What is the absolute value of
x = 8 and x = 18

Answer:

If she bought 2lbs of almonds, she bought 0.4lbs of raisins. If she bought  1lb of almonds, she can buy up to 2.36lbs of raisins. If she bought 0.64lbs of almonds, she can buy up to 1.9lbs of almonds.

Step-by-step explanation:

The total pounds of raisins bought  is 0.47 pounds.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Priya bought 0.47 pounds of raisins, Almonds cost is $5.20 per pound and Raisins cost $2.75 per pound.

The Total cost of almonds purchased = $5.20a

The Total cost of raisins purchased = $2.75r

Where:

a = total pounds of almonds bought

r = total pounds of raisins bought

The Total amount spent on raisins and almonds;  

5.20a +2.75r = 11.70

If 2 pounds of almonds are bought;

5.20(2) +2.75r = 11.70.

10.40 + 2.75r = 11.70

Combine similar terms;

2.75r = 11.70 - 10.40

2.75r = 1.30

Now Divide both sides of the equation by 2.75

r = 0.47 pounds

Hence, the total pounds of raisins bought  is 0.47 pounds.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

The polynomial x3 + 8 is equal to (x + 2)(x2 - 2x + 4).

Answer: the answer would be 2

Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.

2x3=6-4=2

Answer:

70

Step-by-step explanation:

There are 6 numbers that end with 0 and are between 50 and 100 : 50,60,70,80,90,100. And only 70 is the multiple of 7, so 70 is the number.

Answer:

you have to "convert" the one to be set up the same as 3/10:

you subtract fractions, by having a common denominator and then subtracting the numerators.

10/10 -3/10 = 7/10

Step-by-step explanation:

i hope this helped :)

Answer:

2.05

Step-by-step explanation:

Answer:

The length of the side JH is approximately 31.5 feet long.

Step-by-step explanation:

There is a trigonometry law called the law of sines, which states the sine of an angle divided by its opposite side is equivalent to the sine of all the other angles in that right triangle divided by its corresponding opposite side. You can use this law to help you solve for x. By applying the law of sines, you'll get that \(\frac{sin(90^{o})}{88} =\frac{sin(21^{o})}{x}\) ⇒ \(\frac{88}{sin(90^{o})} =\frac{x}{sin(21^{o})}\) ⇒ \(x = \frac{88*sin(21^{o})}{sin(90^o)}\) ⇒ \(x=31.5ft.\)

The problem with using the mean or median as a measure of center is that the distribution of the data is bimodal, indicating that there are two distinct groups of shoe sizes. The correct answer is A

The histogram shows that one group has shoe sizes from 38 to 40, while the other group has shoe sizes from 44 to 49. This suggests that the two groups have roughly the same mean shoe size, but different distributions.

Therefore, the mean or median are not good measures of center because they do not accurately reflect the underlying distribution of the data. It would be more useful to report the modes instead, which represent the most frequent shoe sizes in the data.

Your question is incomplete but most probably your full question is

In the​ U.S., shoe sizes are defined differently for men and​ women, but in​ Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college​ students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of​ center?

a. The distribution is​ bimodal, so it is more useful to report the modes than the mean or median.

b. The distribution does not have any modes, because it is uniform.

c. The distribution has one mode from 44 to 49. This is due to the students having noughly the same mean shoe size.

d. The distribution has one mode from 38 to 40. This is due to the students having noughly the same mean shoe size.

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Option D, the math scores of current 9th-grade students compared with their 8th-grade math scores, would be considered an example of a matched pair or paired data.

This is because the data is collected from the same group of individuals at two different points in time, allowing for a comparison of the change in math scores. The other options involve comparing different groups or populations, which would not be considered paired data. Additionally, the terms "mean" and "percentage" are not relevant in this context as the question is asking about the type of data comparison, not the specific used.

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The histogram below shows the distribution of her 60 tip amounts for one day of work.

a) The distribution of tips is skewed right, whith a gap betwen 15 to 20 and a posible out lier at or above 20. The mean will be larger than the median, and the median will be in the $2,5 to $5 bar. Most tips are $5 or less, but there is some high variability with a range of $22.50.

b) The mean would increase because $18 is farther from the mean than $8. Also, more skew is added to the grapht $18 may be an out lier. This results in a larger mean.

