The weight of Jacob’s backpack is made up of the weight of the contents of the backpack as well as the weight of the backpack itself. Seventy percent of the total weight is textbooks. His notebooks weigh a total of 4 pounds, and the backpack itself weighs 2 pounds. If the backpack contains only textbooks and notebooks, which equation can be used to determine t, the weight of the textbooks? 0. 7(t) = t â€" 4 â€" 2 0. 7(t) = t 4 2 0. 7t(4 2) = t 0. 7(t 4 2) = t.

Therefore, the speed of the boat for the first part was 10 mph, and the speed of the boat for the second part was 7 mph.

Speed is the measure of how quickly something or someone is moving. You can determine an object's average speed if you know how far it travelled and how long it took. Distance times speed equals speed.

Let's call the speed of the boat for the second part "x" mph. Then, according to the problem, the speed of the boat for the first part is "x+3" mph.

Let's also call the distance across the lake "d" miles.

Using the formula distance = rate × time, we can set up two equations based on the information given in the problem:

For the trip across the lake:

d = (x+3) × 7

For the trip back across the lake:

d = x × 10

Since both equations equal "d," we can set them equal to each other and solve for "x":

(x+3) × 7 = x × 10

7x + 21 = 10x

21 = 3x

x = 7 mph

So the speed of the boat for the second part is 7 mph. To find the speed of the boat for the first part, we can add 3 mph to get:

x+3 = 7+3 = 10 mph

Therefore, the speed of the boat for the first part was 10 mph, and the speed of the boat for the second part was 7 mph.

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Answer:

The x-intercepts of this quadratic function would be (-1, 0) and (4, 0).

Step-by-step explanation:

The x-intercepts of a function are where the graph of the function hits the x-axis on a coordinate plane, meaning the y-coordinate of an x-intercept would always be 0. In this quadratic function's graph, the parabola crosses the x-intercept at two points: (-1, 0) and (4, 0). So that would be the correct answer.

Answer:

can you blow the image up or tell me what it says

Step-by-step explanation:

Answer:

Convert from degrees to radians using the ratio

π

180.001989675

radians

We can estimate that the length of the hypotenuse is about 8.6 units.

We can use the Pythagorean theorem to estimate the length of the hypotenuse of the right triangle formed by the given opposite and adjacent sides.

The Pythagorean theorem states that:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

Substituting the given values, we get:

c^2 = 7^2 + 5^2

c^2 = 49 + 25

c^2 = 74

To estimate the length of the hypotenuse, we can take the square root of both sides:

c ≈ √74

c ≈ 8.6 (rounded to one decimal place)

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Answer:

P(A and B) = P(AnB)

Step-by-step explanation:

\(P( \frac{A}{B} ) = \frac{P(AnB)}{P(B)} \\from \: bayes \: theorem \\ P(AnB) = P(B) \times P( \frac{A}{B}) \\ = 0.45 \times 0.7 \\ = 0.315\)

Answer: 0.392

Step-by-step explanation:

So P(A)xP(B|A)= P(AnB)

Plug in

0.56x0.7=0.392

The probability of a particular 3-bit error event, given the error pattern χΦχΦΦΦΦχ, where χ represents an error bit and Φ represents a correct bit, is \(p^3(1-p)^5\).

In the given error pattern χΦχΦΦΦΦχ, there are three error bits (χ) and five correct bits (Φ). The probability of a single-bit error in the channel is p.

For each error bit, the probability of an error occurring is p, and for each correct bit, the probability of no error occurring is (1-p). Since the events of error and no error are independent, we can multiply the probabilities for each bit.

Therefore, the probability of the error pattern χΦχΦΦΦΦχ occurring is:

p * (1-p) * p * (1-p) * (1-p) * (1-p) * (1-p) * p

Simplifying this expression, we have:

\(p^3(1-p)^5\)

Thus, the probability of the particular 3-bit error event, given the error pattern χΦχΦΦΦΦχ, is \(p^3(1-p)^5\).

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Let smaller no be x and bigger be y

Put it in eq(1)

Now

The numbers are 9 and 30

Answer:

(x-5)^2/36 + (y+3)^2/36=1

Step-by-step explanation:

Use the standard form to find the center, (h, k)

The total amount of the loan is $8000. The remaining balance is $2535.68. The payoff amount is:$2535.68 + $17.50 = $2553.18

Here are the solutions to the given problem:

1. The amount of loan Kay has taken is $6000 ($8000 - $2000).

Add-on interest is calculated based on the original loan amount of $6000.

