Consider this literal equation. 3/a x - 4 = 20 Are there any cases where the value of x or a would cause a problem? Use complete sentences to explain your reasoning.

Tessa's cumulative GPA for all four semesters is 3.44.

To find Tessa's cumulative GPA, we first need to calculate the total number of course units she has taken. For the first three semesters, she took 46 course units. For the fourth semester, she took 12 course units. So, in total, she has taken 46 + 12 = 58 course units.

Next, we need to calculate her total grade points. To do this, we multiply her GPA for each semester by the number of course units she took in that semester, and then add up the results. For the first three semesters, her total grade points are:

3.35 x 46 = 154.1

For the fourth semester, her total grade points are:

3.74 x 12 = 44.88

So her total grade points for all four semesters are:

154.1 + 44.88 = 198.98

Finally, we divide her total grade points by the total number of course units she has taken:

198.98 / 58 = 3.44

Therefore, Tessa's cumulative GPA for all four semesters is 3.44.

The lowest average he could obtain on his next two tests and still receive an A is 93 or higher.

To receive an average of 90 or better, W. Orrier needs to score a total of 540 points or more on all six tests

(90 x 6 = 540).

He has already scored a total of 88.5 x 4 = 354 points on his first four tests.

Therefore, he needs to score a total of 540 - 354 = 186 points on his next two tests.

To find the lowest average he could obtain on his next two tests, he needs to divide 186 by 2

186 ÷ 2 = 93.

Therefore, the lowest average he could obtain on his next two tests and still receive an A is 93 or higher.

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Answer: To solve a two-step inequality, undo the addition or subtraction first, using inverse operations, and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.

Step-by-step explanation:

The equation of the straight line shown in the given graph is x = -2

From the question, we are to determine the equation the given straight line in the graph

To determine the equation of the line, we will use the given two points on the line

The given points are (-2, 2) and (-2, -3)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Substitute the given points

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

(y - 2) / (x + 2) = -5 / (-2 + 2)

(y - 2) / (x + 2) = -5 / 0

Cross multiply

0 × (y - 2) = -5 × (x + 2)

0 = -5x - 10

Add 5x to both sides

0 + 5x = -5x + 5x - 10

5x = -10

Divide both sides by 5

5x / 5 = -10/5

x = -2

Hence, the equation is x = -2

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The angles formed by the chords and secants of the circle are;

28) m[tex]\widehat{AB}[/tex] = 60°

29) m[tex]\widehat{GH}[/tex] = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 90°

32) m∠2 = 58°

33) m∠3 = 32°

34) m∠5 = 49°

35) m∠6 = 90°

36) m∠7 = 99°

37) m∠8 = 96°

38) m∠9 = 116°

A chord is a segment that joins two distinct points on the circumference of a circle.

The angles formed by the arcs in the circle indicates that we get;

28) m[tex]\widehat{AB}[/tex] = 360° - 56° - 18° - 42° - 180° = 60°

29) m[tex]\widehat{GH}[/tex] = 90° - 38° = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 180°/2 = 90°

32) m∠2 = (56° + 18° + 42°)/2 = 58°

33) m∠3 = 90° - 58° = 32°

34) m∠5 = (1/2) × (38° + 18° + 42°) = 49° (Angles of intersecting chords theorem)

35) m∠6 = 90° (Supplementary angle to a right angle is 90 degrees angle is )

36) m∠7 = 180° - 32° - 49° = 99°

37) m∠8 = (1/2) × (52° + 38° + 60° + 42°) = 96°

38) m∠9 = m∠3 + (180° - m∠8) (External angles theorem and linear pair angles)

m∠9 = 32° + (180° - 96°) = 116°

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After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.

The number of half-lives in 30 days is 30/5 = 6.

So, after 1 half-life, the amount remaining is 948/2 = 474 grams.

After 2 half-lives, the amount remaining is 474/2 = 237 grams.

After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.

After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.

After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.

After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.

