Ken’s predicted temperature for April is 7ºC. His prediction for May is 2ºC higher than April. He used the number line to solve the problem, starting at 0, moving right to 7, and then moving 2 units to the left. Explain Ken’s error.

Answer:

OPTION C 17=√(27-12)²+(y2-15)² is the correct

Step-by-step explanation:

i hope this will help you :)

Answer:. C

If you are trying to get a value for the unknown y, use C.

Step-by-step explanation:

If there is already a value for y[sub2] and you are trying to find the distance, "A" would be correct.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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Answer:

The percentage increase is 7%.

She paid £160150 for her house.

Step-by-step explanation:

first year : increase 5%

second year : increase 2%

after 2 years : £171360

100%+5%+2%= 107%

107%= £171360

1%= £171360÷107

= £1601.5 (to 5 s.f.)

100%= £1601.5×100

= £160150

Answer:

-5

Step-by-step explanation:

The common difference is

68-73

-5

Answer: i think it is A pls correct me if i'm wrong :)

Step-by-step explanation:

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Answer:

input = 6 leads to output = 15

input = 9 leads to output = 21

==================================================

Explanation:

If the input is x = 6, then,

y = 2x+3

y = 2(6)+3

y = 12+3

y = 15 is the output

Repeat those steps for x = 9

y = 2x+3

y = 2(9)+3

y = 18+3

y = 21 is the output

Answer: 0.33

Step-by-step explanation:

You get 0.33 repeating

Answer:

1/3

Step-by-step explanation:

0.5 divided by 1.5 can also be written as 1/2 divided by 3/2.

So lets rewrite it like this:

(1/2)/(3/2)

From here there are two ways we can solve this. One is to multiply by the reciprocal:

(1/2) × (2/3)= 2/6

which simplifies to 1/3 as your final answer.

The other method is to "oreja"

you multiply the top most number and the bottom most number together and then the two middle ones like so:

(1/2)/(3/2) -> (1×2)/(2×3)

which is 2/6 once again and simplifies to 1/3 the final answer.

A.01 level of significance instead of a .05 level of significance, a researcher is more likely to make a Type II error. This means that they are more likely to fail to reject a false null hypothesis, which could result in inaccurate conclusions being drawn from the research.

The setting a more stringent level of significance, the researcher is requiring stronger evidence in order to reject the null hypothesis. This means that they are less likely to find statistically significant results, even if they are present in the data. This can lead to a higher likelihood of accepting a false null hypothesis, which is a Type II error.

while using a .01 level of significance may help to reduce the risk of Type I errors (rejecting a true null hypothesis), it also increases the risk of Type II errors (failing to reject a false null hypothesis). Researchers must carefully consider their level of significance and balance the risks of these two types of errors in order to draw accurate conclusions from their research.

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To obtain the solution set for a linear inequality in one variable, you first need to isolate the variable on one side of the inequality symbol (either <, >, ≤, or ≥). Then, you can solve for the variable by performing the same operation on both sides of the inequality symbol

To get the solution set for a linear inequality in one variable, follow these steps:

1. Isolate the variable: Rearrange the inequality so the variable is on one side and the constant is on the other side, using addition, subtraction, multiplication, or division as needed.

2. Solve the inequality: Determine the range of values that satisfy the inequality.

3. Express the solution: Write the solution as an interval, using appropriate inequality symbols (e.g., <, >, ≤, or ≥) to show the range of values.

Remember that when multiplying or dividing both sides of an inequality by a negative number, reverse the inequality symbol. The solution set represents all values of the variable that satisfy the inequality.

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Answer:

x = 8 degree

Step-by-step explanation:

8x - 4 = 60 degree (being alternate interior angle)

8x = 60 + 4

8x = 64

x = 64/8

x = 8 degree

Answer:

\( both \: are \: alternate \: interior \: angle \\ \\ = > both \: are \: equal \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > (8x - 4) = 60 \: \: \: \: \: \: \\ \\ = > 8x \: = \: 60 + 4 \\ \\ = > 8x = 64 \\ \\ = > x = 64 \div 8 \\ \\ = > x = 8 \: \\ \\ hope \: it \: is \: helpful \: to \: you\)

Answer:

Well it I hard to find out becasue they both ate alot  of pizza, so I belive Beth ate more pizza

Step-by-step explanation:

Beth had large pizaa and it smaller but she ate alot, the second option is also big but it would make more sense if we do this one

Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

Answer:

x = 19

z = 76

Step-by-step explanation:

The angle that is indicated with (8x - 28) is equal to the angle indicated with (6x + 8):

8x - 28 = 6x + 8 transfer like terms to the same side of the equation

8x - 6x = 8 + 28 add/subtract terms

2x = 36 divide both sides by 2

x = 19

The angle indicated with (6x + 8) and the angle indicated with z are supplementary angles:

6x + 8 + z = 180 replace x with the value we found

6*19 + 8 + z = 180 calculate

104 + z = 180 subtract 104 from both sides

z = 76

12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Divide 8 by 2/3

8÷ 2/3

8× 3/2

12

12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

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Answer:92.84

Step-by-step explanation: 39+27+13.5+13.5 because the two sides are longer than 12

The perimeter of the trapezium is 143.94 ft.

