A motorboat is capable of traveling at a speed of 10 miles per hour in still water. On a particular​ day, it took 15 minutes longer to travel a distance of 6 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that​ day?

Answer:

a) Y = 15,587(1.02)^t

where Y is the population at a certain year t after 2010

b) 22,262 persons

Step-by-step explanation:

a) we want to write an exponential equation;

Generally, we have this as;

Y = P(1 + r)^t

where Y is the value at a time t

P is the initial value

r is the rate of change

t is the time

From the question;

P is 15,587

r is 2% = 2/100 = 0.02

So, we have the equation as;

Y = 15,587(1 + 0.02)^t

Y = 15,587(1.02)^t

b) The population in 2028

To get this, we need the value of t

What we have to do here is to subtract 2010 from 2028

We have this as; 2028 - 2010 = 18

So substituting this value into the exponential equation above, we have

Y = 15,587(1 + 0.02)^18

Y = 15,587(1.02)^18

= 22,262

Answer:

the other answer is wrong, you have to use the function a=Pe^(rt). from then you plug in 0.02 for r and 18 for t and intial value of 15587 for p to become 15587e^(0.02(18)) =  ^0.36 and then solve from there to get 22341. also e not just a random variable but a set value of 2.718282.

The price per pound of cheese is approximately $0.1071.In the given problem, Justin spends $15 at the grocery store. He buys a loaf of bread for $3 and also purchases 112 pounds of cheese. We need to determine the price per pound of cheese.

To find the price per pound of cheese, we can divide the total amount spent on cheese by the number of pounds of cheese purchased.

Let's denote the price per pound of cheese as 'x'. Therefore, the equation representing the problem is:

112 * x = 15 - 3

The right side of the equation represents the total amount spent at the grocery store, which is $15, minus the cost of the loaf of bread, which is $3.

Simplifying the equation, we have:

112 * x = 12

To isolate 'x', we divide both sides of the equation by 112:

x = 12/112

Simplifying further, we have:

x ≈ 0.1071

Therefore, the price per pound of cheese is approximately $0.1071.

In this problem, the unknown quantity is the price per pound of cheese, denoted as 'x'. It represents the value we are trying to determine through the given information and calculations.

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The domain of the inverse function will be y ≥ 6, and the range of the inverse function will be x > 4.

When the domain is restricted to the portion of the graph with a positive slope, it means that only the values of x that result in a positive slope will be considered.

In the given function, f(x) = |x – 4| + 6, the portion of the graph with a positive slope occurs when x > 4. Therefore, the domain of the function is x > 4.

The range of the function can be determined by analyzing the behavior of the absolute value function. Since the expression inside the absolute value is x - 4, the minimum value the absolute value can be is 0 when x = 4.

As x increases, the value of the absolute value function increases as well. Thus, the range of the function is y ≥ 6, because the lowest value the function can take is 6 when x = 4.

Now, let's consider the inverse function. The inverse of the function swaps the roles of x and y. Therefore, the domain and range of the inverse function will be the range and domain of the original function, respectively.

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Step-by-step explanation:

2.

Two pairs of corresponding angles

i. angle C angle D

ii. angle G angle F

Two pairs of alternate angles

i. angle B angle D

ii. angle H angle F

Two pairs of interior angles

i. angle C angle H

ii. angle D angle E

Answer:

X >_-5

Step-by-step explanation:

>_ is greater than or equal to

Answer:

137°

Step-by-step explanation:

90+47= 137°

the sum of two interior angles is equally to the further exterior angle.

The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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Answer:

? = 85°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum of the angles around a point = 360° , so

interior angle on right = 360° - 250° = 110°

sum the interior angles and equate to 540°

110° + 115° + 120° + 110° + ? = 540° , that is

455° + ? = 540° ( subtract 455° from both sides )

? = 85°

Answer:

dont you just subtract 90-61 to get 29 since a triangle is 90 degrees

Answer:

b

Step-by-step explanation:

so 17 squared minus 8 squared is 225. the square root of 225 is 15

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

Answer:

-83

Step-by-step explanation:

25-(4-1)×(-6)^2

25-(3)×36

25-108

The values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

To determine the values of W and X that make NOPQ a parallelogram, we need to find the conditions under which the opposite sides of the quadrilateral are parallel.

The coordinates of the points N, O, P, and Q are given as follows:

N: (w+7, 5w-5)

O: (3/2x, 3)

P: (?, ?)

Q: (?, ?)

For NOPQ to be a parallelogram, the vector from N to O should be equal to the vector from P to Q, and the vector from O to P should be equal to the vector from Q to N.

The vector from N to O is:

NO = (3/2x - (w+7), 3 - (5w-5))

   = (3/2x - w - 7, -5w + 8)

The vector from O to P should be equal to the vector from Q to N. Thus:

OP = (P_x - (3/2x), P_y - 3)

QN = ((w+7) - Q_x, (5w-5) - Q_y)

Equating the corresponding components, we get the following equations:

3/2x - w - 7 = P_x - (3/2x)

-5w + 8 = P_y - 3

w + 7 = (w+7) - Q_x

5w - 5 = (5w-5) - Q_y

Simplifying these equations, we find:

P_x = 3x

P_y = -5w + 11

Q_x = w + 7

Q_y = 5w

Therefore, the values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

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Answer:

-7

-1

2

8

brainliest please

Answer:

front triangle: (6x4)/2 = 12

back triangle: (6x4)/2 = 12

side: 12x5 = 60

other side: 12x5 = 60

bottom: 12x6 = 72

12 + 12 + 60 + 60 + 72 = 216

216 cm squared

Answer: plot a point at (-8, -5)

The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.

