Fernando followed two diagonal paths, Paths 1 and 2, to get from his house, F, to a neighborhood corner store, C, as shown below.

The width of the box whose height is given as 7 inches and length is three inches more than the width given a volume of 910 is; 10 inches.

It follows from the task content that the height of the box is; 7 inches.

Let, x = width of the box and;

x+ 3 = length of the box.

Therefore, since the volume of a box is given by the formula;

V = l × b × h

Therefore, we have;

910 = 7 (x) (x+3)

Divide both sides by; 7

130 = x² + 3x

x² + 3x -130 = 0.

(x+13) (x-10) = 0

Therefore, x = -13 or x = 10.

Ultimately, the possible values of the width are; -13 or 10.

Since the width cannot be a negative number, it follows that the width of the box in discuss is; 10 inches.

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Answer:

99.47

Step-by-step explanation:

86.50/15 =

+86.50 =

99.47

Answer:

Step-by-step explanation:

They are the same angle in the obtuse triangle and same points but mixed up proof: you can highlight the lines and make points for the letters w x and y hope this helps :)

Answer:

x=7

Step-by-step explanation:

1.     -2x+3=-11  << first make sure the x is one one side of the equal sign. so  remove the 3, by subtracting if from 11

2. -2x+3=-11

         -3   -3

         =

3.  -2x= -14    <<  then so isolate the x= divide -2 from -14 (two negatives divided equals a positive)

4. x=7

Answer:

53.67⁰

Step-by-step explanation:

Give the height of the fence to be 2.4 m tall

Height of the tree = 16m

Horizintal distance from the fence to the tree = 10m

Check the diagram in the attachment.

From the attachment, we will need to first calculate the height AB

AC = AB+BC

Given AC = height of the r=tree = 16m

BC is the height of the fence = 2.4m

16 = AB + 2.4

AB = 16-2.4

AB = 13.6m

Using the SOH CAH TOA trig identity on right angled triangle AEB with AB as the opposite and AB and the adjacent as BE

Using TOA;

tan ∝ = opposite/adjacent = AB/BE

∝ is the angle of elevation of the top of the tree from the top of the fence​.

tan∝ = 13.6/10

tan∝ = 1.36

∝ = tan⁻¹1.36

∝ = 53.67⁰

Hence the angle of elevation of the top of the tree from the top of the fence​ is 53.67⁰

Answer:

b) 31 and c) 11

Step-by-step explanation:

IMPORTANT: Order of operations is PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/SUbtraction).

B) Solve inside the parentheses first.

1. 2^3 - 6 = (2*2*2) - 6 = 2.

2. Now the equation looks like 3 + 7 (2)^2, Next we need to do exponents.

3. 2 to the power of 2 is 4, leaving you with 3+7(4)

4. Now multiply 7*4, which is 28 then add 3 to it.

So B) would ultimately be 31.

C) As we did in equation B, we start with parentheses.

1. (6/3) we can just simplify this to 2, so those parentheses are out of the way.

2. Now we need to do exponents, (-3)^2. This is the same as -3 * -3. This would equal 9.

3. So far the equation looks like 4 + 9 - 2 / 2.

4. Next would be to solve any multiplication/division problems we have. We can see from step 3 that we have a -2 divided by a positive 2. This would give us -1.

5. Now the equation looks like 4 + 9 - 2. Now you can just working from left to right.

So C) would solve to 11

Please let me know if I made any errors, good luck!

Answer:

The shadow is not the same image as the lady

Step-by-step explanation:

Had it in a test got it right

The lady’s shadow in the picture not a rigid transformation because the shadow is not the same image as the lady.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.

In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

The transformation of a function may involve any change.

These can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

The lady’s shadow in the picture not a rigid transformation because the shadow is not the same image as the lady.

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Answer:

a) X=5

b)X=-2

Step-by-step explanation:

Using translation concepts, the transformations are given as follows:

a) The function is horizontally compressed by a factor of 3 and shifted down one unit.

b) The function is shifted right 3 units and vertically stretched by a factor of 2.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The transformations are:

Item b:

The transformations are:

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All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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4x - 5y = -9

-4x + y = -7

Step 1

Eliminate variable x

Different sign eliminate x and add.

