Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250. Solve for x in the inequality, and explain what the answer represents.

The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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The volume of the rectangular prism is 428,544 cubic cm.

To find the volume of the rectangular prism, we can start by determining the dimensions of the prism.

Let's assume the length, width, and height of the prism are L, W, and H, respectively.

Given that the rectangular prism is filled exactly with 248 cubes, we can express the total number of cubes as the product of the length, width, and height of the rectangular prism:

\(L \times W \times H = 248\)

Since each cube has an edge length of 12 cm, the volume of one cube can be calculated as follows:

Volume of one cube \(= (12 cm) \times (12 cm) \times(12 cm)\)

Volume of one cube \(= 1728 cm^3\)

Now, we can set up the equation based on the given information:

\(L \times W \times H = 248 \times Volume of one cube\)

\(L \times W \times H = 248 \times 1728 cm^3\)

To find the volume of the rectangular prism, we need to calculate the right side of the equation:

\(248 \times1728 = 428,544 cm^3\)

Therefore, the volume of the rectangular prism is \(428,544 cm^3\).

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Answer:

-6, -5, -1

Step-by-step explanation:

Based on the question, (x+6) is a factor of f(x).

With this, you can do the long division method of dividing f(x) with (x+6) {Refer to the image}.

You'll get x²+6x+5 as a result.

Factorise it and you'll get

x²+6x+5 = (x+1)(x+5)

Then let (x+1)(x+5) = 0, x = -1, -5

Zero's of f(x) are -6, -5 -1

\(\text{Given that,}\\\\f(x) = x^3 +12x^2 +41x +30~~ \text{and} ~~ f(-6)=0\\\\\text{Since f(x)=0 when x = -6,}~ ~x-6 ~\text{is a factor of f(x).}\\\\x^3+12x^2+41x+30 = 0\\\\\implies x^3+6x^2+6x^2+36x+5x+30=0\\\\\implies x^2(x+6) +6x (x+6) +5(x+6)=0\\\\\implies (x+6)(x^2+6x+5)=0\\\\\implies (x+6)(x^2+5x+x+5)=0\\\\\implies (x+6)\textbf{[}x(x+5)+(x+5)\textbf{]}=0\\\\\implies (x+6)(x+1)(x+5)=0\\\\\text{Hence the roots are,}~ x = -6,~ x=-1~ \text{and}~ x = -5\)

Answer:

The answer is that the probability that he will arrive at the theater within 10 minutes of (before or after) the start of the film is 0.83%.

A 2-hour movie runs continuously at a local theater.

Seth leaves for the theater without first checking the show times.

We need to use an appropriate uniform density function to find the probability that he will arrive at the theater within 10 minutes of (before or after) the start of the film.

Solution:

Total time for the movie = 2 hours=120 min.

Let us assume that the start of the movie at time 0.

let's find out the time period between 0 and 120 minutes that represents the movie length.

We can represent it by the following interval: [0, 120]

Let us consider that Seth's arrival time can be any time between 0 minutes and 120 minutes,

that is: [0, 120]

Now, the probability that he will arrive at the theater within 10 minutes of (before or after) the start of the film, can be found by the formula for uniform probability density function f(x) given by:

f(x) = 1 / b-a ,

where b is the upper limit and a is the lower limit of the interval of the random variable x.

f(x) gives the probability of finding the random variable x in the interval [a, b]

Here, the lower limit, a=0 and the upper limit, b=120.

Now, f(x) = 1/120-0

f(x) = 1/120

= 0.0083

Therefore, the probability that Seth will arrive at the theater within 10 minutes of (before or after) the start of the film is 0.0083, or 0.83%.

Hence, the answer is that the probability that he will arrive at the theater within 10 minutes of (before or after) the start of the film is 0.83%.

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Answer:

She worked for about 10.23 hours.

Step-by-step explanation:

I found the unit rate by dividing 45/7.5. I got 6.16. Then I divided 63/6.16. I got 10.23 from this

Answer:

2 2/3 cookies each or 2.66666666....