The median: Should not change very much. The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.

Your question is incomplete, but most probably the complete question can be seen in the attachment.

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The correct answers are a. side a is 189 inches long and side b is 162 inches long, b. side a is 72 inches long and side b is 63 inches long, c. side a is 21 inches long, and side b is 18 inches long, and d. side a is 54 inches long and side b is 45 inches long.

To determine the side lengths of the real object, you need to use the given scale factor of 3:1. This means that for every 1 unit on the scale drawing, the real object has 3 units.

For option (a), if side a on the scale drawing is 63 inches long, then the real object's side a would be 63 x 3 = 189 inches long. Similarly, if side b on the scale drawing is 54 inches long, then the real object's side b would be 54 x 3 = 162 inches long.

For option (b), if side a on the scale drawing is 24 inches long, then the real object's side a would be 24 x 3 = 72 inches long. Similarly, if side b on the scale drawing is 21 inches long, then the real object's side b would be 21 x 3 = 63 inches long.

For option (c), if side a on the scale drawing is 7 inches long, then the real object's side a would be 7 x 3 = 21 inches long. Similarly, if side b on the scale drawing is 6 inches long, then the real object's side b would be 6 x 3 = 18 inches long.

For option (d), if side a on the scale drawing is 18 inches long, then the real object's side a would be 18 x 3 = 54 inches long. Similarly, if side b on the scale drawing is 15 inches long, then the real object's side b would be 15 x 3 = 45 inches long.

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The likelihood of an occurrence regardless of the result of another variable is known as marginal probability.

The likelihood of an occurrence regardless of the result of another variable is known as marginal probability. The likelihood of one event occurring in the presence of another is known as conditional probability.

We already know that marginal probabilities are calculated by dividing marginal frequencies by total frequency.

As a result, in this situation, the gender's marginal probability distribution is given by,

P(Gender=x) ≈ 0.5308                     if x = Male

                     ≈ 0.4692(1-0.5308)    if x = female

                     = 0 otherwise

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It's a geometric sequence

Formula:&

\(\\ \sf\longrightarrow a(n)\)

\(\\ \sf\longrightarrow ar^{n-1}\)

\(\\ \sf\longrightarrow 1.3125(4)^{n-1}\)

The solution of expression for v is v = 9(z - w)/5.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

⇒ 5/9 v = z - w

Multiply by 9 both sides,

⇒ 5v = 9z - 9w

Divided by 5

⇒ v = 9(z - w)/5

Thus, the solution of expression for v is v = 9(z - w)/5.

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She needs to invest $\(300,000\\\) in project A and $\(200,000\) in project B in order to maximize the return on her investment.

Since a financier has $\(500,000\) which she needs to invest in two projects named A and B

Out of the two projects A and B, project B is giving higher rate of return on the investment so maximum investment needs to be done on the project B

Hence in project B total percentage of investment will be \(40%\)% which is also given it needs not to exceed more than \(40\)%

Hence the investment amount on the project B is \(40\)% of $\(500,000\)

which is \((0.4)*$500,000\) which is equal to $\(200,000\) which is an investment in project B

Now the investment in project A will be $\(500,000\)-$\(200,000\)=$\(300,000\)

Hence she needs to invest $\(300,000\) in project A and $\(200,000\) in project B.

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The Correct option is option (A) . Using the minimization , the dimensions of rectangular garden are 30 feet and 15 feet .

We have given that ,

Area of rectangular garden (A) = 450 sq. feet

we trying to minimize L, the length of fencing. Since , one side of the fenced area is covered by the barn, we have got to make two sides perpendicular to the barn plus one side parallel to the barn.

Suppose the length of the perpendicular side be x and the length of the parallel side be y.

