1. 232 is 8 times the sum of Mark's and his sister's ages. His sister is 21. Find Mark's age.

2. George went to the store for a sale on designer socks. Each pair was $3 off. She bought 6 pairs for $31.20. How much was the original price of the socks?

Answer:

3n + 21

Step-by-step explanation:

3(n + 7)

3n + 21

Answer:

(-a, 0)

Step-by-step explanation:

By telling you that the quadrilaretal is a kite the problem is telling you that SQ is perpendicular to PR, and that PS=PQ (by simmetry, it follows that also RS=RQ). So S has to be the symmetric of Q to the center (intersection of the diagonals), which means that, since Py=0, its coordinates are (-a, 0)

Answer:

all I know is the answer for 5 so it is 2.0

Step-by-step explanation:

Answer:

4. 79.17%

5. 2.5

Step-by-step explanation:

4.  Q3 - Q1 = 4.75 - 0 = 4.75

      [tex]\frac{4.75}{6} *100[/tex] = 79.17

5.  Q3 - Q1 = 4.75 - 2.25 = 2.5

The box and whisker plot of the prices of some DVDs:

Minimum: 9.99

First Quartile: 12.99

Median: 15.99

Third Quartile: 19.99

Maximum: 26.99

The box and whisker plot shows that the median price of a DVD is $15.99. The prices range from $9.99 to $26.99. There are two outliers, one at $9.99 and one at $26.99.

The box and whisker plot can be used to identify the distribution of the data. In this case, the data is slightly skewed to the right, meaning that there are more DVDs priced at the lower end of the range than at the higher end.

The box and whisker plot can also be used to compare different sets of data. For example, we could compare the prices of DVDs from different stores or from different years.

Overall, the box and whisker plot is a useful tool for visualizing and summarizing data.

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Each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

Let the cost of an adult-fare bus pass be A student-fare bus pass costs half as much as an adult-fare pass, hence, the cost of a student pass will be $129 - A.

Mathematically, this is represented as:A = 2($129 - A) $A = $258 - 2A 3A = $258 A = $86Therefore, the cost of an adult-fare bus pass is $86.A student pass costs half as much as an adult-fare pass.

Since the cost of an adult-fare pass is $86, therefore the cost of a student pass will be half of $86. Mathematically, this can be represented as:Cost of student pass = 1/2 x $86 = $43

Therefore, each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

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Answer:

#6) A = 72 sq units

Step-by-step explanation:

area of ΔAOB = 6

area of ΔCOB = 6

area of ΔCOD = 30

area of ΔCOD = 30

Answer:

61

Step-by-step explanation:

add the numbers up and divide them by 7

Answer:

Step-by-step explanation:

added up the data = 427

divide by the number of days = 427/7 = 61

Answer:

100degrees

Step-by-step explanation:

Find the diagram attached

From the diagram

<PQT =<TRS = 40

Since the triangle STR is isosceles, here,

<TSR =<TRS = 40

Also the sum of angle in a triangle is 189, hence:

Arc SR+<TSR +<TRS = 18₩

ArcSR +40+40=180

ArcSR +80=180

ArcSR = 180-80

ArcSR = 100degrees

Hence the measure of SR is 100degrees

The measure of arc SR is 100°. The correct option is the third option - 100°

From the question, we are to determine the measure of arc SR.

The measure of arc SR = <STR

Now, we will determine the measure of <STR

In the diagram, T is the center of the circle.

∴ TP and TQ are radii.

Then, we can conclude that ΔPQT is an isosceles triangle.

Recall: Base angles of an isosceles triangle are equal.

∴ <PQT = <TPQ = 40°

Now, consider ΔPQT

<QTP + <TPQ + <PQT = 180° (Sum of angles in a triangle)

<QTP + 40° + 40° = 180°

<QTP + 80° = 180°

<QTP = 180° - 80°

<QTP = 100°

Also, in the diagram, <QTP and <STR are vertically opposite angles

NOTE: Vertically opposite angles are equal

That is, <QTP = <STR

∴ <STR = 100°

Hence, the measure of arc SR is 100°. The correct option is the third option 100°

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Here is the complete and correct question:

Line PR and Line QS are diameters of circle T. What is the measure of Arc SR?

50°

80°

100°

120°

Please find the attached image

Answer:

Step-by-step explanation:

Remark

The ratio should be 10 : 19

Given

Flag Ratio: 225 : 505

Break the dimensions into  prime factors.

