Jen's goal is to run a total of 22 miles in 5 days Monday she ran for three quarters of a mile Tuesday 5:00 and 1/8 Wednesday 0 Thursday 6 and 1/4 how many did she run on Friday

The lengths of the longest sides of the similar triangles are:40 and 16 respectively.

To calculate the lengths of the longest side of each triangle, recall that the corresponding sides of similar triangles are proportional to each other.

Therefore, we have the following:

Longest side of the first triangle = 3x - 8

Longest side of the second triangle = x

Shortest side of the first triangle = 15

Shortest side of the second triangle = 6

Thus:

3x - 8 / x = 15/6

Cross multiply:

6(3x - 8) = 15x

18x - 48 = 15x

18x - 15x = 48

3x = 48

x = 16

Longest side of the first triangle = 3x - 8 = 3(16) - 8 = 40

Longest side of the second triangle = x = 16

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Therefore, Chuck can paint 65 fence posts per hour as per given equation.

Let's call the rate at which Chuck can paint fence posts "c" (in posts per hour). Then, according to the problem, Diana can paint at a rate of "c + 10" posts per hour. Using the given information, we can set up an equation relating their rates:

150 / (c + 10) = 130 / c

To solve for c, we can cross-multiply and simplify:

150c = 130(c + 10)

150c = 130c + 1300

20c = 1300

c = 65

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The area of the trapezoid is 159.8m²(1dp)

A trapezoid is a quadrilateral with one pair of opposite sides parallel.

The area of a trapezoid is expressed as;

A = 1/2( a+b)h

where a and b are the parallel sides

Here ;

a = 23.6 m

b = 14.9m

sin 59= h/9.7

h = sin59 × 9.7

h = 8.3

Area = 1/2( 23.6+14.9) 8.3

Area = 319.55/2

Area = 159.8m² ( 1dp)

therefore the area of the trapezoid is 159.8m²

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A: The point estimate for the mean lifetime of the battery is the sample mean, which is 120.1 hours.
B: The critical value is approximately 1.96.

C: Standard Error = 2.83

D: Margin of Error = 5.55

E: 95% Confidence Interval = (114.55, 125.65)
F: Since the upper bound of the 95% confidence interval is 125.65, which is less than 130, it is unlikely that the population mean μ is greater than 130.

A: The point estimate for the mean lifetime of the battery is the sample mean, which is 120.1 hours.

B: To find the critical value, we'll use the standard normal (Z) distribution for a 95% confidence interval. The critical value, Z, corresponds to 0.025 in each tail (since 95% confidence means 2.5% in each tail). From the Z-table, the critical value is approximately 1.96.

C: To find the standard error, we use the formula:

Standard Error = (Standard Deviation) / √(Sample Size) = 20 / √(50) = 20 / 7.071 = 2.83

D: To find the margin of error, we use the formula:

Margin of Error = (Critical Value) * (Standard Error) = 1.96 * 2.83 = 5.55

E: To construct the 95% confidence interval, we add and subtract the margin of error from the point estimate:

Lower Bound = 120.1 - 5.55 = 114.55 hours
Upper Bound = 120.1 + 5.55 = 125.65 hours

95% Confidence Interval = (114.55, 125.65)

F: Since the upper bound of the 95% confidence interval is 125.65, which is less than 130, it is unlikely that the population mean μ is greater than 130.

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Using circle theorems, the indicated measures are:

1. m<Q = 55°      2. m<E = 39°    3. m(KN) = 190°    4. m<UTS = 69°

1. In the first problem, the circle theorem we would apply is the angle of intersecting tangents theorem, which is:

m<Q = 1/2(235 - (360 - 235)

m<Q = 55°

2. The circle theorem we would apply is the angle of intersecting secants theorem, which is:

m<E = 1/2(139 - 61)

m<E = 39°

3. Apply the angle of intersecting secant and tangent theorem, which is:

65 = 1/2(m(KN) - 60)

130 = m(KN) - 60

m(KN) = 130 + 60

m(KN) = 190°

4. The circle theorem to use is the angle of intersecting tangents theorem, which is:

11x - 8 = 1/2[(37x - 10) - (14x + 13)]

2(11x - 8) = 37x - 10 - 14x - 13

22x - 16 = 23x - 23

22x - 23x = 16 - 23

-x = -7

x = 7

m<UTS = 11x - 8 = 11(7) - 8

m<UTS = 69°

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The 95% confidence interval for the difference in the mean distances between oil changes for all luxury cars and all compact lower-price cars is (-94.86, 310.86) miles.

