A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?

Answer:

See below ~

Step-by-step explanation:

Part 1 - Acceleration when t = 3

Part 2 - Deceleration when t = 12

Part 3 - Total Distance Covered

    2. From t = 4 to t = 8

    3. From t = 8 to t = 15

Total distance = 66 + 88 + 77 = 231 m

Part 4 - Average Speed

    2. Avg. Speed (t = 4 to t = 8)

    3. Avg. Speed (t = 8 to t = 15)

Average Speed = 16.5 + 22 + 11 / 3

Answer:

740

Step-by-step explanation:

The n th term of an arithmetic series is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then

a₁ + 2d = 7 → (1)

a₁ + 6d = 23 → (2)

Subtract (1) from (2) term by term

4d = 16 ( divide both sides by 4 )

d = 4

Substitute d = 4 into (1)

a₁ + 2(4) = 7

a₁ + 8 = 7 ( subtract 8 from both sides )

a₁ = - 1

The sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ] , thus

\(S_{20}\) = \(\frac{20}{2}\) [ (2 × - 1) + (19 × 4) ]

     = 10(- 2 + 76) = 10 × 74 = 740

Answer:

40x + 14

Step-by-step explanation:

7(5x + 2) + 5x

35x + 14 + 5x

40x + 14

\(7(5x + 2) + 5x\)

Distribute:

\((7)(5x)+(7)(2)+5x\)

\(35x+14+5x\)

Combine Like terms:
\((35x+5x)+(14)\)

\(\fbox{40x + 14}\)

For Y:

2x - 5y < 20

2x < 20 + 5y

2x - 20 < 5y

\(\frac{2}{5}x - 4 < y\)

For X:

2x - 5y < 20

2x < 20 + 5y

\(x < 10 + \frac{5}{2} y\)

Answer:

we can find the X and the Y than draw it in the graphic

3x-1=3-x

x=1

y=3-1=2

so the y its 2 and x 1

(1,2)

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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To find the remaining rows a3 and a4 of the 3x4 matrix a, we need to determine the values that satisfy the given reduced row echelon form u=[105101120000]. In this case, a3 and a4 can be calculated as [4 1 0] and [0 0 0], respectively.

The reduced row echelon form of the matrix a, represented by u=[105101120000], indicates that there are two pivot positions (leading 1's) in the first and second columns, while the third and fourth columns are composed of zeros.

Given that a1=[3−1−2] and a2=[−3−12], we can determine the remaining rows a3 and a4 to match the reduced row echelon form. Since the third column of u has a leading 1, we set a3 to be [4 1 0]. As the fourth column consists of all zeros, a4 is set as [0 0 0]. These values ensure that the matrix a satisfies the given reduced row echelon form.

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Answer:

125

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

368 - 243 = 125

Answer:

Step-by-step explanation:

Seven less than the product of a number n and 1/6 is no more than 94, translating:

Solving for n:

It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.

ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.

One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.

In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.

thus we can say that the given statement is true.

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Answer:

X^2 - 3

Is the answer

Step-by-step explanation:

Use a^2 - b^2 = ( a - b) (a + b)

a = x

b =

\(b = \sqrt{3} \)

To solve for taxes in equilibrium, we can start by substituting the given equations into the equation for YD:

YD = Y - T

Since C and T are constant, we can write:

YD = (c0 + c1YD) - (t0 + t1Y)

Now, we can rearrange the equation to isolate YD:

YD = c0 + c1YD - t0 - t1Y

Simplifying further:

YD - c1YD = c0 - t0 - t1Y

Factoring out YD:

YD(1 - c1) = c0 - t0 - t1Y

Dividing both sides by (1 - c1):

YD = (c0 - t0 - t1Y) / (1 - c1)

Now, let's analyze the effects of a drop in c0. If c0 decreases, it implies that consumption decreases. As a result, YD will decrease, leading to a decrease in Y. Taxes will also decrease because they are determined by YD.

If the government cuts spending to balance the budget, it will lead to a decrease in G. This decrease in spending will reduce Y and further decrease YD. However, the impact on Y will depend on the magnitude of the cut in spending.

If the cut in spending is significant, it can counteract the decrease in output caused by the drop in c0. On the other hand, if the cut in spending is small, it may reinforce the effect of the drop in c0 on output. The overall effect on Y will depend on the relative magnitudes of the changes in c0 and G.

A drop in c0 will decrease both Y and taxes in equilibrium. If the government cuts spending to balance the budget, the effect on Y will depend on the magnitude of the cut in spending relative to the decrease in c0.

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The cut in spending required to balance the budget counteracts the effect of the drop in c₀ on output (Y).

In equilibrium, taxes can be solved using the given equations:

C = c₀ + c₁YD

T = t₀+ t₁Y

YD = Y – T

To find taxes in equilibrium, we need to substitute the value of YD into the equation for taxes:

T = t₀ + t₁YD

Now, let's analyze the impact of a drop in c₀ on output (Y) and taxes (T).