The total amount of interest he will pay is:

$6000 × 0.035 × \frac{3}{12} = $52.50

So, he will pay $52.50 in total interest.

2. The monthly payment is calculated by dividing the total amount of the loan plus interest by the number of payments.

The total amount of the loan is the sum of the down payment and the loan amount ($2000 + $6000 = $8000).

The total amount of interest is $52.50.

The number of payments is 36.

The monthly payment is:

{$8000 + $52.50}{36} approx $227.68

So, the monthly payments are $227.68.

3. The annual percentage rate (APR) is the percentage of the total amount of interest charged per year, expressed as a percentage of the original loan amount.

The total amount of interest charged is $52.50.

The original loan amount is $6000.

The duration of the loan is 36 months. The APR value (to the nearest half percent) is:

APR = \frac{($52.50 × 12)}{$6000 × 3} = 0.07

       = 7 \%

So, the APR value is 7%.4.

(a) The unearned interest is the interest that Kay hasn't yet paid but has been charged. If Kay repays the loan before the end of the 36-month period, he will owe the remaining balance on the loan, including any unearned interest.

After 24 months, there are 12 remaining payments. The unearned interest is:

\frac{36-24}{36} × $52.50 = $17.50

So, the unearned interest is $17.50.

(b) If he repays the loan with 12 months remaining, the payoff amount will be the remaining balance plus any unearned interest. The remaining balance is calculated by subtracting the sum of the payments made from the total amount of the loan.

The sum of the payments made is $227.68 × 24 = $5464.32.

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Answer: 3
________________________________
initial value = starting value when x is 0

as you can see when x is 0 y is 3

so your initial value is 3

________________________________

Hoped this helped.

The inequality that determines how many hours it would take Steve to walk at least 21 miles on Day 1 is of:

3.5x ≥ 21.

Hence the solution is of:

x ≥ 6.

(he would need to walk at least 6 hours).

Stevie's velocity is given as follows:

3.5 miles per hour.

Hence the equation that gives the distance that he would walk in t hours is given as follows:

y = 3.5x.

Which is a proportional relationship with a constant of 3.5.

To walk at least 21 miles, the inequality is defined as follows:

3.5x ≥ 21.

Then the inequality is solved similarly to an equality, obtaining the range of values as follows:

x ≥ 21/3.5

x ≥ 6 hours.

Stevie's velocity is of 3.5 miles per hour.

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Answer:

D

Step-by-step explanation:

Answer: Reform

Step-by-step explanation:

Reform means make changes in order to improve it.

The coordinates of the centroid for the region bounded by the curves y = x, y = 1/x, y = 0, and x = 11 are (x, ȳ) = (5.5, ln(11)), where x represents the x-coordinate of the centroid and ȳ represents the y-coordinate of the centroid.

To find the centroid of a region, we need to calculate the coordinates (x, ȳ) using the formulas:

x = (1/A) ∫[a,b] x f(x) dx

ȳ = (1/A) ∫[a,b] (f(x))^2 dx

Where A represents the area of the region.

In this case, the region is bounded by the curves y = x, y = 1/x, y = 0, and x = 11.

To find the x-coordinate of the centroid, we integrate x over the interval [a, b] = [1, 11]:

x = (1/A) ∫[1,11] x dx = (1/22) [x^2/2] |[1,11] = 5.5

To find the y-coordinate of the centroid, we integrate (f(x))^2 (in this case, (1/x)^2) over the same interval:

ȳ = (1/A) ∫[1,11] (1/x)^2 dx = (1/22) [ln(x)] |[1,11] = ln(11)

Therefore, the coordinates of the centroid for the given region are (x, ȳ) = (5.5, ln(11)).

