10 Y What is the vertical change from Point A to Point B? 9 8 What is the horizontal change from Point A to Point B? 7 6 What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary 5 4 3 3 B 2 A 1 X 1 . 2 3 4 5 6 7 8 9 10

Answer:

Since there are 57 varieties of juice and we can choose any number of each variety, we have 57 choices for each of the 6 cans we need to select. Therefore, the total number of ways to select 6 cans of juice is:

57 x 57 x 57 x 57 x 57 x 57 = 57^6

This can be calculated as:

57^6 = (3 x 19)^6 = 3^6 x 19^6 = 729 x 47,287,681

So there are 729 x 47,287,681 = 34,369,561,449 ways to select 6 cans of juice.

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It cannot be concluded that the area of a lateral face is used to find the volume, as the formula for the volume of a pyramid explicitly states that the volume is one-third the product of the base area and height.

Based on the formula V = one-third B h, it can be concluded that the height of the triangular pyramid is 7 cm. It can also be concluded that the base area is 73.5 cm2, and the volume is 171.5 cm3, by substituting the given values in the formula.

However, it cannot be concluded that the volume of a prism with the same base area and height is three times the volume of this pyramid. This is because the volume of a pyramid is one-third the volume of a prism with the same base area and height.

Finally, it cannot be concluded that the area of a lateral face is used to find the volume, as the formula for the volume of a pyramid explicitly states that the volume is one-third the product of the base area and height.

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Answer:

8 in

Step-by-step explanation:

Area of a square = l×w

Since it is a square then l and w are equal to each other.

So we can instead just say l^2 = A

l^2 = 68.2

l = square root of 68.2

l = 8.26

Answer:

±1, ±3/2, ±3/1, ±2/3, ±2/1, ±1/3, ±1/2

Step-by-step explanation:

p/q

{±3,±2,±1}/{±3,±2,±1}

±1, ±3/2, ±3/1, ±2/3, ±2/1, ±1/3, ±1/2

Answer:

Equity

Step-by-step explanation:

A person puts into their relationship is proportional to what they feel they receive; this balance is called equity.

The happiest, most enduring relationships are between best friends, They relish each other's company, trust on one another for love and attention, devote their free time apart, and have a lot of similarities.

A situation when people's benefits from relationships are inversely correlated with their contributions. These consequences don't necessarily have to be equal.

A person who is firmly attached has a strong feeling of merit and anticipates that most others will be receptive and sympathetic.

Because it fosters familiarity—which increases attraction—proximity counts in the attraction process. The probability that we will become interested to someone simply increases when we are in their presence or are exposed to them frequently.

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The expression as a number in scientific notation is 4.2 * 10^5

The expression is given as:

quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared

Rewrite properly as:

[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]

Evaluate the product of 7 and 5.4

So, we have:

[37.8* 10^3 * 10^4]/[9 * 10^2]

Evaluate the product of 10^3 and 10^4

So, we have:

[37.8* 10^7]/[9 * 10^2]

Evaluate the quotient of 37.8 and 9

So, we have:

[4.2 * 10^7]/[10^2]

Evaluate the quotient of 10^7 and 10^2

So, we have:

4.2 * 10^5

Hence, the expression as a number in scientific notation is 4.2 * 10^5

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Answer:

Use distance formula to find the length of the segments

1. H = (-3, 0), F = (3, 2)

2. E = (1, 4), G = (-1, -2)

3. We see the diagonals are congruent, opposite sides are parallel.

The above is the property of a rectangle

Answer:

The Sidewalk is 16 yards^3

Step-by-step explanation:

To find the this answer its quite simple!

Anytime there's an area problem you would have to multiply to numbers to get the area

in this case 16 is the answer because when you multiply 16 * 16 you get the total area of 256 yards. hope this was understand able!