To construct the confidence interval, we use the two-sample t-test with equal variances assumption. We calculate the pooled standard deviation, which is a weighted average of the sample standard deviations based on their degrees of freedom. Then, we compute the standard error of the difference in means using the pooled standard deviation and the sample sizes.

We find the t-value using a t-distribution table with (n1+n2-2) degrees of freedom and a significance level of 0.05. Finally, we construct the confidence interval by adding and subtracting the product of the t-value and the standard error from the difference in sample means. Since the confidence interval includes zero, we conclude that there is no significant difference in the mean distance driven between oil changes for luxury and compact cars.

Therefore, we can infer that the cost of the car is not a significant factor in determining whether people follow the standard recommendation for automobile oil changes.

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The monthly costs are given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The membership costs $20 per month and members get a discounted price of $1.50 per slice of pizza, hence the intercept and the slope are given as follows:

b = 20, m = 1.5.

Hence the cost function for x slices is given as follows:

C(x) = 1.5x + 20.

For 11 slices, the cost is given as follows:

C(11) = 1.5(11) + 20 = $36.50.

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The length of arc BC is 8/3 feet.

To find the length of arc BC, we first need to find the measure of angle BOC, where O is the center of the circle. Since angle BAC is 1/3 of one radian, and the central angle BOC intercepts the same arc BC, we know that angle BOC is three times angle BAC, or one radian.

Since the radius of the circle is 8 feet, the circumference is 2πr, or 16π feet. Since angle BOC is one radian, it subtends an arc on the circumference that is 1/2 of the total circumference, or 8π feet.

Therefore, the length of arc BC is 1/3 of arc BOC, or 8π/3 feet.

To find the length of arc BC, we will follow these steps:

1. Identify the given information: The radius of the circle is 8 feet, and the angle BAC is 1/3 of a radian.

2. Determine the central angle in radians: Since angle BAC is 1/3 of a radian, the central angle (θ) of the circle that corresponds to arc BC is also 1/3 of a radian.

3. Calculate the length of arc BC using the formula: Arc length (L) = radius (r) × central angle (θ).

In this case, r = 8 feet and θ = 1/3 radian.

L = 8 × (1/3)
L = 8/3

4. Simplify the expression: L = 8/3 feet.

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The cost of packaging per weight unit of the box is x^2/(x + 2)

From the question, we have the following parameters that can be used in our computation:

Cost = x^2

Weight = x + 2

The cost of packaging per weight unit is calculated as

Unit rate = Cost/Weight

Substitute the known values in the above equation, so, we have the following representation

Unit rate = x^2/(x + 2)

Hence, the unit cost is x^2/(x + 2)

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It would take a penguin approximately 4.5 hours to travel 112.5 miles at a speed of 25 miles per hour.

To find out how long it would take a penguin to travel 112.5 miles at a rate of 25 miles per hour, we can use the formula:

time = distance ÷ speed

Substituting the values given in the question, we get:

time = 112.5 miles ÷ 25 miles per hour

Simplifying this expression, we get:

time = 4.5 hours

Therefore, it would take a penguin approximately 4.5 hours to travel 112.5 miles at its maximum speed of 25 miles per hour. It's worth noting that this calculation assumes that the penguin would maintain a constant speed throughout its journey, which may not always be the case in reality. Factors such as weather conditions, terrain, and the penguin's energy levels could all affect its speed and travel time.

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The measure of angle C in the quadrilateral is 65 degrees.

A quadrilateral is simply a closed polygon that has four sides, four vertices and four angles

The sum of the interior angles of any quadrilateral is 360°.

The figure in the image is a quadrilateral.

Since the sum of the interior angles of any quadrilateral is 360°.

Hence:

Angle A + Angle B + Angle C + Angle D =  360°

Plug in the given values

90 + 115 + 90 + C = 360

295 + C = 360

C = 360 - 295

C = 65°

Therefore, angle C is 65°

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Let's denote Molly's age as "M" and her father James' age as "J". We know that James is currently 33 years old (J = 33) and his age is three times Molly's age minus three years (J = 3M - 3).We need to find how many years from now (let's call this "Y") will James' age be twice Molly's age. In other words, in Y years, James will be 2 times older than Molly (J + Y = 2(M + Y)).

Now let's solve the problem step by step:

1. We know that J = 33 and J = 3M - 3. So, we can write the equation as: 33 = 3M - 3.
2. Add 3 to both sides: 36 = 3M.
3. Divide both sides by 3: M = 12. So, Molly is currently 12 years old.