Thus, A = x × y = 450 sq. feet --(1)

x + x + y = L --(2)

from (1) , y = 450/x

putting this value in equation (2) we get,

2x + 450/x = L

Now , minimize the L by taking its first derivative with respect to t and then put dL / dt = 0

dL /dx = 2 - 450/x^2

2- 450/x^2 = 0 => 450/x^2 = 2

=> x^2 = 450/2 = 225

taking square root both sides,

=> x = +-√225 = 15 or -15

but sides of any geometry never be negative

so, x = 15 put this x in equation (2)

=> y = 450/15 = 30

Hence , the dimensions of rectangular garden are (15, 30).

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The missing sides of the right triangle are DE = 4.195 and DF = 6.527 and the missing angle is 50°.

In this question we find a right triangle with a known side and two known angles. The missing sides can be found by following trigonometric functions:

tan F = DE / EF

cos F = EF / DF

And the angle D is found by the following expression:

D = 90° - F

If we know that EF = 5 and F = 40°, then missing sides and angle are, respectively:

DE = EF · tan F

DE = 5 · tan 40°

DE = 4.195

DF = EF / cos F

DF = 5 / cos 40°

DF = 6.527

D = 90° - 40°

D = 50°

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Answer:

c

Step-by-step explanation:

c is the point (2,3) in the question

The modal average number of bedrooms is given as follows:

3 bedrooms.

The mode of a data-set is defined as the observation that appears the most times in the data-set.

Hence the modal class in a data-set, considering this problem, in which the absolute frequencies are given, is the class that contains the most observations.

From the data-set given in the Missing Information section, the absolute frequencies in this problem are given as follows:

Hence the modal class is of 3 bedrooms, as it is the class with the highest absolute frequency.

The frequencies for this problem are given as follows:

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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To find the volume of a solid with cross sections perpendicular to the x-axis, we can use the formula V=∫baf(x)dx, where b and a are the lower and upper limits of integration, respectively, and f(x) is the height of the cross section at any given point.

To find the volume of the solid with square cross sections whose base is the curve y=√16−x2 over the interval [−4,4], we can use the formula V=∫baf(x)dx with b=-4, a=4 and f(x)=√16−x2. Substituting these values into the formula gives us the following definite integral:
V=∫-4^4 √16−x2dx
To solve the integral analytically, we can use the chain rule to integrate f(x) with respect to x. This gives us V=∫-4^4 (1/2)(2x)dx. Then, using the power rule, we can integrate with respect to x, giving us V=[1/2(x^2)]-4^4 = -16+64/2 = 24.

For the second question, the volume of the solid whose base is bounded by the functions ????(x)=−x+4 and ????(x)=2x2+3 using cross sections perpendicular to the x axis that are rectangles with the base in the x-y plane and height equal to 4 times the base, we can use the same formula with b=-x+4 and f(x)=4(2x2+3). This gives us the definite integral V=∫-x+4^0 4(2x2+3)dx. To solve this integral analytically, we can use the power rule to integrate with respect to x, giving us V=[8/3(x^3)]-x+4^0 = (8/3)(4^3 - (-4)^3) = 256/3.

For the third question, the volume of the solid whose base is one side of an equilateral triangle that is perpendicular to the x-axis where the length is represented by the curve ????(x)=√x+23 over the interval [-2, 4], we can use the same formula with b=-2, a=4 and f(x)=√x+23. This gives us the definite integral V=∫-2^4 √x+23dx. To solve this integral analytically, we can use the chain rule to integrate f(x) with respect to x, giving us V=∫-2^4 (1/2)(2x)dx. Then, using the power rule, we can integrate with respect to x, giving us V=[1/2(x^2)]-2^4 = 8 - (-4)^2/2 = 24/2 = 12.

For the fourth question, the volume of the solid that has semi-circular cross sections perpendicular to the x-axis bounded by the curve ????(x)=1x over the interval [1, 8], we can use the same formula with b=1, a=8 and f(x)=π(x/2)2. This gives us the definite integral V=∫1^8 π(x/2)2dx. To solve this integral analytically, we can use the power rule to integrate with respect to x, giving us V=[π/3(x^3)]1^8 = π(8^3 - 1^3)/3 = π(512-1)/3 = 511π/3.