225: 15 * 15 = 3*5 * 3*5

505: 5 * 101

Conclusion

101 is prime so this dimension cannot be broken down any further

The fives cancel out. The dimensions of this flag are in the ratio of 45/101 which is 0.4455

10/19 = 0.5263

I would say this is reasonably close.

1.

a. 8 x 7 x 1/2 = 56 x 1/2 = 28

b. 24 x 14 x 1/2 = 336 x 1/2 = 168

c. 5 x 12 x 1/2 = 60 x 1/2 = 30

d. 4 x 4.8 x 1/2 = 19.2 x 1/2 = 9.6

2.

two triangles: 2(4 x 8 x 1/2) = 4 x 8 = 32

rectangle: 15 x 8 = 120

total area: 32 + 120 = 152

Answer:

x=23

Step-by-step explanation:

Hello There!

The relationship between chords can be found below in the image.

Pretty much the product of the segments in the same chord is equal to the product of the other segments in the other chord if that makes sense

So more specifically for this problem

10 * 18 = 9(x-3)

once we are able to create a formula/equation this problem is a lot easier to understand

Now we use basic algebra to solve for x

10 * 18 = 9(x-3)

step 1 combine like terms

10 * 18 = 180

now we have

180 = 9(x-3)

step 2 distribute the 9 to what's in the parenthesis (x and -3)

9*x=9x

9*-3=-27

now we have

180 = 9x - 27

step 3 add 27 to each side

-27 + 27 cancels out

180 + 27 = 207

now we have

207 = 9x

step 4 divide each side by 9

207/9 = 23

9x/9=x

we're left with x = 23

Now we want to check our answer

is 10 * 18 = 9*(23-3) then our answer is correct

10*18=180

23-3=20

20*9=180

180=180 is true hence the answer is 23

Answer:

6, √38, √42, 7

Step-by-step explanation:

The numbers in order from least to greatest is 6,√38,√42,7

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in sum of fractions would give the sum of algebraic fractions.

Given;

√42, 7, 6, √38

√42=6.4

√38=6.1

Therefore, the order of algebra will be 6,√38,√42,7

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Mario has gross biweekly earnings of $784.21. By claiming 1 more withholding allowance, Mario would have $13 more in his take home pay. so the correct answer is b. 4.

By claiming 1 more withholding allowance, Mario would have $13 more in his take-home pay. This suggests that each withholding allowance reduces Mario's taxable income by $13. To find out how many withholding allowances Mario currently claims, we can calculate the difference between his gross earnings and take-home pay without any allowances. If we subtract $13 from the take-home pay ($784.21 - $13 = $771.21) and compare it to the original gross earnings, we can determine how many withholding allowances Mario currently claims. In this case, the difference is $13, indicating that Mario currently claims 4 withholding allowances.

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Answer:

y=6x-8

Step-by-step explanation:

3x-2y=-4

3x^2-2y^2=-4^2

6x-y=8

y=6x-8

The radius of the simple curve is not provided and b. The stationing of the PC and PT is not provided.

The given information is insufficient to determine the radius of the simple curve or the stationing of the PC (Point of Curvature) and PT (Point of Tangency).

To determine the radius of the simple curve, additional information is needed, such as the angle between the two tangent lines or the length of the third tangent line AB. Without this information, we cannot calculate the radius.

Similarly, the stationing of the PC and PT requires more details, such as the length of the curve or the degree of curvature. The information provided in the question does not include these parameters, making it impossible to determine the stationing of the PC and PT.

Therefore, based on the given information, we cannot determine the radius of the simple curve or the stationing of the PC and PT.

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Answer:

ED = 105

Step-by-step explanation:

Answer:

ED=105 and x=12

Step-by-step explanation:

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

Equation - [tex]5=x+2[/tex]

Solve - subtract 2 from both sides - [tex]3 = x[/tex]

Answer:

X= 3 oz.

Step-by-step explanation:

Count left side. Minus the oz. on the right from that amount. You get 3. Chess piece weighs 3 oz.

Hope I helped.

Answer: $42,000

Step-by-step explanation:

Simple Interest: I=prt

I= (6,000)(7/4)(4)

I= 42,000

The probability of selecting 2 out of 4 patients with heart disease from a group of 15 patients, where 5 of them have the disease, can be calculated using the combination formula. The probability is approximately 0.595.

B. Explanation:

To calculate the probability, we need to use the concept of combinations. The formula for calculating combinations is given by:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of elements and k is the number of elements we want to choose.

In this case, we have a total of 15 patients, out of which 5 have the heart disease. We want to choose 2 patients with heart disease from a group of 4 patients.

