a
Solve for a in the figure shown

a. 58°
b. 31°
C. 29°
d. 27°

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

The results of operations between functions:

Case A: (f + g) (x) = x / (x + 9) + x³

Case B: (f - g) (x) = x / (x + 9) - x³

Case C: (f · g) (x) = x⁴ / (x + 9)

Case D: (f / g) (x) = 1 / [x² · (x + 9)]

Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.

According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:

Now we proceed to determine the resulting function:

Case A:

(f + g) (x) = f(x) + g(x)

(f + g) (x) = x / (x + 9) + x³

Case B:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = x / (x + 9) - x³

Case C:

(f · g) (x) = f (x) · g (x)

(f · g) (x) = [x / (x + 9)] · x³

(f · g) (x) = x⁴ / (x + 9)

Case D:

(f / g) (x) = f(x) / g(x)

(f / g) (x) = [x / (x + 9)] / x³

(f / g) (x) = 1 / [x² · (x + 9)]

The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.

x² · (x + 9) = 0

x = 0 or x = - 9

The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.

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we distribute the multiplication of 6 by each term of the parenthesis

the the equivalent expression is (6g+107)

Answer:

The GMAT score corresponding to the 16th percentile is 473.

Step-by-step explanation:

Empirical Rule.

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

68% of the measures within 1 standard deviation of the mean.

This means that they are between the 50 - (68/2) = 50 - 34 = 16th percentile(one standard deviation below the mean) and the 50 + (68/2) = 50 + 34 = 84th percentile(one standard deviation above the mean).

In this question:

Mean of 549, standard deviation of 76.

16th percentile:

One standard deviation below the mean, so 549 - 76 = 473.

The GMAT score corresponding to the 16th percentile is 473.

Answer:

Step-by-step explanation:

Twice the sum of a number of 11 is -38

2( number +11)  = -38

number +11 = -38/2

number = -19 -11

number = - 30

Answer: The entire trip is 62.5 miles

Step-by-step explanation:

25 miles = 0.4x

Divide both sides by 0.4

25/0.4 = 62.5 miles

Answer:

7/10

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)  where ( x1,y1) and (x2,y2) are two points on the line

m = ( 24-17)/(25-15)

   = 7/10

  = 7/10

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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Answer:

x=11 and t=6

Step-by-step explanation:

If ABC and KLM are approximately equal, 44 degrees=4x and 18 inches=3t.

44/4=11

18/3=6

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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The answers for the following questions are mentioned below respectively.

The branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

a. To compute the summaries of this experiment, we need to calculate the mean and standard deviation of each condition.

Condition 1: Low Noise

Mean = (15 + 19 + 13 + 13) / 4 = 15

Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1)) = 2.58

Condition 2: Medium Noise

Mean = (13 + 11 + 14 + 10) / 4 = 12

Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1)) = 1.87

Condition 3: Loud Noise

Mean = 2978

Standard deviation = undefined, as there is only one observation.

b. The appropriate graph for these data is a histogram, with each condition represented by a different color or pattern. The x-axis represents the productivity scores, and the y-axis represents the frequency or percentage of observations in each condition.

c. Assuming that the data are representative, we would envision the populations produced by this experiment as three different normal distributions, each with its own mean and standard deviation. The population distribution for the low noise condition would be centered around a mean of 15, with most scores falling within 2.58 points of this mean. The population distribution for the medium noise condition would be centered around a mean of 12, with most scores falling within 1.87 points of this mean. The population distribution for the loud noise condition is unknown, as we only have one observation.

d. The conclusions that can be drawn from this experiment depend on the research question and hypothesis being tested. However, based on the information given, we can conclude that there is a difference in productivity scores across the three conditions, with the lowest scores occurring in the medium noise condition. However, we cannot draw any conclusions about the effect of noise on productivity without further analysis or experimental manipulation.

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We must determine the means and standard deviation of each circumstance.

Standard deviation = 1.87

Mean = 2978

The area of mathematics concerned with the gathering, examination, interpretation, display, and arrangement of data.

a). We must compute the means and standard deviations of each condition in order to compute the summaries for this exercise.

Condition 1: Low Noise

Mean = (15 + 19 + 13 + 13) / 4

          = 15

Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1))

                                = 2.58

Condition 2: Medium Noise

Mean = (13 + 11 + 14 + 10) / 4

         = 12

Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1))

                                = 1.87

Condition 3: Loud Noise

Mean = 2978

Standard deviation = undefined, as there is only one observation.

b). The suitable graph for these data is a histogram, where the x-axis represents productivity scores and the y-axis represents the frequency or percentage of observations in each condition, with each condition represented by a different color or pattern.

c). We would picture the populations generated by this experiment as three distinct normal distributions, each with its own mean and standard deviation, assuming that the data are representative. Most scores would lie within 2.58 points of the mean for the low noise condition, which would have a population distribution centered around a mean of 15. Most scores would lie within 1.87 points of the mean for the medium noise condition, which would have a population distribution centered around a mean of 12. We only have one observation, so we don't know the population distribution for the loud noise situation.

d). The study query and tested hypothesis determine the conclusions that can be drawn from this experiment. However, based on the available data, we can infer that there is a difference in output scores between the three conditions, with the medium noise condition recording the lowest scores. However, without additional investigation or experimental manipulation, we are unable to make any judgments about how noise affects output.

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Answer: 5a: 5/8

Step-by-step explanation: sorry, thats the only one i can read `:)

Answer:

3a is 8 3b is 6

Step-by-step explanation:

this might be right sorry if it isnt I was straining my eyes till I got a headache

Answer:

n= -35 .................................

