Find two positive numbers whose difference is 5 and the
sum whose squares is 557.

a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

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The result of the transformation of the parent function y = x² are;

13. y =  (x - 2)²

14. y = x² + 5

15. y = (x + 3)² - 4

16. y = (x - 7)² + 4

17. y = -(x²) - 3

18. y = -(x - 5)² - 2

19. y = (1/2)x²

20.  y = (3x²) + 8

The transformations on the parent function y = x² can be described as;

13. Translated 2 units right:

The equation will be y = (x - 2)²

14. Translated 5 units up:

The equation will be y = x² + 5

15. Translated 3 units left and 4 units down:

The equation will be y = (x + 3)² - 4

16. Translated 7 units right and 4 units up:

The equation will be y = (x - 7)² + 4

17. Reflected over the x-axis, then translated 3 units down:

The equation will be y = -(x²) - 3

18. Reflected over the x-axis, then translated 5 units right and 2 units down:

The equation will be y = -(x - 5)² - 2

19. Vertically compressed by a factor of 2:

The equation will be y = (1/2)x²

20. Vertically stretched by a factor of 1/3, then translated 8 units up:

The equation will be y = (3x²) + 8

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Answer:

6 divide by 60 into 100

Step-by-step explanation:

is 10

The required, the students use eighths as their scale, they will be able to plot all of the data points above the label. Option B is correct.

To make a line plot, the students will mark a number line with a scale that includes all the data points. Since the given data includes fractions with denominators of 2, 4, and 8, it would be best to choose a fraction that is a factor of all of these denominators. The only option that satisfies this condition is B. eighths.

To see why, note that 1/8 is a factor of 1/2 (4/8), 1/4 (2/8), and 1/8 (1/8). Therefore, if the students use eighths as their scale, they will be able to plot all of the data points above the label. Using any other fraction would require rounding some of the data points, which could lead to a loss of information.

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Answer:1/1875

Step-by-step explanation:

the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.

The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:

(1/5) * (1/5) * (1/5) * (4/5) = 4/3125

Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.

Step-by-step explanation:

Using rules of logs :

9 loga x =  loga x^9

Then using another rule:

loga x^9 + loga y =   loga (x^9 * y )

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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Answer:

just start scamming

Step-by-step explanation:

Answer:

The Pythagorean Theorem describes the relationship among the three sides of a right triangle

[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle

The value of inequality :  x≤-9

Given,

Inequality 4(x-3) + 4 ≤ 10+ 6x

Firstly,

The distributive property: 4x-12 + 4 ≤ 10+ 6x

Then,

Combine like terms: 4x -8 ≤ 10+ 6x

Then,

The addition property of inequality: 4x ≤ 18 + 6x

Then,

The subtraction property of inequality: -2x ≤ 18

Then,

The division property of inequality:

Divide both sides of inequality by 2,

So,

x≤-9

Hence after last step the value of x is less than or equal to -9 .

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Answer:

40

Step-by-step explanation:

All questions are worth the same, 1 point each.

80% of 50 = 0.8 × 50 = 40

Answer: 40

Answer:

40

Step-by-step explanation:

80/100*50 = 40

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°

None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).

To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.

However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.

We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.

tan(44°) = height/7, where 7 represents half of the base length.

Rearranging the equation, we have: height = 7 * tan(44°).

Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.

Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).

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Answer:

[tex]d < 20[/tex]

Step-by-step explanation:

The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.

All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

We have to given that;

Rule for sequence is,

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Now, WE can find first five terms of sequence as;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Put n = 1;

⇒ a (1) = - 11 × (1/2)¹⁻¹

⇒ a (1) = - 11

Put n = 2;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (2) = - 11 × (1/2)²⁻¹

⇒ a (2) = - 11 × (1/2)¹

⇒ a (2) = - 11 / 2

Put n = 3;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (3) = - 11 × (1/2)³⁻¹

⇒ a (3) = - 11 × (1/4)

⇒ a (3) = - 11 / 4

Put n = 4;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (4) = - 11 × (1/2)⁴⁻¹

⇒ a (4) = - 11 × (1/2)³

⇒ a (4) = - 11 / 8

Put n = 5;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (5) = - 11 × (1/2)⁵⁻¹

⇒ a (5) = - 11 × (1/2)⁴

⇒ a (5) = - 11 / 16

Thus, All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

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The total population of alligators will be 375.

The amount of soy milk that the grocery store should plan to donate is: 158.