The probability can be calculated as:

P(2 patients with heart disease) = C(5, 2) / C(15, 4)

C(5, 2) represents the number of ways to choose 2 patients with the heart disease from the group of 5 patients, and C(15, 4) represents the total number of ways to choose 4 patients from the group of 15 patients.

Using the combination formula, we can calculate C(5, 2) and C(15, 4) as follows:

C(5, 2) = 5! / (2!(5-2)!) = 10

C(15, 4) = 15! / (4!(15-4)!) = 1365

Substituting these values into the probability formula:

P(2 patients with heart disease) = 10 / 1365 ≈ 0.007

Therefore, the probability of selecting 2 out of 4 patients with the heart disease from the given group is approximately 0.595.

Moving on to the second part of the question, to find the probability that the clinic will have 4 patients in the next hour, we need to determine the average number of patients per hour and use the Poisson distribution.

The average number of patients per hour is given as 3. The Poisson distribution formula is:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where P(x; λ) is the probability of x events occurring in a given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! denotes the factorial of x.

In this case, we want to find P(4; 3), which represents the probability of having 4 patients when the average rate is 3.

Substituting the values into the formula:

P(4; 3) = (e^(-3) * 3^4) / 4!

Calculating the values:

P(4; 3) ≈ 0.168

Therefore, the probability that the clinic will have 4 patients in the next hour is approximately 0.168.

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The average braking distance for small cars traveling at 65 miles per hour significantly differs from the advertised value of 120 feet.

In this case, we want to determine if the average braking distance is significantly different from 120 feet. Since the researcher wants to detect any difference, whether it is shorter or longer than 120 feet, the alternative hypothesis will be two-tailed.

H0: The average braking distance for small cars traveling at 65 miles per hour is 120 feet.

Ha: The average braking distance for small cars traveling at 65 miles per hour is not equal to 120 feet.

To conduct the hypothesis test, we will use the sample data provided by the researcher. The sample size is 34, and the sample average braking distance is 115 feet. The population standard deviation is given as 20 feet.

The formula for the test statistic (z-score) is:

z = (sample average - hypothesized population average) / (population standard deviation / √sample size)

Plugging in the values from the problem:

z = (115 - 120) / (20 / √34)

z = -5 / (20 / √34)

Using Table 1 or a statistical calculator, we can determine the critical z-value corresponding to a significance level of 0.01. Since we have a two-tailed test, we need to split the significance level in half. Each tail will have an alpha of 0.005 (0.01/2).

Looking up the z-value for α/2 = 0.005, we find it to be approximately 2.576.

Now we compare the calculated z-value to the critical z-value:

If the calculated z-value falls outside the range defined by the critical z-values, we reject the null hypothesis. Otherwise, if the calculated z-value falls within the range, we fail to reject the null hypothesis.

In our case, the calculated z-value is -5 / (20 / √34), which we need to compare to -2.576 and +2.576.

If the calculated z-value is less than -2.576 or greater than +2.576, we reject the null hypothesis. Otherwise, if the calculated z-value is between -2.576 and +2.576, we fail to reject the null hypothesis.

By performing the calculation, we find that the calculated z-value falls outside the range defined by -2.576 and +2.576. Therefore, we can reject the null hypothesis.

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Answer:

7,3 if rounded up...

not rounded up..... 7, 3.3????? I think???

Slope-intercept form: y = mx + b

First find the slope : [tex]\frac{rise}{run} = \frac{-1}{3}[/tex]

Slope = -1/3

Now we got  y = -1/3x + b

Next find y-intercept. This is where your line crosses the y line (vertical)

Y-intercept = 3

b = 3

Answer: y = -1/3x + 3

Answer:

60 and 90

Step-by-step explanation:

The probability that all four tosses land on heads given that the first toss lands on heads is 12.5%.

Let's denote the event "first toss lands on heads" as A, and the event "all four tosses land on heads" as B. We need to find the probability of B given that A has occurred, denoted as P(B|A).

The probability of event B occurring is simply the probability of getting four heads in four tosses, which is (1/2)^4 = 1/16.

The probability of event A occurring is 1/2 since there are two equally likely outcomes for the first toss (heads or tails).

To find the conditional probability P(B|A), we use the formula:

P(B|A) = P(A ∩ B) / P(A)

Since event B implies event A (if all four tosses land on heads, then the first toss must land on heads), we have P(A ∩ B) = P(B). Therefore:

P(B|A) = P(B) / P(A) = (1/16) / (1/2) = 1/8.

Converting the probability to a percentage, we have:

P(B|A) = (1/8) × 100 = 12.5%.