The rule can be written as \((x,y) \to (x,-y)\)

The value of the additional data point is  \($19.17$\).

Let us first find the mean of the given data:

\(Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6\)

Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is

\($(39+45+43+42+44+x)$\).

Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:

\(32.083 = \frac{(39+45+43+42+44+x)}{6}\)

Multiplying both sides of the equation by 6 we get:

\(6 \times 32.083 = (39+45+43+42+44+x)\)

We have the value of \($39+45+43+42+44$\) which is \($213$\).

Therefore, substituting all the values, we get:

\(193.83 + x = 213\)

On subtracting \($193.83$\) from both sides, we get the value of

\(x. x = 213 - 193.83 = 19.17\)

Therefore, the value of the additional data point is \($19.17$\)

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Answer:

the answer is D (27 + 4.5 ) + 1.5

Hope that helps

Answer:

Amswer is A

Step-by-step explanation:

Stratified Random Sampling is used when dividing a population into subgroups so that a random sample from each subgroup can be collected. (option 3)

Stratified Random Sampling is a type of probability sampling where the population is divided into subgroups (or strata) based on some important characteristic. The purpose of stratifying the population is to ensure that each subgroup is represented in the sample, so that the results of the study can be more accurately generalized to the larger population.

After dividing the population into strata, a random sample is selected from each stratum. This approach is used when there is heterogeneity within the population and it is important to ensure that each subgroup is adequately represented in the sample. This method can result in a more precise estimate of population parameters compared to simple random sampling, as it ensures that each subgroup is proportionately represented in the sample.

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Complete Question:

when dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

The real and imaginary values of w is 86  and - 0.92i respectively.

To find w = √(3 - 4i), we can use the following steps:

Step 1: Find the modulus and argument of z = 3 - 4i

The modulus of z is

|z| = √(3² + (-4)²)

= √(9 + 16) = √25

= 5.

The argument of z is arg(z) = arctan(-4/3) ≈ -0.93 radians (or about -53.13 degrees).

Step 2: Find the principal square root of the modulus of z, which is

√|z| = √5.

Step 3: Find the argument of w, which is half of the argument of z, i.e., arg(w) = arg(z)/2

= -0.93/2

≈ -0.465 radians (or about -26.57 degrees).

Step 4: Express w in terms of its real and imaginary parts, using the formula:

w = √|z| * exp(i*arg(w)).

Substituting the values we found above, we get:

w = √5 x exp(i(-0.465))

= √5 x (cos(-0.465) + i*sin(-0.465))

≈ 1.86 - 0.92i

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If polygons are similar ratio if sides will be same

\(\\ \sf\longmapsto \frac{x}{50} = \frac{48}{40} \\ \\ \sf\longmapsto 40x = 48 \times 50 \\ \\ \sf\longmapsto x = \frac{48 \times 50}{40} \\ \\ \sf\longmapsto x = \frac{2400}{40} \\ \\ \sf\longmapsto x = 60\)

Answer:

−4.6+(−0.4)+(−7.2) =−4.6−(0.4+7.2)

Step-by-step explanation:

Answer:

\(n=-9\)

Step-by-step explanation:

Subtract 10 on both sides giving you: -7n = 63

The divide -7 to both sides giving you -9

Tip: A negative divided by a positive is a negative.

Answer:

£42.30

Step-by-step explanation:

6% of £45 = 2.7

£45-£2.70=£42.30

When you say don't use the dollar sign do you mean I should convert from dollars to pounds?

Step-by-step explanation:

Step 1: Write down the decimal divided by 1, like this: decimal 1.

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction.

The cost of 1.20 kg of carrots is $2.09.

to convert the weight of carrots from pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. Therefore, 1.20 kg of carrots is equivalent to 2.64555 pounds.

Next, we can use the given price of $0.79 per pound to calculate the cost of 2.64555 pounds of carrots.

Cost of 2.64555 pounds of carrots = 2.64555 x $0.79

Cost of 2.64555 pounds of carrots = $2.09 (rounded to the nearest cent)

Therefore, the cost of 1.20 kg of carrots is $2.09.

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Answer:

two hours after the snow started melting, the depth of the snow would be 8 inches.

Step-by-step explanation:

The melting can be represented by a linear function of the snow depth (D(t)) as a function of time (t). We consider that the initial value is: 11 inches deep at time = 0 (zero). and then decreasing at a rate of 1.5 inches per hour (that is a negative slope = -1.5).

\(D(t)=11-1.5\,t\)

Therefore, 2 hours after the snow started melting, one would have:

\(D(2)=11-1.5\,(2)=11-3=8\,\,inches\)

Let f(n) = n2 and g(n) = n log3(10).The big-O notation defines the upper bound of a function, indicating how rapidly a function grows asymptotically. The statement "f(n) = O(g(n))" means that f(n) grows no more quickly than g(n).

Solution:

f(n) = n2and g(n) = nlog3(10)

We can show f(n) = O(g(n)) if and only if there are positive constants c and n0 such that |f(n)| <= c * |g(n)| for all n > n0To prove the given statement f(n) = O(g(n)), we need to show that there exist two positive constants c and n0 such that f(n) <= c * g(n) for all n >= n0Then we have f(n) = n2and g(n) = nlog3(10)Let c = 1 and n0 = 1Thus f(n) <= c * g(n) for all n >= n0As n2 <= nlog3(10) for n > 1Therefore, f(n) = O(g(n))

Hence, the correct option is f(n) = O(g(n)).

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Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.

A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.

Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.


In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.

A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.

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