High Hopes^^

Barry-

Answer:

15x

Step-by-step explanation:

assum 1 day you read 15 pages then after X day you reads 15*X=15X

The distance she must climb to reach the peak is greater than 2,663 feet. An inequality to show the remaining distance, d, in feet she must climb to reach the peak is d > 2,663.

Inequlity represents a relationship between two values that is not equal. That is inequlity means no equal and the symbols which used for not equal is ≠ and for comparison are < , > , ≤ , ≥. For example, ax > b etc. We have, Rina is climbing a mountain and mountain height present in above figure. See the figure carefully, the main two points in figure are the following: height of mountain peak

= 12,358 feet

height of base camp = 9,695 feet

we have to write an inequality for the remaining distance, d, in feet. Also, it is specified that she has not reached base camp yet. So, his climbed distance is less than 9,695 feet. Let the remaining distance be 'd feet '. From the above figures, d + base camp height > 12,358

Substract 9695 from both sides

=> d > 12,358 - 9,695

=> d > 2,663

Hence, required inequalty is d > 2,663.

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Complete question:

Rina is climbing a mountain. She has not yet reached base camp. Write an inequality to show the remaining distance, d, in feet she must climb to reach the peak. See tha above figure.

assuming they are the same unit, -1.2 is colder

when a number is negative, the further the number is from zero the less (colder) it is

Answer:

20% decrease

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

60000/75000 = .8

.8 x 100 = 80%

the actual height of the backboard is 8.18 feet.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given

We have been given that Derek places  a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.

We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.

\(\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\\)

Therefore, the actual height of the back-board is 8.18 feet.

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Answer:

Front = 30

Back = 30

Right = 30

Left = 30

Bottom = 25

Top = 16

Total = 161

Let me know if this helps!

The three options that must be true are △xyz ~ △x'y'z', angle xzy ≅ angle y'z'x', and yx ≅ y'x'.

When triangle δxyz is reflected over a vertical line and then dilated by a scale factor of one-half, resulting in triangle δx'y'z', the following must be true of the two triangles:

△xyz ~ △x'y'z': The two triangles are similar, meaning their corresponding angles are congruent and their corresponding sides are proportional.

angle xzy ≅ angle y'z'x': The angle between yz and xy in triangle xyz is congruent to the angle between y'z' and x'y' in triangle x'y'z'.

yx ≅ y'x': The length of yx in triangle xyz is congruent to the length of y'x' in triangle x'y'z'.

The three options that must be true are △xyz ~ △x'y'z', angle xzy ≅ angley'z'x', and yx ≅ y'x'.

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If Mrs brown uses 1/4 package of graph paper for each class, needs 1 1/2 packages to serve all of her classes, she teaches 6 classes.

If Mrs. Brown uses 1/4 package of graph paper for each class, then the total number of classes she teaches can be found by dividing the total number of packages she needs by the amount used per class.

Let x be the number of classes Mrs. Brown teaches. Then, we can set up the following equation:

1/4 * x = 1 1/2

To solve for x, we need to isolate x on one side of the equation. We can start by converting the mixed number 1 1/2 to an improper fraction:

1 1/2 = 3/2

Substituting this value into the equation, we get:

1/4 * x = 3/2

Multiplying both sides by the reciprocal of 1/4, which is 4/1, we get:

x = 3/2 * 4/1 = 6

Therefore, Mrs. Brown teaches 6 classes. We can check this answer by verifying that 1/4 of a package of graph paper is indeed used per class, and that 1 1/2 packages are needed for all 6 classes:

1/4 * 6 = 1 1/2

So the answer is 6 classes.

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If one diagonal of a kite is twice as long as the other diagonal and the area of the kite is 240 square inches, then the length of the shorter diagonal is 4√15 inches and the length of the longer diagonal is 8√15 inches.