When c₀ decreases, it means that the intercept of the consumption function (C) decreases.

This results in a decrease in consumption at every level of income. As a result, the aggregate demand decreases, leading to a decrease in output (Y).

The decrease in output (Y) leads to a decrease in income and, consequently, a decrease in disposable income (YD).

Since taxes (T) depend on disposable income, a decrease in YD will lead to a decrease in taxes (T).

Next, let's consider the effect of a government spending cut to balance the budget.

When the government cuts spending to balance the budget, it reduces its expenditure (G) without changing its tax revenue (T).

This reduction in government spending decreases aggregate demand, which in turn reduces output (Y).

However, since the government is keeping the budget balanced, the decrease in government spending is offset by the decrease in taxes (T) that occurs as a result of the decrease in output (Y).

Therefore, the cut in spending required to balance the budget counteracts the effect of the drop in c₀ on output (Y).

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If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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Many psychologists consider the distinguishing feature of adolescent thought to be the ability to think in terms of abstract concepts or hypothetical situations.

These cognitive abilities play a crucial role in adolescent development, facilitating problem-solving, decision-making, and the exploration of identity and future possibilities.

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Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer: 3 cups for 1 batch and 60 cups for 20 batches.

Step-by-step explanation: We know that to make 5 batches of bagels, you need 15 cups of flour. We can find out how many cups of flour are needed in a single batch by setting up the following ratios and dividing on both sides:

5 : 15

1 : ?

Divide 5 by 1 and you get 5. We have to divide by five on the other side which is 15 / 5. 15 / 5 is 3, so you need 3 cups of flour for 1 batch.

Now, we need to find how much flour is needed for 20 batches.  We can set up the following ratios below but this time, we need to divide 20 by 5:

5 : 15

20 : ?

20 divided by 5 is 4. What divided by 4 gets you to 15? 60 of course, so that means that to make 20 batches, you need 60 cups of flour.

Let me know if this is right! :)

Answer: 1,560,000

Step-by-step explanation: Since each password must start with two digits and end with three letters, we need to consider the number of possible combinations of digits and letters separately.

For the first two digits, there are 10 choices for each position (since we can repeat digits). Therefore, there are 10 × 10 = 100 possible combinations of digits for the first two positions.

For the last three letters, there are 26 choices for the first letter, 25 choices for the second letter (since we can't repeat the first letter), and 24 choices for the third letter (since we can't repeat the first or second letter). Therefore, there are 26 × 25 × 24 = 15,600 possible combinations of letters for the last three positions.

To find the total number of passwords, we multiply the number of possible combinations of digits by the number of possible combinations of letters:

100 × 15,600 = 1,560,000

Therefore, there are 1,560,000 possible passwords of 5 characters that can be made if each password must start with two digits and end with three letters.

Answer:

Step-by-step explanation:

We'Re making 5 character passwords, so i'm going to put down 5 slots. The first 2 are digits and then the last 3 are the letters the digits are with replacement the letters without okay. So how do we go about doing this? Well, i'll start with the mathematical explanation, i'm going to be intuitive so mathematical. Is that we're going to be looking for for this? It'S quite simple. There are 10 digits because it's it's without a with replacement. You just have to multiply so there's 100 different 2 digit numbers from 00 up to 99 for the letters we have a case of permutations, so it would be 26 different letters and then we're choosing 3 of them and the order matters. If the order didn't matter, it would be a combination, but the order matters here. So it's permutation- and this is equal to n factorial over n minus x, factorial, which here 26 factorial over 23 factorial, which is 26 times 25 times 24 point because of a rest, all cancels. So this becomes 16600 possibilities for 3 letter combinations. When you can't repeat a letter multiply that by this, so this is 15600 and we get a total number of possibilities as being this there's the answer. So all about was with the permutation formula. Now i'm going to do it with just an intuition okay. So how many possible letters can go here any of the 26 point? How many possible letters can go here? Well, any that you haven't already used, you can't repeat them. So there's only 25 letters left and here there's only 24 letters left and you can see you get the same answer as before:

1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:

So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.

2) For the Volume of the Pyramid, we can write out the formula below:

Since the scale factor is 1.5 Then we can state that

the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.

3) Hence, the answers are:

1.k=1.5

2. 32 m³

Answer:

it has unlimited answers.

Step-by-step explanation:

We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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The efficiency of the pump (in %) is 0.35%. Hence, option (c) is correct.

Efficiency of the pump:

According to the question, a centrifugal pump with a performance curve is given. For H, the performance curve is given as,

H = 340 - 1.2(Q²) in feetAnd for BP, the performance curve is given as,

BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5 in horsepower (HP)

Where Q is the flow rate in ft³/s.

We have to find the efficiency of the pump which can deliver 8 ft³/s.

The specific weight of water is given as 62.4 lbf/ft³.