Next, we need to find Y:

1. We know that J + Y = 2(M + Y). Substitute J and M with their values: 33 + Y = 2(12 + Y).
2. Simplify the equation: 33 + Y = 24 + 2Y.
3. Subtract Y from both sides: 33 = 24 + Y.
4. Subtract 24 from both sides: Y = 9.

So, in 9 years from now, James will be twice Molly's age.

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If the talent contest has a total of $1000 in prize money, and there are five prizes to be awarded, we can divide the total prize money by the number of prizes to find the amount of money for each prize.

So, $1000 / 5 = $200 for each prize.

Therefore, the amount of money for each of the five prizes is $200.

The probability that it will rain on Thursday, given that it is sunny on Sunday, is 0.5 or 50%. To set up the transition matrix for this Markov chain, we use the probabilities given in the question. The matrix would be:

P = [ 3/5 1/5 1/5 ]
   [   0  3/5 3/5 ]
   [ 1/5 3/5 1/5 ]

Each row represents the current state, and the entries in the row represent the probabilities of transitioning to each of the three states (in the same order as the states are listed).

To determine the probability that it will rain on Thursday if it is sunny on Sunday, we need to calculate the probability of being in the rainy state on Thursday, given that we are in the sunny state on Sunday. We can use matrix multiplication to find this probability. Starting with the row vector [0 0 1] (representing the initial state of being in the rainy state), we multiply it by the transition matrix three times (since we are interested in the probability on Thursday, which is three days away from Sunday):

[0 0 1] x P x P x P = [0.15 0.35 0.5]

So, the probability that it will rain on Thursday, given that it is sunny on Sunday, is 0.5 or 50%.

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Answer: $8.03

Step-by-step explanation:

All you gotta do is divide 24 by 2.99. (24/2.99)

Answer:

0.124 cent

Step-by-step explanation:

U Can Solve It By Saying If 24 Bottle =$2.99 Then

1 Bottle = X

You Will Criss Cross It And Solve

If there is NO VARIATION in shell thickness within a population of snails, and no mutations occur, shell thickness does not evolve in response to crab predation. This is because, without variation or mutation, there is no basis for natural selection to act upon, and thus no change in shell thickness can occur in the population.

If shell thickness evolution is absent in snail populations, it is unlikely that shell thickness has evolved in response to agriculture. This means that the population will not be able to adapt to the pressure and the thin-shelled snails will continue to be crabs, while the thick-shelled snails have no advantage.

So the correct answer is that the thick shell does not develop in humans. If there is no change in the population, there will be no basis for natural selection and therefore the shell thickness will not develop as a result of the crab.

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the total number of distinct intersection points in the interior of the octagon is (20*5)/2 - 24 = 49. Therefore, the answer is (a) 49.

The number of intersections is equal to the number of intersections between each pair of the 20 diagonals. We can count the number of intersection points by counting the number of ways to choose 4 diagonals out of the 20, and then counting the number of intersection points for each set of 4 diagonals.

To count the number of intersection points for a set of 4 diagonals, note that each intersection point is determined by the intersection of two lines. Thus, we can count the number of intersection points by counting the number of pairs of lines that intersect, and subtracting the number of intersections that occur at the vertices of the octagon.

Each diagonal intersects 5 other diagonals, so there are (20*5)/2 = 50 pairs of diagonals. However, this overcounts each intersection point twice, so we need to divide by 2 to get the total number of intersection points.

At each vertex, 3 diagonals intersect. There are 8 vertices, so there are 8*3 = 24 intersections that occur at the vertices of the octagon.

Thus, the total number of distinct intersection points in the interior of the octagon is (20*5)/2 - 24 = 49. Therefore, the answer is (a) 49.

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There are 45 ways to combine one level from each of the growth factors.

To find the total number of ways to combine one level from each of the growth factors, we need to multiply the number of levels for each growth factor.

For lighting, there are three levels: low, medium, and high.

For age, there are five levels: 1 month, 2 months, 3 months, 4 months, and 5 months.

For temperature, there are three levels: 20 °C, 22 °C, and 24 °C.

To find the total number of ways to combine one level from each growth factor, we multiply the number of levels for each growth factor:

3 (for lighting) x 5 (for age) x 3 (for temperature) = 45

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The surface area of the rectangular prism is 544 square centimeters.

