If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y

Answer:

Step-by-step explanation:

Student's t test for correlated groups reduces to Student's t test for single samples using difference scores. Therefore, the correct answer is (b).

In a t test for correlated groups (also known as paired-samples or dependent-samples t test), the same group of participants is measured twice, under two different conditions or at two different times. The difference between the two measurements for each participant is calculated and used as the sample data. The t test for correlated groups compares the mean difference score to zero to determine if there is a significant difference between the two conditions or times.

This can be seen as equivalent to a t test for single samples using difference scores, where the mean difference score is compared to a known or hypothesized value of the population mean difference. In fact, the formula for calculating the t statistic is the same in both cases.

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The adjacent side of a parallelogram are 15 cm and 9 cm in length. If the perpendicular distance between the shorter side is 7 cm. Distance between longer side will be 4.2 cm

A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of opposite sides parallel and equal. An ABCD parallelogram with AB II CD and AD II BC is seen in the provided illustration. As well, as AB = CD and AD = BC. 

Similar to how the area of a rectangle is calculated, the formula for calculating the area of a parallelogram is base times height.

Since, Area of parallelogram = side × height

So, Area =9 × 7=63 square cm

Again apply area formula along longer side.

Since area remains same so,

Area = side × height

63 = 15 × height

So, height = 63 ÷ 15

height = 4.2 cm

Hence the required perpendicular distance along longer side will be 4.2 cm.

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The requried statements about the number of possible solutions are shown below.

The correct statements are:

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Finally, multiplying by 3/20, we get the result:

(3/20) (10/9) ln|12 + \(3x^3\)| + C

= (1/6) ln|12 + \(3x^3\)| + C

To evaluate the integral ∫(10x^2)/(12+3x^3) dx multiplied by 3/20, we can use the substitution method.

Let u = 12 + \(3x^3\)

Then du = \(9x^2\) dx

Rewriting the integral with the substitution, we have:

∫(\(10x^2)/(12+3x^3)\) dx = ∫(\(10x^2)\)/u * du/9\(x^2\)

Canceling out the \(x^2\) terms and simplifying, we get:

∫(10/9u) du

Integrating with respect to u, we have:

(10/9) ∫ du/u

Applying the natural logarithm integration property, the integral becomes:

(10/9) ln|u| + C

Substituting back u = 12 + \(3x^3\), we have:

(10/9) ln|12 + 3\(x^3\)| + C

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Answer:

0= -42

Step-by-step explanation:

Simplify then add 6 to both sides after simplify again and subtract 2x from both sides then finally combine like terms and simplify the expression.

Answer:

The cost for Thato's usage of 35 kl of water is R702.48.

Step-by-step explanation:

Since Thato used 35 kl of water, she falls into the third category where the rate is R16.20 per kl. We can calculate the cost as follows:

Cost = Fixed charge + (Rate per kl × Usage) + Infrastructure fee

The fixed charge is free for infrastructure, so we don't need to include it in this calculation.

Cost = (Rate per kl × Usage) + Infrastructure fee

= (R16.20 × 35) + R7.15

= R567.00 + R7.15

= R574.15

We also need to add 15% VAT to the cost:

Total cost = Cost × (1 + VAT)

= R574.15 × 1.15

= R702.48

Therefore, the cost for Thato's usage of 35 kl of water is R702.48.

2.4.2. Answer: The new fixed charge would be R92.81.

Explanation:

If the fixed charge is increased by 15%, the new fixed charge would be:

New fixed charge = Old fixed charge + (15% of old fixed charge)

= R80.70 + (0.15 × R80.70)

= R80.70 + R12.11

= R92.81

Therefore, the new fixed charge would be R92.81.

Answer:

I think its 8

Step-by-step explanation:

Step-by-step explanation:

the second one (with the -5 as x values) is not a function, because the valid x value -5 has more than one associated different solution value y.

for a function a valid x value can lead only to exactly one result y value.

Answer: 20

Explanation:

The ratio of the the triangles is 1:2 so, 10×2=20

Answer:

x intercept - = 11/2 (5.50000 as a decimal)

y intercept - = 11/1 (11.00000 as a decimal)

Step-by-step explanation:

The correct statement regarding whether the pattern is linear is given as follows:

It is nonlinear because a constant number is not added to each row.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope is the constant rate of change, meaning that a relationship is linear when the output is changed by a constant amount when x is changed be one.

In the table, we have different additions, hence the relation is not linear.

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Answer:

$16152.5 0

Step-by-step explanation:

The two decision while performing hypothesis, these are -

an assertion on a population's makeup. Frequently, a population parameter is used to express it. A statistical hypothesis that is to be tested is known as a null hypothesis.

Alternative hypothesis: A hypothesis that differs from the null hypothesis.

In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

These claims list certain factors as well as their suggested outcomes. Cavities arise as a result of the variable in this case, which is the sugar intake.

The decisions are -

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Answer:

Step-by-step explanation:

We need to compare √8 and 4

To compare the numbers they should both be in the same format

√8 is not a perfect square so we'll put number 4 under root

Now we compare

So √8 is less than 4

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * \(r^{(n-1)}\)

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To write the explicit formula for both an arithmetic and geometric sequence, the following values must be known:

For an Arithmetic Sequence:

The first term (a1) of the sequence.

The common difference (d) between consecutive terms in the sequence.

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

d is the common difference between consecutive terms.

n is the position of the term in the sequence.

For a Geometric Sequence:

The first term (a1) of the sequence.

The common ratio (r) between consecutive terms in the sequence.

