Find an ordered pair that represents the vector from (-3.7,2) to (-4, -5).

a.
(-7.7,-3)

c.
(1.3,7)
b.
(-0.3,-7)
d.
(7.7,3)

In order to determine whether an equation is separable, we need to look at its structure. A differential equation is called separable if it can be expressed in the form g(y)dy=f(x)dx, where g(y) and f(x) are functions of only y and x, respectively. If the equation can be written in this form, it can be solved by integrating both sides with respect to their respective variables.

Example of a separable equation: dy/dx = 2x/(1+y^2)

Here, we can rearrange the equation to put all y terms on one side and all x terms on the other:

dy/(1+y^2) = 2x dx

Then we can integrate both sides to get:

y = tan^-1 (x^2 + C), where C is the constant of integration.

If an equation cannot be written in separable form, it cannot be solved using this method.

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Answer:

BC ≈ 11.8 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tanΘ = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{x}{BC}\) , that is

tan32° = \(\frac{7.4}{BC}\) ( multiply both sides by BC )

BC × tan32° = 7.4 ( divide both sides by tan32° )

BC = \(\frac{7.4}{tan32}\) ≈ 11.8 m ( to 3 sf )

The amount of ice cream consumed in the United State would be 5,650 millions of pounds in 2028.

Based on the information provided about the mount of ice cream consumed in the United State, a quadratic equation that models the amount of ice cream consumed, in millions of pounds, since 2010 is given by;

y = 12(x - 6)² + 3922

Where:

By substituting the value of y, the number of years can be calculated as follows;

5,650 = 12(x - 6)² + 3922

5,650 - 3922 = 12(x - 6)²

1728 = 12(x - 6)²

144 = (x - 6)²

12 = x - 6

x = 12 + 6

x = 18 years.

Since 2010; 2010 + 18 = 2028.

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Answer:

\(28\)

Step-by-step explanation:

The formula for the area of the shape is given is equal to its base multiplied by its height. We're given a base of 7 and height of 4, hence the area is \(7\cdot 4=\boxed{28}\)

Answer:

Yes its correct the unhighlighted is complement

Answer:

I think it is 24 but I don't know the rest sorry 乁( •_• )ㄏ

Answer:

Step-by-step explanation:

Girls Basketball = x

Girls Soccer = x + 3

Total = 51

x + x + 3 = 51        Combine like terms

2x + 3 = 51            Subtract 3 from both sides

     - 3   - 3

2x = 48                 Divide by 2

2x/2 = 48/2

x = 24

The basketball team has 24 players

The soccer team has       27

Answer:

The rectangle is 3.5 yd x 4 yd

Step-by-step explanation:

Area = length x width = lw

l = length = 2w - 3

w = width

Area = 14(2w - 3)(w) = 14

2w² - 3w - 14 = 0

Use quadratic equation to find the 2 roots of w:  a = 2, b = -3, c = -14

w = 3.5, -2     disregard the negative root

width = 3.5 yd

length = 2(3.5) - 3 = 4 yd

The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.

We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:

14 = (2x - 3) x x

Expanding the brackets:

14 = 2x² - 3x

Put this equation=0:

2x² - 3x - 14 = 0

Using the quadratic formula:

x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)

x = (3 ± √97) / 4

We can ignore the negative root, since the width cannot be negative. Therefore,

x ≈ 2.23

This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:

length = 2x - 3

length ≈ 1.46

Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards

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Answer:

250 hamburgers

Step-by-step explanation:

Explanation: Because IK

Answer:

(if am not wrong)

The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².

Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.

Let V be the volume of the solid formed.

⇒ volume of the solid formed - V = 2 ( \(\frac{1}{3} *B*h\) )

Now substitute the values,

⇒V = 2 ( \(\frac{1}{3}\) * \(28^{2}\) * 10.5 )

⇒V = 2 ( \(\frac{1}{3}\) * 784 * 10.5 )

⇒V = 2 ( 261.3 * 10.5 )

⇒V = 2 ( 2,743.65 )

⇒V = 5,487.3 unit ²

Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².