Step-by-step explanation:

In order to get the answer you have to divide the cookies between three people.

8/3=2 2/3

Thats the answer, i hope you found it helpful!

Answer:

2.6 cookies per child or simplify it and get 3

Step-by-step explanation:

8 divided by 3 is 2.66666666667 but just get 2.6

Answer:

y=3x-4

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute the 3

3(x) = 3x

3(1) = 3

We now have 45 = 3x + 3

Subtract 3 from both sides

45 - 3 = 42

3 - 3 cancels out

We now have 42 = 3x

Divide both sides by 3

42/3 = 14

3x / 3 = x

We're left with x = 14

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute

45 = 3x + 3

-3           -3

----------------

42 = 3x

----    ----

3       3

14   =  x

Answer:

1 1/4 or 5/4

Step-by-step explanation:

one is simplified just in case

Answer:

1/1024

Step-by-step explanation:

If you want the steps, just ask and ill give them in comments :)

Hope this helped!

If so, can you mark brainiest!

Thanks!

Have a great day!

The expression 2 sin(4x) cos(9x) can be written as the difference of two functions using trigonometric identity as: sin(13x) - sin(5x).

To write the expression 2 sin(4x) cos(9x) as the sum or difference of two functions, we can use the trigonometric identity:

sin(A) cos(B) = (1/2)[sin(A + B) + sin(A - B)]

Applying this identity to the given expression:

2 sin(4x) cos(9x) = 2 * (1/2)[sin(4x + 9x) + sin(4x - 9x)]

Simplifying:

= sin(13x) + sin(-5x)

Note that sin(-θ) = -sin(θ), so we can rewrite sin(-5x) as -sin(5x):

= sin(13x) - sin(5x)

Therefore, the expression 2 sin(4x) cos(9x) can be written as the difference of two functions: sin(13x) - sin(5x).

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Initial velocity=0

Height=45m

G=10m/s^2

By the 2 nd equation of motion …(Under free fall)-

H = ut + 1/2 g t^2

45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]

45 = 5 t^2

45/5 = t^2

9 = t^2

√9=t

3=t

Answer-: The time taken would be 1.3 seconds to reach the ground.

Answer:

Step-by-step explanation:

Here is your workings

(3x)^3  Apply the rule of exponents

Step 2

(3x)^3=3^3x^3  Simplify

Step 3

3^2=27  Solve

27x^3

Piggy simon and the littlun have in common Piggy, Simon, and the littlun share commonalities of vulnerability, insight, innocence, and tragic destinies in "Lord of the Flies."

Piggy, Simon, and the littlun from William Golding's novel "Lord of the Flies" share several commonalities despite their differences in character and role within the story.

Firstly, all three characters are depicted as vulnerable and marginalized within the group of boys stranded on the island. Piggy, with his physical and intellectual limitations, is often ridiculed and excluded by the other boys.

Similarly, the littlun represents the youngest and weakest members of the group, often overlooked or dismissed by the older boys. Simon, while possessing a kind and gentle nature, is introverted and withdrawn, making him somewhat of an outcast.

Secondly, all three characters demonstrate a sense of insight or wisdom beyond their years. Piggy, with his intelligence and rational thinking, often offers logical suggestions and insights to problems.

Simon possesses a deep sense of spirituality and connection with nature, providing profound observations about the island and the boys' behavior. The littlun, though less explicitly portrayed, is seen as perceptive in their observations of the island and the unfolding events.

Additionally, these characters exhibit a certain degree of innocence and purity amidst the growing savagery and chaos on the island.

Piggy, Simon, and the littlun are not driven by the same primal instincts and desires for power and control that dominate the other boys. They retain a sense of morality and empathy that is gradually eroded in the majority of the group.

Furthermore, these characters all meet tragic fates in the story. Piggy is brutally murdered by Roger, Simon is mistaken for the "beast" and killed in a frenzied act of violence, and the littlun's fate is left ambiguous but implied to be bleak.