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

A

Step-by-step explanation:

Given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

f(x) = x² + 8x ← is in standard form

with a = 1 , b = 8 , then

x = - \(\frac{8}{2}\) = - 4

substitute x = - 4 into f(x) for corresponding y- coordinate

f(- 4) = (- 4)² + 8(- 4) = 16 - 32 = - 16

vertex = (- 4, - 16 ) → A

Answer:

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

Therefore;

∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement \({}\)                                       Reason          

\(\underset{BD}{\rightarrow}\) bisects ∠CBE \({}\)                            Given

Therefore;

∠EBD ≅ ∠CBD  \({}\)                              Definition of angle bisector

∠FBE ≅ ∠CBA \({}\)                                Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD \({}\)     Transitive property

∠FBE + ∠EBD = ∠FBD \({}\)                    Angle addition postulate

∠CBA + ∠CBD = ∠ABD \({}\)                   Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD        \({}\)                          Transitive property.

The cost of each Child ticket is  £ 15

Total number of people = 54

Number of adults = 30

Number of Children = Total number of people - Number of adults

                                 = 54 - 30 = 24

Cost of each adult ticket =£ x

Cost of each Child ticket = £x-25

Total Cost of tickets = £1560

The total cost of tickets =( Number of adults * Cost of each adult ticket) + (Number of Children*Cost of each Child ticket)

1560 = (30*x) + (24*(x-25))

1560 = 30x + 24 x - 600

1560 + 600 = 54x

2160 = 54x

40 = x

Therefore,

The cost of each adult ticket is £ 40

The cost of each Child ticket is  £(x - 25) = £ 15

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We will prove this statement using mathematical induction.

Base case: For n = 4, we have 3n = 3(4) = 12 and (n+1)! = 5! = 120. Clearly, 12 ≤ 120, so the statement is true for the base case.

Induction hypothesis: Assume that the statement is true for some non-negative integer k ≥ 4, i.e., 3k ≤ (k+1)!.

Induction step: We need to prove that the statement is also true for k+1, i.e., 3(k+1) ≤ (k+2)!.

Starting with the left-hand side:

3(k+1) = 3k + 3

By the induction hypothesis, we know that 3k ≤ (k+1)!, so:

3(k+1) ≤ (k+1)! + 3

We can rewrite (k+1)! + 3 as (k+1)(k+1)! = (k+2)!, so:

3(k+1) ≤ (k+2)!

This completes the induction step.

Therefore, by mathematical induction, we have proven that for any non-negative integer n ≥ 4, 3n ≤ (n+1)!.

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The surface area of the cone is about 1, 256. 64 in ²

To find the surface area of the cone, the formula to be used is:

= π x radius x slant height +  π x radius ²

First find the radius to be:

= Diameter / 2

= 20 / 2

= 10 in

The surface area of the cone is :

= π x radius x slant height +  π x radius ²

= 3. 14 x 10 x 30 +  3. 14 x 10 ²

= 1256.63706

= 1, 256. 64 in ²

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Answer:

B.

Step-by-step explanation:

Answer is b

lmk if im wrong

(answer got deleted, lost my brainliest :(. )

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

When you input values for x, you can determine a single output for y. ... f(x)= 4x + 1 is written in function notation and is read “f of x equals 4x plus 1. ... perimeter, P = 4s, as the function p(x) = 4x, and the formula for area, A = x2, as a(x) = x2. ... in both cases, you substitute 2 for x, multiply it by 4 and add 1, simplifying to get 9

Step-by-step explanation:

got it off of google

The sum of a regular polygon's exterior angles will always equal 360 degrees.

Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).

Here,

The sum of the exterior angles of a regular polygon will always equal 360 degrees.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

hi, where is the question?

Step-by-step explanation:

Answer:   C

Step-by-step explanation:

 Since from your original g(x) went to f(x) which is up 6

add 6 to g(x)

g(x)= f(x) +6

Answer:

The y intercept is 3

The slope is -2

The equation is y= -2x +3

Answer:

The answer is below

Step-by-step explanation:

A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field position after the 3 plays.

Solution:

Number line is a straight line on which numbers are marked and are separated at regular intervals. A number line can be used for both addition and subtraction. Addition is done by counting to the right while subtraction is done by counting to the left.

Given that the football team lost 5 yards in each of their three downs, this is the same as 3(-5) = (-5) + (-5) + (-5)

Hence since it is negative we move to the left. Starting from 0, we move 5 units to the left 3 times, this gives -15

Answer:

b^itch as^s do ur own work

Step-by-step explanation:

ANSWER

221

use a calculator