Therefore, after 30 days, 14.8125 grams of the element remains

The linear equation for the scenario is y = x - 12

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

Represent the original amount with x

and the amount left with y

So, we have

Amout left = x - 12

Using the variable representtaion, we have

y = x - 12

Hence. the scenario is y = x - 12

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The equivalent value of the expression is A = 12 + 6x + 6x + 6y

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 6(2 + x + x + y)

On simplifying the equation , we get

A = 6 ( 2 ) + 6x + 6x + 6y

On further simplification , we get

A = 12 + 6x + 6x + 6y

Hence , the expression is A = 12 + 6x + 6x + 6y

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The complete question is attached below :

which expression uess exactly terms and is equivalent to 6(2 + x + x + y)

Answer: [tex]x_1 = -\frac{3}{2} \\x_2 = \frac{3}{2} \\\\[/tex]

X could equal either -3/2, or 3/2 because x is made into an absolute value

Answer:

[tex]x = 1 \frac{1}{2} \: \\ x = - 1 \frac{1}{2} [/tex]

Step-by-step explanation:

If we're solving for x, then we should divide both sides by 2 and then simplify.

[tex](2 |x| = 3) \div 2[/tex]

[tex] |x| = \frac{3}{2} [/tex]

This gives us the final answer of

[tex]x = ±\frac{3}{2} [/tex]

Which can be simplified into:

[tex]x = 1\frac{1}{2} , \: - 1\frac{1}{2} [/tex]

Answer:

  42 units³

Step-by-step explanation:

You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.

The formula for the volume of a prism is ...

  V = Bh

where B is the base area and h is the height perpendicular to the base.

Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...

  V = (5 1/4 u²)(8 u) = 42 u³

The volume of the prism is 42 cubic units.

If in the set A ⊂ B then the statement A U B = B

A set is a collection of well defined items.

Since we have A ⊂ B, we want to determine which statement of the set is true. To determine that, we proceed as follows.

So, if A ⊂ B then the statement A U B = B

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The value of 5cos(tetha) + 4/sin(beta) is 9

Complementary angles are two angles that sum up to 90°. This means that in a right angled triangle sin( beta) is thesame as cos(90-tetha) and cos (beta) is sin(90-tetha).

Examples of complementary angles include: 30 and 60, 50 and 40 e.t.c

Therefore if tan ( tetha ) = 3/4, and tan(tetha) = opp/adj. This means opp is 3 and adj is 4

therefore hyp = √3²+4²

= √9+16 = √25

= 5

therefore cos(tetha) = 4/5

and sin beta = 4/5

therefore 5cos(tetha) + 4/sin(beta) = 5 × 4/5 +(4÷4/5)

= 4+5 = 9

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Answer:

Answer: Test One

Parent 1: FF

Parent 2: FF

Phenotype ratio:

short fur: long fur

Test Two

Parent 1: Ff

Parent 2: FF

Phenotype ratio:

short fur: long fur

Test Three

Parent l: ff

Parent 2: ff

Phenotype ratio:

short fur: long fur

Step-by-step explanation:

Answer: Test One

Parent 1: FF

Parent 2: FF

Phenotype ratio:

short fur: long fur

Test Two

Parent 1: Ff

Parent 2: FF

Phenotype ratio:

short fur: long fur

Test Three

Parent l: ff

Parent 2: ff

Phenotype ratio:

short fur: long fur

The line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  u = -4

Step-by-step explanation:

You want the solution to the equation 16u -5u +18 = 3u -14.

The equation can be simplified by combining like terms:

  11u +18 = 3u -14

Adding (-18-3u) to both sides, we have ...

  8u = -32

  u = -32/8 = -4 . . . . . . divide by the coefficient of u

The solution is u = -4.

Answer:

Step-by-step explanation:

Answer:

C = 117.92° or 118°

Step-by-step explanation:

Law of Cosine: [tex]c^2=a^2+b^2-2ab*cos(C)[/tex]

Plug in your values to solve for C°

A = 50 , B = 55 , C = 90

[tex]90^2=50^2+55^2-(2*50*55)*cos(C)[/tex]

[tex]8100=2500+3025-5500*cos(C)[/tex]

Subtract 2500 and 3025 to move to other side.

[tex]8100-2500-3025=-5500*cos(C)[/tex]

[tex]2575=-5500*cos(C)[/tex]

Divide -5500 to leave cos(C) byitself

[tex]-\frac{2575}{5500} =cos(C)[/tex]

Inverse Cos(C) to get C byitself solving it in degree.

[tex]C=cos^{-1}(-\frac{2575}{5500} )[/tex]

C = 117.916339°

Round to Hundredths place or Whole Degree.

