Round your answer to the tenths place if necessary

Help me please:(

Answer:

The length of a leg is 12.5 and its base is 15

Step-by-step explanation:

Using Heron's formula, the area of the triangle A = √[s(s - a)(s - b)(s - c)] where s = (a + b + c)/2. Now, for an isosceles, a = b and c = its base.

So,  A = √[s(s - a)(s - a)(s - c)] = √[s(s - a)²(s - c)] = (s - a)√[s(s - c)] and s = (a + a + c)/2 = a + c/2 ⇒ s = a + c/2 (1)

Given that the perimeter a + b + c = 2a + c = 40 = 2s ⇒ s = 40/2 = 20 and A = hc/2 where h = length of altitude to base = 10.

So, A = 10c/2 = 5c

So, 5c = (s - a)√[s(s - c)]

From (1) s - a = c/2.

So, 5c = (s - a)√[s(s - c)]

5c = (c/2)√[s(s - c)]

10 = √[s(s - c)]

squaring by sides, we have

100 = s(s - c) since s = 20,

s(s - c) = 100

20(20 - c) = 100

20 - c = 100/20

20 - c = 5

c = 20 - 5

c = 15

From (1),

s = a + c/2

a = s - c/2

= 20 - 15/2

= 20 - 7.5

= 12.5

Since a = b = 12.5

So, the length of a leg is 12.5 and its base is 15

American jurists (fill in the names) defined law as predictions of how a court will decide specific legal questions, based on a functional perspective.

American jurists Oliver Wendell Holmes Jr. and Benjamin Cardozo are known for their functionalist approach to defining law. They viewed law not merely as a set of abstract principles or rules, but as a prediction of how courts will decide specific legal questions in practice. According to their perspective, the law should be seen as a dynamic and evolving system that adapts to societal changes and reflects the judgments and decisions of the judiciary. By emphasizing the functional aspect of law, Holmes and Cardozo recognized the importance of considering how legal principles are actually applied and interpreted in real-world scenarios. Their approach acknowledges that the interpretation and application of law by judges can vary and evolve over time, depending on factors such as legal precedent, social context, and the specific facts of the cases before them.

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The formula to calculate the total value of a single row is to use the SUM function (e.g., "=SUM(A1:F1)").

The formula to calculate the total value of a single row in a table or spreadsheet depends on the specific context and structure of the data.

If you have a row of values in Excel or a similar spreadsheet program, you can use the SUM function to calculate the total. The SUM function adds up all the numbers within a specified range or cell references. For example, if your row of values is in cells A1 to F1, you can use the formula "=SUM(A1:F1)" to calculate the total value of that row.

Alternatively, if you have a row of values in a programming language or mathematical notation, you can manually sum up the values by adding them together. For example, if you have a row of values represented as an array or list in Python, you can use a loop or a built-in function like `sum()` to calculate the total.

In general, the specific formula or method to calculate the total value of a row depends on the software or programming language you are using and the structure of the data.

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Answer: 21

Step-by-step explanation:

The answer is on the picture!!

Answer: 9

Step-by-step explanation:

The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B),  and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

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Answer:

6:06

Step-by-step explanation:

After 13 minutes, at exactly 5:53, your bowl was half full. At what time will your bowl be full of dough?

We have;

1/2 full = 13 minutes

1 (full of dough) = x minutes

1/2x = 13 × 1

x = 13 ÷ 1/2

x = 13 × 2

x = 26 minutes

Hence the bowl would be full of dough after 26 minutes.

26 minutes - 13 minutes

= 13 minutes

This means dough increased in size

= After 13 minutes again.

The time at which your bowl be

full of dough is calculated as:

The initial time is was 1/2 full + 13 minutes

5:53 + 13 minutes

=5:66 minutes

= 6 hours 6 minutes = 6:06

The bowl would be full of dough at 6:06

If the ANOVA test is statistically significant, then we can determine which groups are different by means of the F statistic, which is defined by the ratio of the mean sum square to the average square error (none of the options are correct).

The ANOVA test can be defined as a strategy to assess when differences between two or even more groups and or populations in the same are statistically significant.

Moreover, the F statistic refers to the results of the ANOVA, which is used to show statistically significant differences between groups in the sample.

Therefore, with this data, we can see that the ANOVA test is used to determine when differences between groups in the sample are significant enough to explain a given working hypothesis, and it is associated with the F statistics.

Complete question:

Your ANOVA is statistically significant. How will you determine which groups are different?

Use planned or unplanned comparisons.

Look at what the means in each group are.

Conduct Levene's test.

None of the above

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All the angles in the given diagram are;

∠5 = 81°

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = 133°

We are given different angles. Thus;

52 + ∠5 + 47 = 180

This is because sum of angles on a straight line is 180°. Thus;

99 + ∠5 = 180

∠5 = 180 - 99

∠5 = 81°

∠1 = ∠5 + 47° because of the definition of corresponding angles. Thus;

∠1 = 81° + 47°

∠1 = 128°

∠2 = 52° because they are corresponding angles.