To calculate the total population of alligators in the area, we will assign the following variables:

30 Tagged alligators = m

12 Counted alligators = k

150 alligators seen = n

The total population size (N bar) of alligators is calculated with the formula:

N bar = mn/k

= 30 * 150/12

= 4500/12

375

For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.

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We can see here that it is true that the inverse of the function shown is also a function. This is true because the graph of the inverse of the function shown by reflecting the red graph about the line y = x.  

A function in mathematics is a unique connection between a group of inputs and their results. A function is a rule that specifically assigns one element from another set to each element in a set.

The set of inputs is referred to as the function's domain, while the set of outputs is referred to as the function's codomain.

From the given graph, we can deduce that the resulting graph is true for all x values and for all y values; it passes the vertical line test.

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The measure of the angle B of the triangle is 78.15 degrees

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

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A

The formula for calculating the surface area of a cone is expressed as;

SA = πr² + πrl

Such that the parameters are;

Substitute the values, we have;

Surface area= 3.14 × 16 = 3.14 × 4 × 8

Multiply the values

Surface area = 50.24 + 100.48

Add the values

Surface area = 150.8 in²

Volume of the cone is;

Volume = 3.14 × 4² × 6.9/3

Volume = 3.14 × 16 × 6.9/3

Volume =116. 1in³

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The numerical value of side length x in the right triangle is 8.

The figures in the image are two similar right triagles.

Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.

x/6 = (x + 4)/9

Cross multiply and solve for x:

6( x + 4 ) = x × 9

Apply distributive property:

6 × x + 6 × 4 = x × 9

Simplifying, we get:

6x + 24 = 9x

Subtract 6x from both sides:

6x - 6x + 24 = 9x - 6x

24 = 9x - 6x

24 = 3x

3x = 24

Divide both sides by 3:

x = 24/3

x = 8

Therefore, the value of 8.

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Answer:

i think 25.019mm2 is the correct answerrrrrrrr.

Answer:

175.130 mm^2

Step-by-step explanation:

Took the test.

The probability of getting Blue then Green while spinning the wheel is

3 / 32

Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.

From the given figure we can find out the following information

The probability of getting Blue While spinning the wheel = 3/8

The probability of getting Green While spinning the Wheel = 2 / 8

The probability of getting Blue then Green while spinning the wheel

= 3/8 * 2/8

= 6/64

= 3/32

Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32

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The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For the mileages, we have that:

Hence the functions are given as follows:

Cost B is the better plan when:

A(x) > B(x)

Hence:

30 + 0.14x > 50

0.14x > 20

x > 20/0.14

x > 142.9 miles -> rounded to 143.

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Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.

Hence the correct option is (A).

From the given Maria's Income Statement we can see that,

Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.

Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36

So here net income = $ (630 - 98.36) = $ 531.64.

Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59

So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.

Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.

Hence the correct option will be (A).

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Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:

Marginal Product = Change in Total Product / Change in Labor

Marginal Revenue Product = Price x Marginal Product

Using the given information, we can fill in the missing values as follows:

Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product

0 0 - $12 $0 -

2 48 24 $12 $288 $288

4 66 9 $12 $792 $108

6 82 7 $12 $984 $84

8 96 5 $12 $1,152 $60

10 114 9 $12 $1,368 $108

12 132 9 $12 $1,584 $108

14 150 9 $12 $1,800 $108

So the missing values are:

Total Product for labor = 0 and 14: 0 and 150, respectively.

Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.

Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.

Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.

Step-by-step explanation: :)

Answer:

55.0ml is answer = 22.05

Step-by-step explanation:

If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.

If 144 members represent 90% of the total group, we can set up the equation:

144 = 0.9x

where x is the total number of members on the green team.

To solve for x, we can divide both sides of the equation by 0.9:

144 ÷ 0.9 = x

This simplifies to:

160 = x

To check our answer, we can verify that 144 is indeed 90% of 160:

144 ÷ 160 = 0.9

which confirms that our answer is correct.

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The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

Using the Central Limit Theorem.

The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.

Calculate the standard error of the mean (SEM):

SEM = σ / √n

SEM = 0.52 / √30

SEM ≈ 0.095

Calculate the z-scores for the lower and upper limits:

z1 = (94.7 - μ) / SEM

z2 = (95.3 - μ) / SEM

z1 = (94.7 - 95) / 0.095 ≈ -0.526

z2 = (95.3 - 95) / 0.095 ≈ 0.316

Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.

Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.

Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

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