-5y + y = -9 + (-7)

- 4y = -9 - 7

- 4y = -16

y = -16/-4

y = 4

Step 2

Substitute y in any equation and find x.

-4x + y = -7

-4x + 4 = -7

-4x = -7 - 4

-4x = -11

x = -11/-4

x = 11/4

X = 11/4 Y = 4

The correct answer is 475 and 525. To find the range of values that 95% of the observations lie between.

We can use the empirical rule, which states that for a normal distribution with mean μ and standard deviation σ, about 95% of the observations will fall within 2 standard deviations of the mean.

In this case, the mean is 500 and the standard deviation is 10. So, 2 standard deviations below the mean is 500 - 2(10) = 480, and 2 standard deviations above the mean is 500 + 2(10) = 520.

Therefore, about 95% of the observations lie between 480 and 520, or approximately between 475 and 525.

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(a) To form a seven-letter word by mixing up the letters in the word "PICTURE," we have 7 different letters. The number of ways to arrange these letters can be calculated using the concept of permutations. Since all the letters are distinct, the total number of arrangements is given by 7 factorial, denoted as 7!, which is equal to 5040.

(b) If all the vowels (I and U) have to be at the beginning of the word, we treat them as a single unit. So, we have 5 units to arrange: Vowels (IU), P, C, T, R, and E. The number of ways to arrange these 5 units is 5 factorial, denoted as 5!, which is equal to 120.

(c) If no vowel is isolated between two consonants, we can consider the arrangement of consonants (P, C, T, R) and vowels (I, U, E) separately. For the consonants, we have 4 units to arrange, and for the vowels, we have 3 units to arrange. The number of ways to arrange the consonants is 4 factorial (4!), which is equal to 24, and the number of ways to arrange the vowels is 3 factorial (3!), which is equal to 6. To find the total number of arrangements satisfying the given condition, we multiply these two values together: 24 * 6 = 144. Therefore, the number of ways to form a seven-letter word by mixing up the letters in the word "PICTURE" is:

(a) 5040

(b) 120

(c) 144.

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Answer:

Step-by-step explanation:

(b)

(i)

(ii)

(a) Cumulative frequency is 500, median is at 249, 250, the horizontal line from point 250 on y-axis intersecting the graph at approximately 52%, this is the median

(b)  Vertical line from the 45% mark intersects the graph at approximately 177th point. The number of candidates passed the test:

(iii) P(pass) = 323/500 = 0.626 or 62.6%

The property of real numbers illustrated by each equation depends on the specific equation. However, some common properties of real numbers include the commutative property, associative property, distributive property, identity property, and inverse property.

The property of real numbers illustrated by each equation depends on the specific equation. However, there are several properties of real numbers that can be applied to equations:

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Answer: 7.7 years

Step-by-step explanation:

Given

The cost of HD TV is $700 and it is decreasing at the rate of 15% per year

After one year it becomes

\(\Rightarrow 700-700\times 15\%\\\Rightarrow 700(1-0.15)\)

after 2 year it becomes

\(\Rightarrow 700(1-0.15)-700(1-0.15)\times 15\%\\\Rightarrow 700(1-0.15)(1-0.15)\\\Rightarrow 700(1-0.15)^2\)

Suppose, after x years it becomes $200

\(\Rightarrow 200=700(1-0.15)^x\\\\\Rightarrow \dfrac{2}{7}=0.85^x\\\\\text{Taking log both sides}\\\\\Rightarrow x=\dfrac{\ln (\frac{2}{7})}{\ln (0.85)}\\\\\Rightarrow x=7.7\ \text{years}\)

Thus, it takes 7.7 years for the cost to come under $200.

1. the general solution of the differential equation is given by: y(x) = c₁e⁻ˣ + c₂xe⁻ˣ + c₃e^(-2x) cos(x) + c₄e⁻²ˣ sin(x)

2.  the general solution of the differential equation is: y(x) = c₁ + c₂x + c₃eˣ - (3/2)eˣ + (3/2)x + (3/2)sin(x) + (3/2)cos(x)

3. The general solution of the differential equation is: y(x) = c₁e⁴ˣ + c₂eˣ + (10/3)e⁴ˣ.

1. To solve the differential equation (D⁴ + 6D³ + 17D² + 22D + 13)y = 0, we can use the characteristic equation method. Let's denote D as the differentiation operator d/dx.