We have,

The perimeter of an isosceles trapezium can be found by adding the lengths of all four sides.

In this case, the trapezium has height = 12 ft and parallel sides of length 27 ft and 39 ft.

To find the length of the non-parallel sides we can use the Pythagorean theorem:

a² = (39 - 27/2)² + 12²

a² = 1440

a ≈ 37.95 ft

Therefore,

The perimeter of the trapezium is:

P = 27 + 39 + 2a

P ≈ 27 + 39 + 2(37.95)

P ≈ 143.9 ft

Rounding to the nearest hundredth place,

we get P ≈ 143.94 ft.

Thus,

The perimeter of the trapezium is 143.94 ft.

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It would take approximately 0.47 years longer for Fatoumata's money to triple than for Josue's Money to triple.

To compare the time it takes for Fatoumata's money to triple with Josue's money to triple, we need to calculate the time it takes for each investment to grow by a factor of 3.

For Josue's investment, we can use the continuous compounding formula:

A = P * e^(rt)

Where:

A is the final amount (3 times the initial investment)

P is the principal amount (initial investment)

r is the interest rate (in decimal form)

t is the time (in years)

e is Euler's number (approximately 2.71828)

For Fatoumata's investment, we can use the compound interest formula:

A = P * (1 + r/n)^(nt)

Where:

A is the final amount (3 times the initial investment)

P is the principal amount (initial investment)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time (in years)

Let's calculate the time it takes for each investment to triple:

For Josue's investment:

3 * 3300 = 3300 * e^(0.075t)

Dividing both sides by 3300:

3 = e^(0.075t)

Taking the natural logarithm of both sides:

ln(3) = 0.075t

t = ln(3) / 0.075 ≈ 12.31 years

For Fatoumata's investment:

3 * 3300 = 3300 * (1 + 0.0775)^t

Dividing both sides by 3300:

3 = (1 + 0.0775)^t

Taking the logarithm of both sides:

log(3) = t * log(1 + 0.0775)

t = log(3) / log(1 + 0.0775) ≈ 12.78 years

To find the difference in time, we subtract the time it takes for Josue's investment from the time it takes for Fatoumata's investment:

12.78 - 12.31 ≈ 0.47 years

Therefore, it would take approximately 0.47 years longer for Fatoumata's money to triple than for Josue's money to triple.

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Answer:

1

Step-by-step explanation:

sin²x = (sinx)²

cos²x = (cosx)²

Step 1: Define

sin²45° + cos²45°

Step 2: Rewrite

(sin45°)² + (cos45°)²

Step 3: Evaluate

sin45° = √2/2

cos45° = √2/2

(√2/2)² + (√2/2)²

1/2 + 1/2

1

The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.

There are four multiples: 4,8,12,16,20,24.

6, 12, 18, and 24 are multiples of 6.

12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.

LCM of 24 and 15 is equal to 222235 = 120.

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Answer:

Angle number 5

Step-by-step explanation:

The sum of supplementary angles equal 180°.

Angle AED, in the diagram given is labelled angle 4.

The angle labelled 4 forms a linear pair with the angle labelled 5.

Since a linear pair of angles = 180°, therefore:

m<AED + m<AEI = 180°.

That is:

m<4 + m<5 = 180°.

Both angles are supplementary.

Therefore, angle number 5 is supplementary to angle AED.

The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.

It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.

It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.

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The equation x² + y² = 9 is the equation of a circle with a radius of 3.

To calculate the radius of a circle, we use the formula r = √(x² + y²), where x and y are the coordinates of the circle's center. In this case, x = 0 and y = 0, so the radius can be found by substituting these values into the formula:

r = √(0² + 0²)

r = √(0)

r = 0

Therefore, the radius of the circle x² + y² = 9 is 3.

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The products of the fractions given are:

1. (-3/4)(7/8) → -21/32

2. (2/3)(-4)(9) → -24

3. (5/16)(-2)(-4)(-4/5) → -2

4. (2 3/5)(7/9) → 91/45

To multiply two or more fractions, multiply the denominators of both fractions together, and their numerators together.