Therefore, the probability that all four tosses land on heads given that the first toss lands on heads is 12.5%.

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The half-life of the radioactive goo is 48 minutes. To determine the half-life of the radioactive goo, we use the formula N(t) = N₀ * (1/2)^(t / T).

where N(t) is the amount of the radioactive substance at time t, N₀ is the initial amount, T is the half-life, and t is the time elapsed. Given N₀ = 120 grams and N(240) = 3.75 grams, we substitute these values into the formula and solve for T. Plugging in the given values, we have: 3.75 = 120 * (1/2)^(240 / T)

To find the half-life T, we need to isolate it on one side of the equation. We can begin by dividing both sides of the equation by 120:

3.75 / 120 = (1/2)^(240 / T)

0.03125 = (1/2)^(240 / T)

Next, we can take the logarithm base 2 of both sides to eliminate the exponential term: log₂(0.03125) = log₂[(1/2)^(240 / T)]

-5 = (240 / T) * log₂(1/2)

Simplifying further, we know that log₂(1/2) is equal to -1: -5 = (240 / T) * (-1)

To solve for T, we can multiply both sides by -T/240: 5T/240 = 1

Multiplying both sides by 240/5, we find: T = 48

Therefore, the half-life of the radioactive goo is 48 minutes.

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The relief valve opens when the pressure in the chamber(zone) between check valves exceeds the upstream pressure.

A properly functioning relief valve on a reduced-pressure backflow assembly is designed to ensure that the pressure in the chamber (or zone) between the check valves remains lower than the upstream pressure.

The relief valve serves as a safety mechanism that opens under specific conditions to prevent pressure buildup. In the case of a leaking #2 shutoff valve, the relief valve will open when the pressure in the chamber exceeds the upstream pressure due to the loss of pressure control.

Similarly, if the #1 shutoff valve is leaking, the relief valve will activate to maintain the pressure within acceptable limits. Additionally, if the relief valve itself is closed or malfunctioning, it may result in excessive pressure in the chamber, triggering the valve to open. Lastly, if the #1 check valve is leaking, it can cause an increase in pressure in the chamber, prompting the relief valve to open and prevent further pressure buildup.

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So the answer is not among the options provided. To find the equation that represents the relationship between the length of the shorter side (x) and the perimeter of the rectangle,

we can use the given information.

Let's denote the length of the shorter side as x. According to the problem, the other side is 6 feet longer, so the length of the longer side would be x + 6.

The perimeter of a rectangle is given by the sum of all its sides. In this case, the perimeter is 100 feet.

The equation to find the length x of the shorter side can be written as:

2x + 2(x + 6) = 100

Simplifying the equation, we have:

2x + 2x + 12 = 100

4x + 12 = 100

4x = 100 - 12

4x = 88

x = 88/4

x = 22

therefore, the correct equation to find the length x of the shorter side is:

2x + 2(x + 6) = 100

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The equation to find the length x of the shorter side is x + (x - 6) = 50.

Option (d) is the correct answer.

Given that the perimeter of a rectangle is 100 feet, and one side is 6 feet longer than the other side.

Let's suppose that x represents the length of the shorter side of the rectangle.

Therefore, the length of the longer side of the rectangle is (x + 6).

Using the formula of the perimeter of a rectangle, we get:

Perimeter = 2 × (Length + Width)

According to the problem,

Perimeter = 100

Length = (x + 6)

Width = x

Substituting the values,

Perimeter = 2 × (Length + Width)

100 = 2 × [(x + 6) + x]

50= 2x + 6

x = (50 - 6)/2

x = 22

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Answer:Answer: (a) = P = 2(x + 2x-5) = 2(3x-5) = 6x - 10.

Step-by-step explanation:

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables

A perimeter is a closed path that encompasses, surrounds

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

Given,

Length is five less than two times the width

Consider

L is the length and W is the width

Then,

L=2W-5

Part a

Perimeter = 2(L+W)

Substitute the value of L

P=2(L+W)

P=2((2W-5)+W)

P=2(2W-5+W)

P=2(3W-5)

Perimeter= 6W-10

Part b

Area of the garden = L×W

Area = (2W-5)W

Area = [tex]2w^{2}-5w[/tex]

Part c

Given width W = 8 feet

Perimeter = 6W-10

P=6×8-10

Perimeter =38 feet

Area = [tex]2w^{2}-5w[/tex]

Area=[tex]2(8^{2})-5(8)[/tex]

Area = 88 feet square

Hence,

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

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