The figure can be observed to be a large rectangle at the center with two identical smaller rectangles by the sides

area of rectangle = length × width

area large rectangle at the center = 28 cm × 16 cm

area large rectangle at the center = 448 cm²

area of one identical rectangle by the side = 8 cm × 6 cm

area of one identical rectangle by the side = 48 cm²

area of 2 identical rectangle by the side = 96 cm²

Surface area of the rectangular prism = 448 cm² + 96 cm²

Surface area of the rectangular prism = 544 cm²

Therefore, the surface area of the rectangular prism is 544 square centimeters.

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Therefore, the differential of y = x² sin 2x is dy/dx = 2x³ cos 2x + 2x sin 2x. Therefore, the differential of y = √(4+ 5x) is dy/dx = 5/(2√(4+ 5x)).

(a) To find the differential of y = x² sin 2x, we will use the product rule of differentiation, which states that if y = f(x)g(x), then the differential dy/dx is given by:

dy/dx = f(x)g'(x) + g(x)f'(x)

where f'(x) and g'(x) represent the derivatives of f(x) and g(x) with respect to x, respectively. Applying this rule to the given function, we get:

y = x² sin 2x

f(x) = x², g(x) = sin 2x

f'(x) = 2x, g'(x) = 2 cos 2x

dy/dx = f(x)g'(x) + g(x)f'(x)

dy/dx = x²(2 cos 2x) + sin 2x(2x)

dy/dx = 2x³ cos 2x + 2x sin 2x

(b) To find the differential of y = √(4+ 5x), we will use the chain rule of differentiation, which states that if y = f(g(x)), then the differential dy/dx is given by:

dy/dx = f'(g(x))g'(x)

where f'(x) and g'(x) represent the derivatives of f(x) and g(x) with respect to x, respectively. Applying this rule to the given function, we get:

y = √(4+ 5x)

f(x) = √x, g(x) = 4+ 5x

f'(x) = 1/(2√x), g'(x) = 5

dy/dx = f'(g(x))g'(x)

dy/dx = (1/(2√(4+ 5x)))(5)

dy/dx = 5/(2√(4+ 5x))

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Theorem 9.6.1 states that when the origin is an asymptotically stable critical point, the system will approach the origin as t → ∞. In order for the origin to be asymptotically stable, the eigenvalues of the Jacobian matrix evaluated at the origin must have negative real parts.

This means that the system is stable and any small perturbation away from the origin will eventually decay and return to the origin.

To determine stability, we can use the Routh-Hurwitz stability criterion or examine the signs of the eigenvalues of the Jacobian matrix. If all eigenvalues have negative real parts, the system is asymptotically stable.

If some eigenvalues have zero real parts, we need to further analyze the system to determine stability.

Overall, in order for the origin to be asymptotically stable, the system must satisfy certain conditions that ensure stability and decay towards the origin over time.

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Answer:

565,482

Step-by-step explanation:

As the mosquito population grows by a constant rate of 6% each day, we can use the exponential growth formula to create an equation to find the number of mosquitoes in the city "t" days after May 10th.

[tex]\boxed{y=a(1+r)^t}[/tex]

where:

Given the size of the mosquito population on May 10th is 210,000:

Given the growth rate is 6%:

Substitute the values of a and r into the formula to create an equation for the number of mosquitos in the city "t" days after May 10th.

[tex]y=210000(1+0.06)^t[/tex]

[tex]y=210000(1.06)^t[/tex]

To calculate how many mosquitoes will inhabit the city on May 27th, substitute t = 17 into the equation.

[tex]\implies y=210000(1.06)^{17}[/tex]

[tex]\implies y=210000(2.69277278...)[/tex]

[tex]\implies y=565482.285011...[/tex]

[tex]\implies y=565482\; \sf(nearest\;whole\;number)[/tex]

Therefore, the number of mosquitoes that will inhabit the city on May 27th is approximately 565,482 to the nearest whole number.

The other angles of rotation that take point A to point B are -13π/4 radians (negative value) and 3π/4 radians (positive value).

We can locate coterminal angles by adding or subtracting integer multiples of 2π (a full turn) to the given tilt.

The given angle is -5π/4 radians.

We will have to take away 8π/4 from the value above

-5π/4 - 8π/4 =

-13π/4

Hence the negative is -13π/4 radians.

Next we have to solve for the positive

-5π/4 + 8π/4

= 3π/4

Therefore the other angles of rotation that take point A to point B are -13π/4 radians (negative value) and 3π/4 radians (positive value).