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(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

4 sigfig is 164.4

3 sigfig is 164.

1 sigfig is 200

hope that answers your question

comment for more explanation

The area of the painted face of the brick is given as follows:

108 in².

The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:

A = lw.

The dimensions for this problem are given as follows:

Hence the area of the painted face of the brick is given as follows:

A = 12 x 9 = 108 in².

(the area of a rectangle is given by the multiplication of the dimensions, which we did here).

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The integral of 1/ (x √(x²-a²)) is (1/2) ln[(x/ a) + √((x/a)² - 1)] + (1/2) sin⁻¹(x/a) + C, where C is a constant of integration.

To find the integral of 1/ (x √(x²-a²)), we can use a trigonometric substitution.

First, let's rewrite the denominator as:

√(x² - av) = a sin(θ)

where θ is an angle in the right triangle formed by a, x, and √(x² - a²).

Differentiating both sides with respect to x, we get:

(x / √(x² - a²)) dx = a cos(θ) dθ

Solving for dx, we get:

dx = (a cos(θ) / √(x² - a²)) dθ

Substituting this into our integral, we get:

∫ [1 / (x √(x²-a²))] dx = ∫ [1 / (a² sin(θ) cos(θ))] (a cos(θ) / √(x² - a²)) dθ

Simplifying, we get:

∫ [1 / (x √(x²-a²))] dx = ∫ [1 / (a sin(θ) cos(θ))] dθ

We can use the trigonometric identity:

1 / (sin(θ) cos(θ)) = 1 / (2 sin(θ) cos(θ)) + 1 / 2

to rewrite the integral as:

∫ [1 / (x √(x²-a²))] dx = (1/2) ∫ [1 / (sin(θ) cos(θ))] dθ + (1/2) ∫ dθ

Using the substitution u = sin(θ), we get:

∫ [1 / (x √(x²-a²))] dx = (1/2) ∫ [1 / (u(1-u²\()^{0.5}\))] du + (1/2) θ + C

where C is the constant of integration.

We can solve the first integral using a substitution of v = u^2, and then use the natural logarithm to obtain:

∫ [1 / (x √(x²-a²))] dx = (1/2) ln[(u + (1-u²\()^{0.5}\)) / u] + (1/2) θ + C

Substituting back in terms of x, we get:

∫ [1 / (x √(x²-a²))] dx = (1/2) ln[(x/ a) + √((x/a)² - 1)] + (1/2) sin⁻¹(x/a) + C

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(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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Answer:

240 cm², A = 300 cm², and 540 cm²

Step-by-step explanation:

1) The area of a parallelogram is A = bh, so:

A = (20)(12)

A = 240 cm²

2) Similarly, the area of a rectangle is A = bh, so:

A = (15)(20)

A = 300 cm²

3) The composite area is the sum of both the rectangle's area and the parallelogram's area, so:

240 cm² + A = 300 cm² = 540 cm²

Answer:

P=

20x12=240

R=

20x15=300

240+300

Step-by-step explanation:

Answer:

1. 3 cookies

2. 2 cups

3. 300 calories

4. $35 per month

5. k = y/x

6. If there is no constant (k)

Step-by-step explanation:

1. The number of cookies the factory makes in one minute = (The number of cookies the factory makes in 12 minutes)/(12 minutes)

∴ The number of cookies the factory makes in one minute = 36 cookies/(12 minutes) = 3 cookies/minute

The correct answer is 3 cookies

2. The number of cups of water that leak every minute = (The number of cups of water that leak in 1/4 minute) × (The number of 1/4 minute per minute)

The number of cups of water that leak every minute = 1/2 cup per 1/4 minute × 4_1/4 minute per minute

The number of cups of water that leak every minute = 1/2  × 4 = 2

The number of cups of water that leak every minute = 2 cups

3. 5 glazed donuts contains 750 calories

∴ 1 glazed donuts contains 750/5 = 150 calories

2 = 2 × 1 glazed donuts will contain 2 × 150 = 300 calories

4. The charge of the cell phone company for 2 months = $70

The charge of the cell phone company for 6 months = $210

The constant rate per month = The rate of change of the cell phones companys charges

∴ The constant rate per month = (210 - 70)/(6 - 2) = 140/4 = 35

The constant rate (per month) for the service = $35 per month

5. The formula to find the constant of a chart, k = y/x

6. A chart is not considered proportional if there is no constant (k)

By using the concept of Compound interest, Number of payment periods in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = 12

What is Compound interest?