C = 117.92° or 118°

Answer:

P((1 + r)^6) = 1,675.80

P((1 + r)^5) = 1,606.50

------------------------------

b) 1 + r = 266/255, so r = 11/255 = .04 = 4%

a) P((1 + 11/255)^5) = 1,606.50

P = $1,300.69

Result:

The probability of getting a sum greater than 25 = 1/9.

The answer is not among the given options.

To find the probability, we would need to consider the possible combinations of the spinner and number cube that result in a sum greater than 25.

First, note that the highest possible sum we can get is 12 (that is 6 from the spinner and 6 from the number cube). Therefore, we can remove all combinations that result in a sum of 24 or less.

Next, we can consider the combinations that result in a sum of 25 like this:

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 4

Finally, we can consider the combinations that result in a sum greater than 25:

Spinner lands on 5, number cube lands on 5

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 6

Here, 4 possible combinations can result in a sum greater than 25 from a total of 6 x 6 = 36 possible outcomes.

So, the probability of getting a sum greater than 25 is 4/36 = 1/9.

Therefore, none of the given answer choices matches this result.

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The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

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Step-by-step explanation:

For a RIGHT triangle   tan Φ = opposite leg / adjacent leg

 for this triangle

         tan 71 = x / 5.7

       5.7 * tan 71 = x    =   16.6  units

There is enough data to indicate that Jordanian children are at risk of anemia.

The null hypothesis is that the true mean hemoglobin level for Jordanian children is greater than or equal to 12 g/dl, and the alternative hypothesis is that it is less than 12 g/dl.

Using the P-value method:

The test statistic for the one-sample t-test is given by:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population means (here, μ = 12), s is the sample standard deviation, and n is the sample size.

Substitute the given values,

t = (11.3 - 12) / (1.6 / √50) = -2.98

Using a t-distribution table with 49 degrees of freedom (df = n - 1), find that the p-value for this test is approximately 0.002.

Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Jordanian children are at risk of anemia.

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Answer:

A. 45(x+3)=60x

Step-by-step explanation:

Тhе sum оf thе first 6 tеrms оf thе given sеquеncе is аpproximаtely 14.56.

First detеrmine thе common rаtio (r) аnd thе first tеrm (а1).

Eаch tеrm is obtаined by multiрlying thе prеvious tеrm by 1/3. Тherefоre, thе common rаtio is r = 1/3.

Тhe first tеrm is а1 = 12.

Now wе cаn use thе fоrmulа fоr thе sum оf а finite geоmetric series:

Sn = а1(1 - r^n) / (1 - r)

whеrе n is thе number оf tеrms.

Plugging in thе vаlues, wе gеt:

Sn = 12(1 - (1/3)^6) / (1 - 1/3) ≈ 14.55

Rounding to thе neаrest hundredth, wе gеt:

Sn ≈ 14.55 ≈ 14.56

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To install the gas riser in 10 days, a total number of 11 plumbers would be needed.

We can use the formula:

(number of workers) × (time) = (constant amount of work)

Let's let x be the number of plumbers needed to install the gas riser in 10 days. We can set up the equation:

(7 workers) × (15 days) = (x workers) × (10 days)

Simplifying the left side, we get:

105 worker-days = (x workers) × (10 days)

Dividing both sides by 10 days, we get:

10.5 workers = x

Since we can't have a fraction of a worker, we need to round up to the nearest whole number.

Therefore, we would need 11 plumbers to install the gas riser in 10 days.

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Answer:

The correct answer is A.

Step-by-step explanation:

The correct answer is A.

To find the length of one side of the square, we need to take the square root of the area. Therefore, the square root of 90 is approximately 9.49 feet. Since this value falls between 9 feet and 10 feet, but is closer to 9 feet, the statement "√90 feet is between 9 feet and 10 feet but is closer to 9 feet" is true. So, Jimmy should cut the carpet to 9.49 feet to fit the square-shaped room.

The polynomial long division of (5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4) gives a quotient of 5x^2 - 12x + 37

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

(5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4)

Using the polynomial long division setup, we have

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

Evaluating the division, we have

                         5x^2 - 12x + 37

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

                         5x^4  + 10x^3 - 20x^2

                         ---------------------------------------

                                      -12x^3 + 13x^2 - 39

                                      -12x^3 - 24x^2 - 48

                         ---------------------------------------

                                                    37x^2 + 9

                                                    37x^2 + 74x - 148

                         ---------------------------------------

                                                    -74x + 157

Hence, the quotient is 5x^2 - 12x + 37

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