Efficiency of the pump,η = (output power/input power)

Where input power = power supplied to the

pump = g × Q × H × w

Where g is acceleration due to gravity, w is the specific weight of the water.

Given, g = 32.2 ft/s², w = 62.4 lbf/ft³ = 32.2 × 62.4 = 2009.28 lbf/ft³'

Using the performance curves,

H = 340 - 1.2(Q²)BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5

Substituting Q = 8 ft³/s, we get

H = 304 ftBP = 77.87 HP Power supplied to the pump = g × Q × H × w

= 32.2 × 8 × 304 × 2009.28

= 16.57 × 10^6 ft-lbf/s

Output power of the

pump = BP × 746

= 77.87 × 746

= 58.17 × 10^3 ft-lbf/s

Efficiency of the pump,η = (output power/input power)η

= (58.17 × 10³)/(16.57 × 10^6)η

= 0.003509

= 0.3509%.

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Answer:

7

Explanation:

The cardinality of a set is the number of elements in the set

Given the set W = {x | x is a day of the week}

The days of the week are {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Hence the set W will be;

W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

n(W) = 7 (since there are 7 days in a week)

Hence the cardinality of the set W is 7

Answer:

1-4x

Step-by-step explanation:

For a quadratic function f(x) = ax² + bx + c, we can find the minimum and maximum value using the formula -b/2a or by graphing the function.

We know that the general form of quadratic function is f(x) = ax² + bx + c ; a ≠ 0

The graph of quadratic function is a parabola. The graph is parabola that either opens upward or downward.

For a quadratic function is f(x) = ax² + bx + c,

if a is positive (a > 0) then the parabola opens upward.

In this case you will be finding the minimum value of f(x) at the vertex of parabola.

if a is negative (a < 0), then the parabola opens downward.

In this case you will find its maximum value of f(x) at the vertex of parabola.

Also, the value of -b/2a will tell you the minimum or maximum value of f(x) which is the vertex of the parabola.

Therefore, to find the minimum and maximum of a quadratic function f(x) = ax² + bx + c :

1) find vertex of function from the graph

2) use formula -b/2a

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The value of ay can be obtained as follows:

ay = ∂F/∂u * ∂u/∂y + ∂F/∂v * ∂v/∂y= [- 2 cos(u) + 2u sin(u)] (- 7/2y²) + 2v * (x/y)= [2 cos(In) + 2 In sin(In)] (- 7/2 (7/2)²) + 2 (7/4) (1/2)= [2 * 0.5403 + 2 * 0.8415] (- 1/14) + 0.875= - 0.2535Therefore,

ar = 1.6518 and ay = - 0.2535.

To find ar and ay using the chain rule for partial differentiation,

given u

= In and v

= xy, F(u, v)

= 1² + v2 – 2u cos(u)

at the point (x, y)

= (1/2, 7/2).The given function is,

F(u, v)

= 1² + v² – 2u cos(u)And the values of u and v are u

= In and v= xy

Where x

= 1/2 and y

= 7/2

Thus, u

= In and v

= (1/2) (7/2)

= 7/4

Now, we need to find the partial differentiation of F(u, v) with respect to r and y using the chain rule of partial differentiation.First,

let's find the value of ∂F/∂u and ∂F/∂v.∂F/∂u

= - 2 cos(u) + 2u sin(u)∂F/∂v

= 2vSo,

the value of ar can be obtained as follows:

ar

= ∂F/∂u * ∂u/∂r + ∂F/∂v * ∂v/∂r

= [- 2 cos(u) + 2u sin(u)] (- 1/2r) + 2v * (y/r)

= [2 cos(In) + 2 In sin(In)] (1/2) + 2 (7/4) (2/√53)

= [2 * 0.5403 + 2 * 0.8415] (1/2) + 0.9884

= 1.6518

Similarly, the value of ay can be obtained as follows:

ay

= ∂F/∂u * ∂u/∂y + ∂F/∂v * ∂v/∂y

= [- 2 cos(u) + 2u sin(u)] (- 7/2y²) + 2v * (x/y)

= [2 cos(In) + 2 In sin(In)] (- 7/2 (7/2)²) + 2 (7/4) (1/2)

= [2 * 0.5403 + 2 * 0.8415] (- 1/14) + 0.875

= - 0.2535

Therefore,

ar

= 1.6518 and ay

= - 0.2535.

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A line will have a positive slope if it makes an acute angle with a positive x-axis while if it makes an obtuse then the slope will be negative thus point (x₁,y₁) can be (2,5) and (x₂,y₂) could be (-7,5).

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.

A line will have a positive slope if it makes an acute angle with a positive x-axis while if it makes an obtuse then the slope will be negative.

As shown below,

The purple line makes an acute angle (less than 90 °) thus slope will be positive and the blue line makes an obtuse angle (greater than 90°) thus the slope is negative.

Hence "point (x₁,y₁) can be (2,5) and (x₂,y₂) could be (-7,5)".

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