To find the length of the diagonals, follow these steps:

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Remainder theorem tells about the remainder of division of a polynomial with x - a. The roots of given function are: 1, -1, -3

If there is a polynomial p(x), and a constant number 'a', then

\(\dfrac{p(x)}{(x-a)} = g(x) + p(a)\)

where g(x) is a factor of p(x)

For the given case, we've got:

\(f(x) = x^3 + 3x^2 -x - 3\)

and

f(1) = 0

Thus, for a = 1, from remainder theorem, we get:

\(\dfrac{p(x)}{(x-a)} = g(x) + p(a)\\\\\dfrac{f(x)}{(x-1)} = g(x) + f(1)\\\\\dfrac{x^3 + 3x^2 - x - 3}{(x-1)} = g(x) + 0\\\\ \dfrac{x^2(x+3) -1(x+3)}{x-1} = \dfrac{(x^2-1)(x+3)}{(x-1)} = g(x)\\\\(x+1)(x+3) = g(x)\)

Thus, the other factor of f(x) is g(x) = (x+1)(x+3)

And we have:

\(\dfrac{f(x)}{x-1} = g(x)\\\\f(x) = (x+1)(x+3)(x-1)\)

Putting it equal to 0, we get:

\(f(x) = 0\\(x+1)(x+3)(x-1) = 0\\x = 1, -1, -3\)

Thus,

The roots of given function are: 1, -1, -3

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Answer:

A

Step-by-step explanation:

got it right on Edge 1943 whilst fighting the German Forces in Northern Italy while my friends were on the beaches of Normandy.

Answer:

There was an initial balance of at least $60 on Peter's gift card.

Step-by-step explanation:

Inequalities

Is a relation that makes a non-equal comparison between two mathematical expressions. Usual comparators are >, <, ≠, ≤, and ≥.

Let's call x to the original amount Peter had on his gift card balance. We know he spent half of it on coffee. Thus the remaining balance is x/2.

He loaded $10 to his balance, so the new balance is x/2+10. Knowing he now has at least $40, we set the inequality as:

x/2+10 ≥40

Subtracting 10:

x/2 ≥40-10

Operating:

x/2 ≥30

Multiplying by 2:

x≥60

There was an initial balance of at least $60 on Peter's gift card.

Answer:

answer is 4.0 it is the answer

we can use the law of conservation of energy. Since the two planets are released from rest, their initial kinetic energy is zero. Therefore, the speed of each planet as they crash together is approximately 5.99 × 10^3 m/s.

we can use the law of conservation of energy. Since the two planets are released from rest, their initial kinetic energy is zero. Therefore, the total initial energy is just the gravitational potential energy, given by:

\(U = -G * M^2 / r\)

where G is the gravitational constant, M is the mass of each planet (assumed to be equal), and r is the initial separation between them. We can then set the final kinetic energy to be equal to the initial potential energy (since the total energy is conserved), and solve for the final speed:

\((1/2) * M * v^2 = G * M^2 / r\)

\(v =\sqrt{(2 * G * M / r)}\)

Substituting the given values of G (6.674 × 10^-11 N m^2/kg^2), M (assuming Jupiter mass of 1.898 × 10^27 kg), and r (1.00 × 10^11 m), we get:

v = sqrt(2 * 6.674 × 10^-11 * 1.898 × 10^27 / 1.00 × 10^11) = 5.99 × 10^3 m/s

Therefore, the speed of each planet as they crash together is approximately 5.99 × 10^3 m/s.

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The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.

According to the given question.

The linear form of the function is

f(x) = mx + b

Also, the function is passing through the points (0, 5) and (1, 20).

So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.

Now,

At (0, 5)

f(0) = m(0) + b

⇒ 5 = 0 + b

⇒ b = 5 ..(i)

Also,

at (1, 20)

f(1) = m(1) + b

⇒ 20 = m + 5     (from i)

⇒ m = 20 - 5

⇒ m = 15

Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by

f(x) = 15(x) + 5   (on substituting the vale of m and b in f(x) = mx + b).

⇒ f(x) = 15x + 5

Hemce, the formula of the function is f(x) = 15x + 5.