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Put this together using the conditions given: 319.14 / (1- 19%)

Determine the total or difference: 319.14 / 0.81

Diminish the fraction: 394

Response: 394

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

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Answer:y=2.50x+5

Step-by-step explanation:

y=2.50x+5

that's all i can do with the information provided

Answer   A is 28

Step-by-step explanation:

Answer:

oop

Step-by-step explanation:

Answer: x>5 or x<−19

The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Answer:

Step-by-step explanation:

The answer is, no!

Step-by-step explanation:

The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.

So, here is the given information on what we need to classify a shape as a parallelogram:-

1) Parallel Sides

2)Opposite Sides are equal.

3) Adjacent sides are not equal.

4) Opposite angles are equal.

5)Adjacent angles are not equal.

Based on this, we can classify a shape as a parallelogram.

Hope, this answer helps!

The product of sum of the expression (2x+1)(5x-8) is  10\(x^2\)-11x-8.

What is product of sum?

Expressions that are a product of sums are Boolean expressions made up of sums of one or more variables, either in their true form or complemented form. Boolean expressions known as "product of sum expressions" are constructed by adding together sums of one or more variables in either their true form, complemented form, or a combination of both.

Here the given expression is ,

=> (2x+1)(5x-8)

=> [2x.5x - 8.2x+5x-8]

=> 10\(x^2\)-16x+5x-8

=> 10\(x^2\)-11x-8.

Hence the product of sum is 10\(x^2\)-11x-8.

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The 6th-grade students filled approximately 65% of the seats in the theater on their field trip.

To find the percentage of seats filled by the 6th-grade students on the field trip, we first need to calculate the number of seats that were filled.

This can be done by subtracting the number of vacant seats (231) from the total number of seats in the theater (660).

Seats filled = Total seats - Vacant seats

= 660 - 231

= 429

Now, to find the percentage of seats filled, we divide the number of filled seats by the total number of seats and multiply by 100.

Percentage of seats filled = (Seats filled / Total seats) * 100

= (429 / 660) * 100

= 0.65 * 100

= 65

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Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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The simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.

To simplify the expression (2^-6)(5)(2^3*5)^2, let's break it down step by step:

First, we can simplify 2^-6. A negative exponent indicates taking the reciprocal of the base raised to the positive exponent. In this case, 2^-6 can be written as 1/(2^6).

Next, we can evaluate (2^35)^2. Inside the parentheses, we have 2^35. This can be simplified to 8*5, which equals 40. Then, we raise 40 to the power of 2, resulting in 40^2.

Now, let's put everything together:

(2^-6)(5)(2^3*5)^2 = (1/(2^6))(5)(40^2)

To simplify further, we can simplify the powers of 2 and 40:

2^6 = 64

40^2 = 1600

Substituting these values back into the expression:

(1/64)(5)(1600) = (5/64)(1600)

We can further simplify by multiplying 5 and 1600:

(5/64)(1600) = 800/64

Finally, we can simplify 800/64 by dividing both numerator and denominator by 8:

800/64 = 100/8 = 25/2

Therefore, the simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.

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Answer:

y = -2x-1

Step-by-step explanation:

The formula for a line is \(y-y_{1} = m(x-x_{1})\).

Plug in the information given in the problem: y-(-7) = -2(x-3)

So you get y+7 = -2x+6.

The final form you want needs to be equal to y (that means you want y by itself on the left side of the equals), so subtract 7 from both sides.  

You get y = -2x-1

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})~\hspace{10em} m = -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-2}(x-\stackrel{x_1}{3}) \\\\\\ y+7=-2x+6\implies \blacktriangleright y=-2x-1 \blacktriangleleft\)

Answer:

Use the given functions to step up and then simplify (x, -7).

Step-by-step explanation:

0 - 4 = -4

(x, -7) = -4

m = 3/2

Answer:

the answer would be X=-2

Answer:

Step-by-step explanation:

The expression 3s + s + 3 represents the total amount Alex and his family will spend to go to the movies. To simplify this expression, we can combine like terms.

The terms 3s and s are like terms because they both have the variable "s" raised to the power of 1. To combine them, we add their coefficients:

3s + s = (3 + 1)s = 4s

Therefore, the simplified expression is 4s + 3, which represents the total amount Alex and his family will spend to go to the movies.

Answer:

x= 5.25

Step-by-step explanation:

You have to get x alone, so do inverse operations.

(Basically, reverse what it is)

4(x-3)=9

divide 4 by both sides to get rid of 4 on left side

9/4 = 2.25

(x-3) = 2.25

Now add 3 to both sides, to get x alone

2.25 + 3 = 5.25

x=5.25

Check work

4(5.25-3) = 9

4(2.25) = 9

9=9

Answer:

To determine if (0,3) is a solution to y>2, we need to check if y is greater than 2 when x=0 and y=3. Since 3 is greater than 2, the point (0,3) satisfies the inequality y>2.

To graph the inequality y>2, we need to shade the region above the horizontal line y=2. The line y=2 is a solid line since it includes the points where y=2, but the region above the line is shaded with a dashed line since it does not include the points where y=2.

Here is a description of the graph:

Draw a horizontal line passing through the point (0,2).

Shade the region above the line with a dashed line.

The graph visually represents all the points that satisfy the inequality y>2. Since the point (0,3) is above the line, it is part of the shaded region and satisfies the inequality.

Answer:

x=1

Explanation:

When x=-1, the value of y=3.

The other domain value whose range is y=3 from the graph is x=1.