For the fifth question, the volume of the solid whose base is a circle centered at the origin with radius of 4 using cross sections perpendicular to the y-axis that are isosceles right triangles with one leg in the coordinate plane, we can use the same formula with b=0, a=2π and f(x)=4cos(x). This gives us the definite integral V=∫0^2π 4cos(x)dx. To solve this integral analytically, we can use the power rule to integrate with respect to x, giving us V=[4sin(x)]0^2π = 4(sin(2π) - sin(0)) = 4(0 - 0) = 0.

Finally, for the sixth question, the base of a solid is the region in the first quadrant that is bound by the graph of y=3+co????(x) over the interval [0,????]. To find the volume using cross sections that are perpendicular to the x-axis, where the cross sections are isosceles right triangles with the hypotenuse in the coordinate plane, we can use the formula V=∫baf(x)dx with b=0, a=???? and f(x)=3+co????(x). This gives us the definite integral V=∫0^???? (3+co????(x))dx. To solve this integral analytically, we can use the power rule to integrate with respect to x, giving us V=[3x+1/2(co????(x))]0^????. Then, we can substitute in the value of ???? to find the final value of the integral.

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Answer:

D. Katie has 175 more guitar picks than Lawrence

Step-by-step explanation:

Katie has 256 picks

Lawrence has 81 picks

In a lumped parameter analysis, the temperature profile with time is typically represented by an exponential curve, option a

1. Lumped parameter analysis: This analysis assumes that the system being studied can be represented by a single node or point with uniform properties. It simplifies the problem by neglecting spatial temperature variations within the system.

2. Temperature profile: The temperature profile refers to how the temperature changes within the system over time.

3. Exponential curve: In many cases, the temperature profile in a lumped parameter analysis follows an exponential curve. This curve represents an exponential decay or growth of temperature over time. The rate of change of temperature decreases exponentially as time progresses.

4. Reasoning: The exponential curve is commonly observed in situations involving heat transfer, such as the cooling or heating of objects. It occurs due to the exponential relationship between the temperature difference and the rate of heat transfer. As the temperature difference decreases, the rate of heat transfer decreases, resulting in a gradual approach to equilibrium.

Therefore, the correct answer is (a) Exponential.

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Answer:

15 ft.

Step-by-step explanation:

the ratio of the real room to the blueprint is 21/3.5, which simplifies to 6.

You have to multiply 6 by 2.5 to get 15

Answer:

The greater number is \(- 8\)

Step-by-step explanation:

Let the numbers be x and y

We have x · y = 160

x= 160/y

let x be the smaller number

x = 2y - 4

x - 2y = -4

Substitute x = 160/y in the above equation

160/y - 2y = -4

Multiply throughout by y
160 - 2y² = -4y

Add 4y to both sides

160 - 2y² + 4y = 0

Rearrange

-2y² + 4y + 160 = 0

Divide by -2

y² - 2y + 80 = 0

Factor expression on left side

(y - 10)(y + 8) = 0

y - 10 = 0 ==> y = 10

y + 8 = 0 ==> y = -8

Since both numbers are negative y = -8

So the greater number is - 8

The lesser number = 160/y = 160/-8 = -20

Remember that both numbers are negative and -20 < -8

The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity

The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.

To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.

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Answer: Phillip has 262 more cards than Nicholas

Step-by-step explanation:

Since we are looking for how many more cards Phillip has compared to Nicholas we can subtract Nicholas' amount from Phillip's amount to see how much more he has.

721-459=262

Taking a simple difference, we can see that Phillip has _262_

more cards than Nicholas.

To find this, we need to take the difference between the number of cards that Philip has and the number of cards that Nicholas has, so we just need to solve a subtraction:

Phillip's cards - Nicholas' cards

Where:

Phillip's cards = 721

Nicholas' cards = 459

Then the difference is:

721 - 459 = 262

So we can see that Phillip has 262 more cards than Nicholas.

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ANSWER:

AAA Similarity Theorem

STEP-BY-STEP EXPLANATION:

We can see that the two triangles have the same interior angles and are corresponding.

Therefore, we can state that these two triangles are congruent using the AAA Similarity Theorem, where if two triangles have equal corresponding angles, then their corresponding sides are proportional and the triangles are similar.