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False. In a two-factor ANOVA, if two significant main effects emerge, it does not necessarily mean that the interaction between factors is significant. Main effects and interaction effects are independent of each other and can have different levels of significance.

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The presence of significant main effects does not necessarily indicate a significant interaction between factors in a two-factor ANOVA. It is possible for there to be significant main effects without a significant interaction.

Therefore, it is important to examine both the main effects and the interaction effects in a two-factor ANOVA to fully understand the relationship between the variables being studied.
False

In a two-factor ANOVA, there are three possible significant effects: two main effects for each factor and one interaction effect between the factors. When two significant main effects emerge, it means that there are significant differences in the levels of both factors. However, this does not automatically mean that the interaction between the factors must also be significant. The interaction effect is an entirely separate effect and can be significant or non-significant regardless of the significance of the main effects.

If two significant main effects emerge in a two-factor ANOVA, it does not necessarily mean that the interaction between factors must be significant.

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The key word here is "may" meaning that we could easily have 3 rational roots as well. An example of a cubic having 3 irrational roots would be

(x-1)(x-2)(x-3) = x³ - 6x² + 11x - 6

This has the rational roots x = 1, x = 2, x = 3.

However, we could easily replace 1,2,3 with any irrational numbers we want. So that's why the statement "a cubic has three irrational roots" is sometimes true.

In some cases, a cubic may only have 1 real root and the other 2 roots are imaginary.

Answer:

SSS

Step-by-step explanation:

They have the same ratio

In a 1-year semi-annually paid interest rate swap, with a notional amount of £1,000,000, the swap rate is 3.0%. The floating rate is based on the 6-month LIBOR plus 1%. The market rate refers to the prevailing interest rate for the specified time period.

An interest rate swap involves the exchange of cash flows between two parties based on different interest rate benchmarks. In this case, the swap has a 1-year maturity and payments are made semi-annually.

The fixed rate, also known as the swap rate, is determined at the beginning of the swap agreement and remains fixed throughout the swap's duration. In this scenario, the swap rate is 3.0%.

The floating rate is determined by a reference rate plus a spread. The reference rate used here is the 6-month LIBOR (London Interbank Offered Rate), which is a widely used benchmark for short-term interest rates. The floating rate in this swap is the 6-month LIBOR plus 1%.

The market rate refers to the prevailing interest rate for the specified time period. It represents the current market conditions and influences the pricing and valuation of the interest rate swap.

To fully analyze the swap and its implications, further calculations and considerations, such as the present value of cash flows and potential valuation changes based on market rate movements, would be necessary.

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The Pythagorean Theorem does not hold for any of the three combinations of sides, you can conclude that the triangle is obtuse.

To determine whether three numbers can form an obtuse triangle, you can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.For example, let's say you have three numbers, a, b, and c, and you want to know if they can form an obtuse triangle. To do this, you can use the Triangle Inequality Theorem as follows:

If a is the longest side, then b + c > a

If b is the longest side, then a + c > b

If c is the longest side, then a + b > c

If any of these three inequalities are satisfied, then the three numbers can form a triangle. However, to determine whether the triangle is obtuse, you also need to check whether any of the angles of the triangle is obtuse. To do this, you can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

If the Pythagorean Theorem does not hold for any of the three possible combinations of sides, then the triangle is obtuse.

For example, let's say you have the following three numbers: 3, 4, and 5. Using the Triangle Inequality Theorem, you can determine that these numbers can form a triangle, since 3 + 4 > 5, 4 + 5 > 3, and 3 + 5 > 4. To determine whether the triangle is obtuse, you can use the Pythagorean Theorem as follows:

a^2 + b^2 = c^2: 3^2 + 4^2 = 25 ≠ 5^2

a^2 + c^2 = b^2: 3^2 + 5^2 = 34 ≠ 4^2

b^2 + c^2 = a^2: 4^2 + 5^2 = 41 ≠ 3^2

Since the Pythagorean Theorem does not hold for any of the three combinations of sides, you can conclude that the triangle is obtuse.

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