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2/63 as a percentage round to the nearest tenth of a percent can be written as 31.7%

Fractions refer to a part of a whole. The word fraction comes from Latin word Fractus meaning broken. A percentage is a number that can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol %.

Fractions can be converted into percentages by the following steps:

1. Convert the fraction into decimals.

Therefore, on converting 2/63 to decimal we get 0.317

2. Multiply the given decimal by 100 to get a percentage

Hence, the percentage we get after multiplication is 31.7%.

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The expressions when simplified are (x^2-2x-35) ÷ (x^2-6x+8) × (x^2-2x) = x(x + 5)(x - 7)/(x - 4) and (x^2 - x - 12) - (x^2 - 4x - 21) = 3x + 9

From the question, we have the following expressions that can be used in our computation:

(x^2-2x-35) ÷ (x^2-6x+8) × (x^2-2x)

Factorize

So, we have

(x + 5)(x - 7) ÷ (x - 2)(x - 4) × x(x - 2)

Apply the product rule

(x + 5)(x - 7) × 1/(x - 2)(x - 4) × x(x - 2)

Cancel out the common factors

So, we have

(x + 5)(x - 7) × x/(x - 4)

Multiply

x(x + 5)(x - 7)/(x - 4)

For (x^2 - x - 12) - (x^2 - 4x - 21), we have

(x^2 - x - 12) - (x^2 - 4x - 21) = 3x + 9

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An inscribed square is a square whose vertices lie on the circumference of a circle.

An inscribed square is a square that is drawn inside a circle, in such a way that all four vertices of the square lie on the circle's circumference. In other words, the square is inscribed within the circle.

To construct an inscribed square, the circle's diameter is divided into four equal parts, and perpendicular lines are drawn at the endpoints of each division. These lines intersect at the center of the circle. The length of each side of the square is then equal to the radius of the circle. The square can be seen as inscribed because its vertices all lie on the circle's circumference.

An inscribed square has some interesting properties, such as the fact that its diagonal is equal in length to the diameter of the circle that circumscribes it. Additionally, the area of an inscribed square can be used to approximate the area of a circle, and vice versa.

Hence, An inscribed square is a square whose vertices are on the circle's circumference.

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Answer: Based on the given scatter plot, it appears that the relationship between the number of mold spores and the number of hours is non-linear and may be better represented by an exponential function rather than a linear function. Therefore, option 4 (an exponential function) would best model this data.

Step-by-step explanation: In the given scatter plot, the number of mold spores is decreasing as the number of hours increases, but not at a constant rate. This indicates that the relationship between the two variables is non-linear.

An exponential function is a type of non-linear function that has the general form:

y = ab^x

where a and b are constants and x is the input variable. In this case, we can think of the number of mold spores as the output variable (y) and the number of hours as the input variable (x).

An exponential function is a good choice for modeling this data because it captures the idea that the rate of mold growth (or decay) changes over time. For example, when there are many mold spores present, the rate of growth may slow down due to competition for resources, and as the number of spores decreases, the rate of decay may also slow down due to the decreased availability of food for the mold.

In contrast, a linear function (such as a straight line) assumes that the rate of change is constant over time, which does not seem to be the case for this data. Therefore, an exponential function would be a better fit for modeling the relationship between the number of mold spores and the number of hours in this experiment.

Answer:

Step-by-step explanation:

5.5x5.5x4.8=145.2

just multiply lxwxh

Answer:

145.2 c,

Step-by-step explanation:

False.

The number of vectors in the span of a set of vectors depends on the linear independence of the vectors.

The number of vectors in the span of a set of vectors depends on the linear independence of the vectors. If a set of vectors is linearly independent, then only the zero vector is in the span of the set. If a set of vectors is linearly dependent, then the span of the set contains infinitely many vectors.

So, the number of vectors in span {a1, a2, a3} can be 1, 2, or 3, depending on whether the set {a1, a2, a3} is linearly dependent or independent.

For example, if a1 = (1,0,0), a2 = (0,1,0), and a3 = (0,0,1), then {a1, a2, a3} is a linearly independent set, and the span of {a1, a2, a3} is just the set of all linear combinations of these vectors, which is the entire space R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.

On the other hand, if a1 = (1,0,0), a2 = (2,0,0), and a3 = (0,1,0), then {a1, a2, a3} is a linearly dependent set, since a2 is a scalar multiple of a1. In this case, the span of {a1, a2, a3} is just the set of all linear combinations of a1 and a3, which is a plane in R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.

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Answer: 5

Step-by-step explanation: I don't know