is defined as follows:

2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7

The solution to the first inequality is given as follows:

2(x + 7) – 1 > 15

2x + 14 > 16

2x > 2

x > 1.

The solution to the second inequality is given as follows:

3(x + 2) < 2x + 7

3x + 6 < 2x + 7

x < 1.

The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:

all real numbers except x = 1.

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Step-by-step explanation:

(540×45) + ( 540×55)

(24300) +(29700)

54000

Answer:

540*45+540*55=540*45=24300 540*55=29700=24300+29700=54000

Step-by-step explanation:

by solving the the first bracket to get the answer then the other one, after getting the both answer, then add it together

The missing reason in the proof is "mZDEC = 90°" or "Angle DEC is a      right angle."

The missing reason in the proof is the statement "mZDEC = 90°". This statement implies that the angle DEC is a right angle, which is a crucial piece of information in proving that ABCD is a square.

In a square, all angles are right angles, so if we can establish that an angle in the figure is 90°, we can conclude that the figure is a square. In this case, the angle DEC being 90° is the key piece of evidence that supports the claim that ABCD is a square.

The statement "mZDEC = 90°" indicates that the measure of angle DEC is 90 degrees. This is significant because it confirms that one of the angles in the figure is a right angle, meeting the definition of a square.

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Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².

To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.

To find the fraction of a circle shaded, divide the number of degrees in the sector by

360.4x = (40/360) × πr² = (1/9) × πr².

We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:

A = (40/360) × πr² = πr²/9 =  π(4²)/9 = 16π/9 cm²

Therefore, the correct answer is 16π/9 cm².

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Answer:

82.8°

Step-by-step explanation:

We can solve for θ by first isolating cosθ:

8 cosθ - 1 = 0

8 cosθ = 1

cosθ = 1/8

We can find the inverse cosine of 1/8:

θ = cos⁻¹(1/8) = 82.8191°

Rounding to the nearest 0.1°, we get:

θ ≈ 82.8°

Answer:

=

Step-by-step explanation:

0.67 is the same as 0.670

The solution of the system of equations is (-2, 2).

Here we want to find the solution of the system of equations:

x + 2y = 2

y = -2x- 2

To solve this, we can replace the second equation into the first one, then we will get:

x + 2*(-2x - 2) = 2

Now we can solve that for x:

x - 4x - 4 = 2

-3x = 2 + 4

-3x = 6

x = 6/-3 = -2

Thus, the value of y is:

y = -2*-2 - 2

y = 4 - 2 = 2

The solution of the system is (-2, 2)

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Complete question:

"Which is the solution of the system of equations?

x + 2y = 2

y = -2x- 2"

Answer:

k = - 4

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the product of the roots is [tex]\frac{c}{a}[/tex]

3x² + 5x + 3k = 0 ← is in standard form

with a = 3 and c = 3k , then

[tex]\frac{c}{a}[/tex] = - 4 , that is

[tex]\frac{3k}{3}[/tex] = - 4 ( multiply both sides by 3 to clear the fraction )

3k = - 12 ( divide both sides by 3 )

k = - 4

The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units

From the question, we have the following parameters that can be used in our computation:

The right triangles

The right triangles are special triangles with acute angles of 45 degrees

This means that the relationship between the legs and the hypotenuse of the triangles is

Hypotenuse = Leg√2

Leg = Hypotenuse/√2

Using the above as a guide, we have the following:

Leg = 14√2/√2

Leg = 14

i.e. the legs of the big triangle are 14 units

Leg = 14/√2

Leg = 7√2

i.e. the legs of the small triangle are 7√2 units

See attachment for the triangles

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Answer:

Step-by-step explanation:

The trigonometric ratios are expressed as;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

To determine the trigonometric ratios, we need to know the six identities.

These trigonometric identities are listed thus;

From the information given, we have that;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We have that;

The hypotenuse is labeled as 5.

The adjacent leg is 4

The angle opposite the side labeled 3 is theta

Now, substitute the value to determine the ratios for each identity, we have that;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

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The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]

In 20 days was the whole job done.

Let efficiency of each worker is 1 unit / day .

So, Total work = 10 x 1 x 15 = 150 units .

Now, in first 5 days 6 worker completes

= 5 x 6 x 1 = 30 units .

and, in next 3 days 8 workers completes

= 3 x 8 x 1 = 24 units .

Now, 4 more workers joined then total workers are = 12 workers .

So, amount of work left = 150 - 30 - 24 = 96 unit

Thus, the time taken by 12 workers to complete remaining work

= 96/12

= 8 days .

So, the Whole job was done in = 5 + 3 + 12 = 20 days

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The question attaches here seems to incomplete the complete question is

10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?

Your ability to borrow money at lower rates improves as your credit score increases. Option D.

Your ability to borrow money at lower rates improves as your credit score increases.

A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.

Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.

While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.

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Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

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The expected value for a person who buys a ticket is $0.35.

We have,

Number of tickets sold = 100

Price of each ticket = $1

Prize value (1st prize) = $25

Prize value (2nd prize) = $10

Let's calculate the expected value step by step:

Calculate the probability of winning each prize:

Since there is only one 1st prize and one 2nd prize, the probability of winning each prize is:

Probability of winning the 1st prize = 1/100

Probability of winning the 2nd prize = 1/100

Calculate the expected value:

Expected value = (Probability of winning 1st prize x Value of 1st prize) + (Probability of winning 2nd prize x Value of 2nd prize)

= (1/100 x $25) + (1/100 x $10)

= $0.25 + $0.10

= $0.35

Therefore, the expected value for a person who buys a ticket is $0.35.