1. (-3/4)(7/8)

Multiply the denominators of the fractions together, and also multiply their numerators:

= (-3 × 7) / (4 × 8)

= (-21) / (32)

(-3/4)(7/8) → -21/32

2. (2/3)(-4)(9)

Multiply the denominators of the fractions together, and also multiply their numerators:

= (2 × -4 × 9) / (3)

= -72/3 = -24

(2/3)(-4)(9) → -24

3. (5/16)(-2)(-4)(-4/5)

= (5 × -2 × -4 × -4) / (16 × 5)

= -160/80 = -2

(5/16)(-2)(-4)(-4/5) → -2

4. (2 3/5)(7/9)

= (13/5)(7/9)

= (13 × 7)/(5 × 9) = 91/45

(2 3/5)(7/9) → 91/45

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Answer: Nicole rented the scooter for 10 days.

Step-by-step explanation:

50 + 25 = 75 (Day 1)

75 + 25 = 100 (Day 2)

100 + 25 = 125 (Day 3)

125 + 25 = 150 (Day 4)

150 + 25 = 175 (Day 5)

175 + 25 = 200 (Day 6)

200 + 25 = 225 (Day 7)

225 + 25 = 250 (Day 8)

250 + 25 = 275 (Day 9)

275 + 25 = 300 (Day 10)

(a) To find the volume of the solid obtained by rotating the region bounded by the curves y = e^(-x^2), y = 0, x = -4, and x = 4 about the x-axis, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula V = 2πx(f(x)-0)dx, where f(x) represents the height of the shell at x.

The integral for the volume is then given by V = ∫[-4, 4] 2πx(e^(-x^2) - 0) dx.

Using a calculator or numerical integration software, we can evaluate this integral to find the volume of the solid.

(b) To find the volume of the solid obtained by rotating the region bounded by the parabola y = 4 - 2x^2 and the x-axis, where the cross-sections perpendicular to the y-axis are squares, we can use the method of slicing.

Each square cross-section will have side length equal to the height of the parabola at a given y-value. The height of the parabola at a given y is given by solving the equation y = 4 - 2x^2 for x, which gives x = ±√((4-y)/2).

The volume of each square cross-section is then given by V = (side length)^2 = (2√((4-y)/2))^2 = 4(4-y)/2 = 8(4-y).

The integral for the volume is then given by V = ∫[0, 4] 8(4-y) dy.

Using a calculator or numerical integration software, we can evaluate this integral to find the volume of the solid.

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The acute angle that the ladder makes with the ground is 70.94°.

To work out the size of the acute angle that the ladder makes with the ground, we need to use trigonometry. Let's call the angle we're trying to find "theta" (θ). We know that the ladder is the hypotenuse of a right-angled triangle, with the wall being one side and the ground being the other. Using the Pythagorean theorem, we can work out the length of the ladder's side of the triangle:
a² + b² = c²
where a = 1.8m (the distance from the wall to the base of the ladder), b =? (the distance from the base of the ladder to the ground), and c = 5.1m (the length of the ladder).
Rearranging this formula, we get:
b² = c² - a²
b² = (5.1)² - (1.8)²
b² = 24.21
b = √24.21
b = 4.92m (to 2 decimal places)
Now that we know the lengths of the sides of the triangle, we can use trigonometry to find the angle θ. Specifically, we can use the tangent function:
tan(θ) = opposite/adjacent
where opposite = b (the distance from the base of the ladder to the ground) and adjacent = a (the distance from the wall to the base of the ladder).
tan(θ) = 4.92/1.8
tan(θ) = 2.7333 (to 4 decimal places)
Now we need to find the inverse tangent (or arctan) of this value to get the angle θ:
θ = arctan(2.7333)
θ = 70.94° (to 1 decimal place)
Therefore, the acute angle that the ladder makes with the ground is 70.94°.

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Answer:

1.95

Step-by-step explanation:

area = (1/2 ×1 ×1 )×3 = 1.5 ( for sides)

area = ( 1/2 ×1 ×0.9) = 0.45 for base

area =1.5+0.45 = 1.95

To find the angle that maximizes the range of the projectile, we can differentiate the x-coordinate equation with respect to θ, set it equal to zero, and solve for θ. This will give us the critical angle that yields the maximum range. We can then substitute this angle back into the x-coordinate equation to find the maximum range.

To find the angle that maximizes the arc length of the trajectory, we can use the arc length formula for parametric curves. The arc length formula for a parametric curve given by x = f(t) and y = g(t) is given by ∫[a,b] √[f'(t)² + g'(t)²] dt. By differentiating this arc length equation with respect to θ and setting it equal to zero, we can find the critical angle that maximizes the arc length. We can then substitute this angle into the x and y coordinate equations to find the coordinates of the point on the trajectory that corresponds to the maximum arc length.

Please note that the exact stepwise solution with specific numbers will depend on the given values of θ and the range of integration for the arc length calculation.

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