The characteristic equation is obtained by substituting y = \(e^{rx\) into the differential equation:

r⁴ + 6r³ + 17r²+ 22r + 13 = 0

Factoring the equation, we find that r = -1, -1, -2 ± i

Therefore, the general solution of the differential equation is given by:

y(x) = c₁e⁻ˣ + c₂xe⁻ˣ + c₃e^(-2x) cos(x) + c₄e⁻²ˣ sin(x)

To find the specific solution satisfying the initial conditions, we substitute the given values of y(0), y'(0), y''(0), and y'''(0) into the general solution and solve for the constants c₁, c₂, c₃, and c₄.

2. To solve the differential equation D²(D-1)y = 3eˣ + sin(x), we can use the method of undetermined coefficients.

First, we solve the homogeneous equation D²(D-1)y = 0. The characteristic equation is r³ - r² = 0, which has roots r = 0 and r = 1 with multiplicity 2.

The homogeneous solution is given by,  y_h(x) = c₁ + c₂x + c₃eˣ

Next, we find a particular solution for the non-homogeneous equation D²(D-1)y = 3eˣ + sin(x). Since the right-hand side contains both an exponential and trigonometric function, we assume a particular solution of the form y_p(x) = Aeˣ + Bx + Csin(x) + Dcos(x), where A, B, C, and D are constants.

Differentiating y_p(x), we obtain y_p'(x) = Aeˣ + B + Ccos(x) - Dsin(x) and y_p''(x) = Aeˣ - Csin(x) - Dcos(x).

Substituting these derivatives into the differential equation, we equate the coefficients of the terms:

A - C = 0 (from eˣ terms)

B - D = 0 (from x terms)

A + C = 0 (from sin(x) terms)

B + D = 3 (from cos(x) terms)

Solving these equations, we find A = -3/2, B = 3/2, C = 3/2, and D = 3/2.

Therefore, the general solution of the differential equation is:

y(x) = y_h(x) + y_p(x) = c₁ + c₂x + c₃eˣ - (3/2)eˣ + (3/2)x + (3/2)sin(x) + (3/2)cos(x)

3. To solve the differential equation y'' - 3y' - 4y = 30e⁴ˣ, we can use the method of undetermined coefficients.

First, we solve the associated homogeneous equation y'' - 3y' - 4y = 0. The characteristic equation is r²- 3r - 4 = 0, which factors as (r - 4)(r + 1) = 0. The roots are r = 4 and r = -1.

The homogeneous solution is

given by: y_h(x) = c₁e⁴ˣ + c₂e⁻ˣ

Next, we find a particular solution for the non-homogeneous equation y'' - 3y' - 4y = 30e⁴ˣ. Since the right-hand side contains an exponential function, we assume a particular solution of the form y_p(x) = Ae⁴ˣ where A is a constant.

Differentiating y_p(x), we obtain y_p'(x) = 4Ae⁴ˣ and y_p''(x) = 16Ae⁴ˣ.

Substituting these derivatives into the differential equation, we have:

16Ae⁴ˣ - 3(4Ae⁴ˣ) - 4(Ae⁴ˣ) = 30e⁴ˣ

Simplifying, we get 9Ae⁴ˣ = 30e⁴ˣ which implies 9A = 30. Solving for A, we find A = 10/3.

Therefore, the general solution of the differential equation is:

y(x) = y_h(x) + y_p(x) = c₁e⁴ˣ + c₂e⁻ˣ + (10/3)e⁴ˣ

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Answer:

a) 5:3

b) 7.5:5.3

Step-by-step explanation:

150min : 90min (1 and a half hour)

10 : 6

5 : 3

150 × 10 mm : 1060 mm

1500 : 1060

750 : 530

7.5 : 5.3

Answer:

Tn2= 6

Tn3=-12

Tn4= 24

Tn5= -48

Step-by-step explanation:

Tn= ar^n-1

Now

Tn1= -3×-2^1-1

=-3×-2^0

= -3×1= -3

Tn2= -3×-2^2-1

= -3×-2=6

Tn3= -3×-2^3-1

= -3×-2^2

=-3×4= -12

Tn4= -3×-2^4-1

= -3×-2^3

= -3×-8= 24

Tn5= -3×-2^5-1

= -3×-2^4

= -3×16= -48

Answer:

Refer to the attachment

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by

Expression; \(\rm \dfrac{4+2i}{8-3i}\)

A complex conjugate is formed by changing the sign between two terms in a complex number i.e. a+ ib has conjugate a-ib and a- ib has conjugate like a+ ib.