The explicit formula for a geometric sequence is:

an = a1 * r^(n-1)

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

r is the common ratio between consecutive terms.

n is the position of the term in the sequence.

Therefore, The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * \(r^{(n-1)}\)

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Answer:

Step-by-step explanation:

If a shoemaker makes three new souls every four minutes, the number of soles he will make in an hour can expressed as shown;

3 souls = 4 minutes

x souls = 1hour (60 minutes)

Cross multiplying to get the number of souls;

4 * x = 3 * 60

4x = 180

x = 180/4

x = 45souls

Hence the number of souls made by this shoemaker in an hour is 45 souls.

Similarly, If another shoemaker makes two new souls every three minutes, the number of soles he will make in an hour can expressed as shown;

2 souls = 3 minutes

y souls = 1hour (60 minutes)

Cross multiplying to get the number of souls;

3 * y = 2 * 60

3y = 120

y = 120/4

y = 30souls

Therefore the number of souls made by this shoemaker in an hour is 30 souls.

The difference in the number souls they made in an hour will be x - y where x = 45 souls and y = 30 souls.

x - y = 45 - 30

The difference is equal to 15 souls

Answer:

Solve for b: b = 6 - a

Solve for a:  a = 6 - b

Step-by-step explanation:

There are two ways we can solve this, solve for a and solve for b.

Lets solve for b first

\(4-b=2-a\)

Add 4 on both sides

\(b=2-a+4\)

Simplify

\(b=6-a\)

Now lets solve for a

\(4-b=2-a\)

Flip the equation

\(2-a=4-b\)

Add 2 on both sides

\(a=4-b+2\)

Simplify

\(a=6-b\)

Answer:

Step-by-step explanation:

I have the same question :(((

sry

Answer:

15.56%

Step-by-step explanation:

The force applied, F,  to the surface is 90N.

The area, A, of the surface is \(20 cm^2\) = \(0.002m^2\)

The pressure on the surface is:

P = F / A = 90 / 0.002 = 45000 Nm^2

The force is increased by 5N, the new force is 95N.

The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.

The pressure is now:

P = 95 / 0.0025 = 38000 Nm^2

The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.

=> Difference = 45000 - 38000 = 7000

% decrease is therefore:

= 7000 / 45000 * 100 = 15.56%

There was a 15.56% decrease.

The ratio of the applied force to the area to which the force is applied,

gives the amount of pressure applied.

The outcome decreases by \(\underline{15.\overline 5 \%}\)

Reasons:

\(\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}\)

The initial force, F₁ = 5 N

The initial area, A₁ = 20 cm²

\(\mathrm{ } P_1=\dfrac{F_1}{A_1 }\)

\(\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa\)

The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N

The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²

The new pressure after the increase is given by the equation;

\(\mathrm{ } P_2=\dfrac{F_2}{A_2 }\)

\(\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}\)

\(Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100\)

\(Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%\)

The outcome decreases by 15.\(\overline 5 \%\)

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Answer:

Hyperbole

Step-by-step explanation:

because i did that test

Answer:

Both r hyperbole

Step-by-step explanation:

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

1

Step-by-step explanation:

because 1/2 time 1 = 1/2

Mixed number is the combination of the whole number and the proper fraction. One is integer and other is fraction in a mixed number. When you multiply a mixed number by another mixed number the product is equal to the another mixed number. For exact same mixed number, when you multiply a mixed number by one  number the product is equal to the mixed number.

Mixed number is the combination of the whole number and the proper fraction. One is integer and other is fraction in a mixed number. As it is the combination of two types of number thus it is known as mixed number.

Mixed number are used to count the whole and part of a thing together.

For example five and a half of a thing can be written as,

\(5+\dfrac{1}{2} =5\dfrac{1}{2}\)

Now when a mixed number is multiplied by the another mixed number the product of both is a another mixed number.

For example let multiply 2 and a half with 3 and a half. The result is,

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =\dfrac{7}{2} \times \dfrac{9}{2}\)

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =\dfrac{63}{4}\)

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =15\dfrac{3}{4}\)

Thus when you multiply a mixed number by another mixed number the product is equal to the another mixed number.

If the product should be equal to the given mixed number thus it need to be multiplied by the one. Thus when you multiply a mixed number by one  number the product is equal to the mixed number.

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Answer:

(d) 22

Step-by-step explanation:

1 to 4 difference is 3

4 to 10 difference is 6

10 to 22 difference is 12

22 to 46 difference is 24

46 to 94 difference is 48

so, you can see that the difference multiplies by 2 (3x2 = 6, 6x2 = 12, etc.)

thus the answer is d. 22

A) One cup of white paint requires 3/7 cups of red paint.

B) The constant of proportionality is 7/3.

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, and even the rate of change.

Given:

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

So,

7 cups of white paint are needed for every 3 cups of red paint

One cup of white paint requires 3/7 cups of red paint.

To calculate the constant of proportionality, we find the ratio of the white and red paints which is

Cups of white paint: Cups of red paint = 1: 3/7 = 7/3

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did u say the answer ?

C. Whole

Answer:

m

Step-by-step explanation:

a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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The measure of the smallest angle in the triangle is 10.8°

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.

using cosine rule c² = a²+b²+2abcosC

a = 8, b = 8 and c = 3

3² = 8²+8²+2×8×8cos C

9 = 64+64+128cos C

128cosC = 9- 128

cos C = -119/128

cos C = -0.93

C = cos^-1 0.93

C = 158.4°

therefore 158.4 + A+ B = 180

A= B

2A = 180-158.4

2A = 21.6

A = 21.6/2

A = 10.8°

therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°

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Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.