In summary,  They serve as contrasting figures to the destructive tendencies of the other boys and offer glimpses of humanity and morality amidst the descent into savagery.

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Answer:

1) Is 90° because that's what the little square in the corner means.

2) Is 60° because if you take everything to the right of the vertical line and add them up, and then subtract the total from 180° you can find the missing angle.

3) Is 30° because if you use what's below the horizontal line and do the same thing as number 4 (add the existing angles together and subtract the total from 180) you can find the missing angle.

4) Is 20° because if you add the existing angles together (40° + 90° + 30°), you'll get 160°, and since the diagonal line that's separating everything from 40° to 30° looks as though it equals 180°, you'd subtract 160° from 180° in order to get the missing angle.

5) Is also 90° because the angle across from it (1) looks to be around the same size.

I solved for each in the following order:

1, 5, 4, 3, 2.

I hope this helps. Also please let me know if I got something wrong or if you still need help :)

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.

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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."


The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.


To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.

In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.

The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.

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Answer:

11.6 i think sorry if i am wrong

Step-by-step explanation:

just do 70 divided by 6 = 11.6

Answer: 420 miles

Step-by-step explanation: 70 miles in 1 hour and then another 70 miles 2 hrs

70+70= 140+70=210+70=280+70=350+70=420

70+70+70+70+70+70= 420

or 70 X 6= 420

A z-score of z = -3.00 indicates that the raw score occupies 3 standard deviations below the mean in a distribution.

The correct option is d) 3 standard deviations below the mean.

A z-score is a way of expressing a data point's distance from the mean in standard deviations. It is also known as a standard score or a z-value.

It is used in a wide range of statistical analyses to compare scores on different scales, among other things.

When a z-score is positive, the data point is above the mean, and when it is negative, it is below the mean.

In this situation, a z-score of z = -3.00 indicates that the raw score is three standard deviations below the mean in a distribution.

Therefore, the correct option is d) 3 standard deviations below the mean.

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Line Intergral value is 2/3 (5√5-2).

In this problem, we have to evaluate the line integral C xy ds, where C is the given curve C:

x = t2, y = 2t, 0 ≤ t ≤ 1.

We have to find the values of the given line integral. A line integral is a type of integral that involves integrating over a curve. The value of line integral is calculated as follows:

∫Cf(x, y) ds=∫ba f(x(t), y(t))|r'(t)| dtHere, f(x, y) = xy and the curve is given by C:

x = t2, y = 2t, 0 ≤ t ≤ 1. So, we have to find the value of the line integral as follows:

∫Cf(x, y) ds=∫ba f(x(t), y(t))|r'(t)| dt∫01 (t2)(2t)√[4t2+4] dt=∫01 2t3√[4t2+4] dtLet 4(t2+1) = u, then 8t dt = du.

Substituting the values we get,

∫01 2t3√[4t2+4] dt=∫05√(u)du=2/3 u3/2|05= 2/3 (5√5-2)

Thus, the value of the line integral is 2/3 (5√5-2).

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Answer:

70

Step-by-step explanation:

35 times 4 = 140. 210-140= 70

Step-by-step explanation:

get x alone by using opposite operation

x and y are subtracting.the opposite of subtraction is addition

add y on both sides to cancel y on the left side and move it to the right

x-y+y=w+y

x=w+y

Answer:

b but i am not sure if it is correct

According to the described way the volume of solid S is 156.25π.

Since the cross sections perpendicular to the x-axis and the base are semicircles, we know that the radius of each cross section is given by:

r = y = √(25 -\(x^{2}\) )  

where x is the distance from the center of the circle to the cross section, which lies along the x-axis.

The circle  \(x^{2}\)+ \(y^{2}\) = 25 has a radius of 5, and its center is at the origin (0,0). Thus, the farthest a cross section can be from the center of the circle is at x = 5 or x = -5.