The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

This problem can be solved by using the concept of compound interest

Number of  payment periods are in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = \(6 \times 2 = 12\)

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Answer:

3x-x+2=4

Step-by-step explanation:

Number of boys = x

Number of girls = x plus 15% of x = 1.15x

Ratio of boys to girls x:1.15x = 1:1.15 = 20:23\(\\\)

\(\\\)\(\\\)

The direct variation equation that relates x and y is given by :-

y = 2.6x.

We are given that y varies directly with x.

Hence, we can write,

y ∝ x

y = kx

Where, k is the constant of proportionality

We know that,

When y = 10.4 , x = 4.

Hence, we can write,

10.4 = k*4

k = 10.4/4

k = 2.6

Hence, the equation becomes:-

y = 2.6x

Constant of proportionality

The constant of proportionality is a number that relates two variables in direct or inverse variation. In variable form, the constant of proportionality is commonly denoted as k.

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Answer:

Step-by-step explanation:

The statistical range that takes random error into account, with a given probability, is known as the confidence interval. It provides a measure of uncertainty associated with a particular estimate or sample statistic. In the first paragraph, we'll provide a summary of the answer.

A confidence interval consists of two values, an upper and a lower bound, within which the true population parameter is likely to fall. The range is determined by the desired level of confidence, often expressed as a percentage (e.g., 95% confidence interval). The confidence interval considers both the variability within the sample data and the desired level of certainty. It acknowledges that due to random sampling error, the estimate obtained from a sample may differ from the true population parameter. In the second paragraph, we'll delve into an explanation of the answer.

To understand confidence intervals, we need to consider the concept of sampling variability. When we collect a sample from a population, it's rare for the sample to perfectly represent the entire population. There will be inherent variation due to random chance. This variability is known as sampling error. Confidence intervals take into account this sampling error and provide a range of values within which the true population parameter is likely to exist.

The level of confidence chosen for the interval represents the desired probability that the range will contain the true parameter. Commonly used confidence levels are 90%, 95%, and 99%. For example, a 95% confidence interval implies that if we were to repeat the sampling process many times, 95% of the resulting intervals would contain the true population parameter. The wider the interval, the higher the level of confidence, and vice versa.

In conclusion, a confidence interval is a statistical range that incorporates random error and provides an estimate of the likely range within which the true population parameter exists. It considers the desired level of confidence and takes into account the inherent variability due to random sampling error. Confidence intervals are an essential tool in statistical inference, allowing researchers and analysts to quantify the uncertainty associated with their estimates and draw meaningful conclusions from sample data.

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Answer: (-∞,2)

Step-by-step explanation: 2 is not included in the interval since at x=2, the function crosses the x axis, meaning it is not positive, and instead 0.

All x values below 2 are positive.

If \(\displaystyle\sf f(x)=-2x+3x+5\) and \(\displaystyle\sf g(x)=x^{2}+2x\), we need to find the graph of \(\displaystyle\sf (f+9)(x)\).

To find \(\displaystyle\sf (f+9)(x)\), we add 9 to the function \(\displaystyle\sf f(x)\). So we have:

\(\displaystyle\sf (f+9)(x)=-2x+3x+5+9\)

Simplifying this expression, we get:

\(\displaystyle\sf (f+9)(x)=x+14\)

Therefore, the graph of \(\displaystyle\sf (f+9)(x)\) is a straight line with a slope of 1 and y-intercept at 14.

Answer:

B and D are the answers!

Hope this helps!

Answer:

A. 8 ÷ 1

B. 2 ÷ 16