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

\(=\rm \dfrac{4+2i}{8-3i}\\\\= \rm \dfrac{4+2i}{8-3i}\times \dfrac{8+3i}{8+3i}\\\\= \dfrac{(4+2i) \times (8+3i)}{(8)^2-(-3i)^2}\\\\= \dfrac{32+12i+16i+6i^2}{64+9}\\\\=\dfrac{32+28i+6i^2}{73}\)

Hence, The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

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Answer:

70

Step-by-step explanation:

Hello there! Let's work this through:

Firstly, we might want to simply 2 1/2 into 5/2, for simplification.

So, we now have 4 * 7 * 5/2

Simplifying we have \(\frac{4*7*5}{2}\)

We see that we can easily simplify 4/2 into 2 * 7 * 5

Further simplifying we get 10*7

Last bit and we get our answer of 70

From here we get 2

the graph that adequately fits the description would be a pictograph

because shows a symbol for a word or phrase

By using differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5. It will be 32,572.03 in³. Which is option (d).

The possible error in measuring the radius of the sphere is 0.5 in

The formula for the volume of a sphere is given by V(r) = 4/3πr³

The volume of the sphere when r=72 in is given by V(72) = 4/3π(72)³

When r= 72 + 0.5 in= 72.5 in, the volume of the sphere can be calculated using the formula:

V(72.5) = 4/3π(72.5)³

The difference between these two volumes, V(72) and V(72.5), gives us the maximum error while measuring the volume of a sphere. It can be calculated as follows:

V(72.5) - V(72) = 4/3π(72.5)³ - 4/3π(72)³= 4/3π [ (72.5)³ - (72)³ ]= 4/3π [ (72 + 0.5)³ - 72³ ]= (4/3)π [ 3(72²)(0.5) + 3(72)(0.5²) + 0.5³ ]≈ (4/3)π [ 777.5 ]= 3.28 × 10⁴ in³

Therefore, the maximum error while measuring the volume of a sphere with a radius of 72 in, where the possible error in measuring the radius is 0.5 in, is approximately 3.28 × 10⁴ in³ or 32,572.03 in³. Therefore coorect option is (D).

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The decreasing part of the curve has negative gradient, i.e for x = (-1.67, 1.67).

Given that,
C is the curve with the equation \(y=x^3-2x^2-15x+5\),
the domain for the negative gradient to g=be determined.

The slope is defined as the gradient of y relative to the x and also the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

Here, Curve c with \(y=x^3-2x^2-15x+5\) is plotted on the graph, when the curve has a negative gradient it implies that the curve is a decreasing curve so from this we can conclude that through the bof x  = (-1.67, 1.67) the curve is decreasing.

Thus, the decreasing part of the curve has negative gradient, i.e for x = (-1.67, 1.67).

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The radial distances from the center (-3, -2), to the points on the circumference (0, -6), and (a, 0), found using the distance formula, indicates that a = -3 ± √21

The distance between points (x₁, y₁), and (x₂, y₂), on the coordinate plane, can be found using the formula; d = √((x₂ - x₁)² + (y₂ - y₁)²).

The coordinates of the center of the circle = (-3, -2)

The coordinates of the locations (on the circumference of the circle), through which the circle passes = (0, -6) and (a, 0)

Therefore the distances between points (0, -6) and (-3, -2) and (a, 0) and (-3, -2) are the same;

The distance from (0, -6) to (-3, -2) = The distance from (a, 0) to (-3, -2)

(-3 - 0)² + (-2 - (-6))² = (-3 - a)² + (-2 - 0)²

25 = a² + 6·a + 9 + 4 = a² + 6·a + 13

a² + 6·a + 13 = 25 (symmetric property)

a² + 6·a + 13 - 25 = 0

a² + 6·a - 12 = 0

a = (-6 ± √(6² - 4×1×(-12)))/(2×1) = (-6 ± √(84))/2

a = (-3 ± √(21))

a ≈ 1.58 and a ≈ -7.58

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