∠3 = 47° because they are corresponding angles.

∠4 = 180 - 47° because sum of angles on a straight line is 180°.

∠4 = 133°

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Answer:

73u/ - 11

Step-by-step explanation:

Answer:

-5.05. U -6

Step-by-step explanation:

Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6

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:

62.4

Step-by-step explanation:

Sam's score= x

John's score= 2/3x-4

john's score + sam's score=100

x+2/3x-4=100

5/3x-4=100

5/3x=104

5x=312

x=62.4

Sam's score is 62.4

John's score is 37.6

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

f(x) = max{0,x} then f(x)=0 if x<0 and f(x)=x if x≥0.

f(x)=7x-2xlnx

When x tends to -∞, f is the constant function zero, therefore limit n tends to infinity f(x) = 0.

When x tends to ∞, f(x)=x and x grows indefinitely. Thus limit n tends to infinity f(x) = infinity.

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x) = x and if x<0, f'(0)=0 (the derivative of the constant zero).

In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

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Answer:

7

Step-by-step explanation:

17 times 60 is 1020

1020 plus 30 is 1050

2 times 60 is 120

120 plus 30 is 150

1050 divided by 150 is 7

Answer:

B.7

Step-by-step explanation:

17.5 divided by 2.5 is 7

Answer:

SAS

Step-by-step explanation:

SAS is side, angle, side so two sides are congruent and one angle is congruent.

If you look at the picture the side that is shared by both triangles is equal.(side)

The two sides with the line through them means they're equal.

(side)

The picture shows the two angles are equal.

(angle)

=SSA or SAS

Answer:

The last year value of the house will be $230,000.

Step-by-step explanation:

GIVEN: Decrease in house price = 20%

            Current house price = $184,000

TO FIND: Value of the house last year

SOLUTION:

If the value of the house decreased by 20% during last year, this means the value of the house this year is 80% of last year's value.

Let the value of the house last year be 'x'.

If the value of the house today is  $184,000, then:

                           \(80/100 * x = 184,000\\\\0.8x = 184,000\\\\x = 184,000/0.8\\\\x = 230,000\)

Therefore, the last year value of the house will be $230,000.

Answer:

all real numbers

Step-by-step explanation:

Answer:

all real numbers

Step-by-step explanation:

The answer is all real numbers on Edge.   (VERIFIED Edge Answer)

Make sure to click "thanks" and rate this answer to let others know this is the correct answer for this question.  

Edge Tip: Answers do not mix or change.

The output of the function can be calculated by plugging in 2 for x and evaluating the equation:\(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation \(f(x) = ax^n + bx^n-1 + cx^n-2 + … + z\), where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: \(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

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Complete question:

What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?

The length of the hypotenuse is z = √(23² + 12²) and the length of the other side is y = 12z. is the answer.

Consider a right triangle with a side of length x opposite angle A, a side of length y opposite angle B, and a hypotenuse of length z opposite the right angle.

If sinB= 12 and x=23, then we can find the length of the other side (y) and the length of the hypotenuse (z) using the following method: We have, sinB = 12, and B is the angle opposite the side y.

Using the sin ratio, we have: sinB = y/z

We are given the value of sinB as 12.

Substituting this value in the above equation, we get:12 = y/z

This means that y = 12zWe are also given x=23.

Using the Pythagoras theorem, we have:x² + y² = z²

Substituting the value of y from above, we get:23² + (12z)² = z²

Solving for z, we get: z = √(23² + 12²)

Therefore, the length of the hypotenuse is z = √(23² + 12²) and the length of the other side is y = 12z.

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Step-by-step explanation:

US nickels are .077  inches thick per nickel

1250 ft = 1250  ft * 12 inches / ft = 15 000 inches

15000 inches /  ( .077 in / nickel ) =

        194 805  nickels  ( stacked on their flat sides) equals the Empire State building

Answer:

Step-by-step explanation:

12

Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).

Answer:

See below.

In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a

Step-by-step explanation:

Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1

If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a

An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.

But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.

Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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The wrapping paper area needed to create the gift box is equal to 358 square feet.

In this problem we need to determine the area of the wrapping paper, needed to create a gift box in the form of a right rectangular prism, whose area is the sum of six rectangular sections, the area formula of a rectangle is equal to:

A = w · h

Where:

The area of the wrapping paper is now calculated:

A = 2 · (5 ft) · (7 ft) + 2 · (12 ft) · (5 ft) + 2 · (7 ft) · (12 ft)

A = 70 ft² + 120 ft² + 168 ft²

A = 358 ft²

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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28sinθ is the maximum area of the triangle

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The two sides of triangle are of length 7 and 8.

Triangle has an included angle has a measure of θ degrees.

We need to find the maximum area

A=1/2×7×8×sinθ

A equal to one by two time of seven times of eight times sin theta.

A=7×4×sinθ

A=28sinθ

Hence, 28sinθ is the maximum area of the triangle

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