To find the volume of the solid S, we need to integrate the area of each cross section over the range from x = -5 to x = 5. The area of each cross section is given by:

A = (1/2)πr^2

Substituting the expression for r above, we get:

A = (1/2)π(25 - x^2)

Integrating this expression over the range from x = -5 to x = 5 gives us:

V = ∫(-5)^5 (1/2)π(25 - x^2) dx

Using integration rules, we can evaluate this integral to get:

V = (1/2)π ∫(-5)^5 (25x - x^3) dx

V = (1/2)π [ (25/2)x^2 - (1/4)x^4 ]|_-5^5

V = (1/2)π [ (25/2)(5^2) - (1/4)(5^4) - (25/2)(-5^2) + (1/4)(-5^4) ]

V = (1/2)π [ 625/2 - 625/4 + 625/2 - 625/4 ]

V = (1/2)π (625/2)

V = (312.5/2)π

V = 156.25π

Therefore, the volume of solid S is 156.25π.

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Answer:

  11.4

Step-by-step explanation:

You want the distance between C(-5, 5) and D(4, -2).

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is computed to be ...

  d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130

  d ≈ 11.4

The length of CD is about 11.4 units.

__

Additional comment

The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

Answer: See explanation

Step-by-step explanation:

1. 4 apples cost $1.59

1 apple would cost $1.59 ÷ 4

1.59 ÷ 4 = 0.3975

0.3975 ≈ 0.40

1 apple would cost approximately 40 cents.

2. 3 apples cost $1.00

1 apple would cost $1.00 ÷ 3

1.00 ÷ 3 = 0.3333

0.3333 ≈ 0.33

1 apple would cost approximately 33 cents.

3. Loose apples are the better buy because 1 apple costs approximately 33 cents while packaged apples cost approximately 40 cents.

4. 15 ounces cost $1.05

1 ounce would cost $1.05 ÷ 15

1.05 ÷ 15 = 0.07

1 ounce would cost 7 cents.

5. 48 ounces cost $2.39

1 ounce would cost $2.39 ÷ 48

2.39 ÷ 48 = 0.0497

0.0497 ≈ 0.05

1 ounce would approximately cost 5 cents.

6. The 48-ounce jar of applesauce is the better buy because 1 ounce costs approximately 5 cents while a 15-ounce jar of applesauce costs 7 cents.

7. 15 ounces cost $1.54

1 ounce would cost $1.54 ÷ 15

1.54 ÷ 15 = 0.1026

0.1026 ≈ 0.10

1 ounce would approximately cost 10 cents.

8. 6 (six 1 ounce) ounces cost $1.15

1 ounce would cost $1.15 ÷ 6

1.15 ÷ 6 = 0.1916

0.1916 ≈ 0.19

1 ounce would approximately cost 19 cents.

9. The larger box of raisins has a lower unit cost of 10 cents.

10. When buying fruits, you might think about the quality of the fruit, the size.. etc.

Hope I helped!

Answer:

30

Step-by-step explanation:

45/3=15

15 days on track

30 days not on track

The volume of the pyramid is 66.7 cm cube. Therefore, the answer is c.

The above diagram is a square base pyramid. The volume of the square base pyramid can be represented as follows:

volume of the pyramid = 1 / 3 BH

where

Therefore,

base area = l²

where

Hence,

base area = 5²

base area = 25 cm²

Therefore, let's find the volume of the pyramid.

Hence,

volume of the pyramid =  1 / 3 × 25 × 8

volume of the pyramid =  200 / 3

volume of the pyramid = 66.6666666667

Therefore,

volume of the pyramid = 66.67 cm³

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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Answer:

x = 6

Step-by-step explanation:

If polygons are similar then the side lengths are proportional, so we can write the following equation to find the value of x:

15/6 = (5x + 10)/16 cross multiply fractions

240 = 30x + 60 subtract 60 from both sides

180 = 30x divide both sides by 30

6 = x

The word phrase which correctly represents the algebraic expression as given in the task content is; the product of 3 and a number, t.

It follows from the task content that the algebraic expression which is to be expressed as a word phrase is; 3t.

Therefore, the word phrase representation of the algebraic expression is; the product of 3 and a number, t.

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