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The area of the sector is 297π units squared.

The arc length of a 330° sector is 33π. Therefore, let's find the area of the sector.

Let's find the radius of the circle.

length of arc = ∅/ 360 × 2πr

where

Therefore,

33π = 330 / 360 × 2π × r

cross multiply

660πr = 11880π

divide both sides by 660π

r = 11880π / 660π

r = 18 units

Therefore,

area of the sector = 330 / 360 × π × 18²

area of the sector = 106920 / 360 π

area of the sector = 297π units²

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The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:

[tex]\sqrt{44} = 6.63[/tex]

The estimate of a non-exact square root of x is done finding two numbers, as follows:

For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:

44 x 10^4 = 440000.

(as each 10² is equivalent to the square root of a decimal digit).

Then the numbers are:

Hence the square root is approximated as follows:

663/100 = 6.63.

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Answer:

Step-by-step explanation:

To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.

In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).

Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.

Answer:

25

Step-by-step explanation:

There are only additions, so do each addition, in the order it appears, from left to right.

-11 + 3 + 10 + (-25) + 48 =

= -8 + 10 + (-25) + 48

= 2 + (-25) + 48

= -23 + 48

= 25

1. All angles of a rectangle are right angles (90 degrees), while the angles of a parallelogram can be any angle other than 90 degrees.

2. The opposite sides of a rectangle are equal in length, whereas in a parallelogram, opposite sides are of equal length as well, but they may not be perpendicular to each other.

The questions are a bit unclear and have some spelling errors, but I will try my best to provide an answer:

- Mention the transformation of the brick when it is flipped or turned sideways:

If the brick is flipped over, the transformation it undergoes is called a reflection. This can also be thought of as a mirror image of the original brick. If the brick is turned sideways, the transformation it undergoes is called a rotation. In a rotation, the object is turned about a point, and the image of the object appears to have been rotated around that point.

- When the key is pushing the brick, without using or flipping the brick, what... (I'm not sure what the question is asking for, as it seems incomplete or there is some text missing.)

- What are the two differences between a rectangle and a parallelogram?

  In summary, the transformation of a flipped brick is a reflection, while a turned sideways brick undergoes a rotation. The differences between a rectangle and a parallelogram include the angles (all right angles for a rectangle and any angle other than 90 degrees for a parallelogram) and the opposite sides (equal length and perpendicular for a rectangle, equal length but not necessarily perpendicular for a parallelogram).

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The value of y from the given right angled triangle is 9.2 cm.

Given that, a right angled triangle has 8.2 cm, y cm and 12.3 cm.

Let, hypotenuse = 12.3 cm, perpendicular = 8.2 cm and base = y cm.

By using Pythagoras theorem, we get

8.2²+y²=12.3²

67.24+y²=151.29

y²=151.29-67.24

y²=84.05

y=9.2 cm

Therefore, the value of y from the given right angled triangle is 9.2 cm.

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The detergent with the coupon is the better buy since it has a lower price per ounce.

To determine which option is the better buy, we need to compare the prices per ounce for each detergent brand.

First, let's calculate the price per ounce for the 32-ounce bottle of detergent after applying the coupon:

Price per ounce = (Price - Coupon) / Ounces

Price per ounce = ($1.39 - $0.35) / 32

Price per ounce = $1.04 / 32

Price per ounce ≈ $0.0325

Next, let's calculate the price per ounce for the 20-ounce bottle of the other brand:

Price per ounce = Price / Ounces

Price per ounce = $0.79 / 20

Price per ounce = $0.0395

Comparing the two price per ounce values, we can see that the price per ounce for the detergent with the coupon is approximately $0.0325, while the price per ounce for the other brand is $0.0395.

Therefore, the detergent with the coupon is the better buy since it has a lower price per ounce.

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ΔAOB will be neither isosceles nor a right angled triangle.

Given,

In Parallelogram ABCD diagonals bisect at the point O.

Parallelogram and its properties:

Hence from the above properties it is clear that the triangles formed will neither be isosceles nor a right angled triangle.

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Answer: I have this same exact question

Step-by-step explanation: So someone please help this person, or animal which ever you perfer

Cos = 20/27 = 0.7407

so

angle that stream makes with the road = 42.2

answer

42 (Round only your final answer to the nearest degree)

Answer:

[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:

[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]

Set each factor equal to zero and solve for x using the unit circle.

[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]

[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]

Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:

[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]

Answer:

(-6,0)

Step-by-step explanation:

An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.

For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.

For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)

Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.

So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:

[tex]\displaystyle{y=-x-6}[/tex]

Then we find the x-intercept of the line by letting y = 0. Thus,

[tex]\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}[/tex]

Therefore, the x-intercept of line t is at (-6,0).

Answer:

(-6,0)

Step-by-step explanation:

We need to determine the equation of line r first to find the x-intercept of line t.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

[tex]slope = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

For line r passing through (3, 0) and (0, 3), the slope is:

[tex]slope = \frac{3 - 0}{0 - 3} = -1[/tex]

Since line t has the same slope as line r, its slope is also -1.

The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).

We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:

y = -x - 6

To find the x-intercept, we set y = 0 and solve for x:

0 = -x - 6

Adding x to both sides:

x = -6

Therefore, the x-intercept of line t is (-6,0).