if a shop owner purchased 20 pairs pf gloves at $12 each and some hats for $25 each, how many hats did he buy if he spent a total of $490

Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

here a₁ = - 1 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-5}{-1}\) = 5

then nth term is

\(a_{n}\) = - 1 \((5)^{n-1}\)

Answer:

The square root of 7

Step-by-step explanation:

Answer:

√7

Step-by-step explanation:

To find AC, use half of the base and the hight. Use the pythagorean theorm to help. 2^2+√3^2=x^2, 7=x^2, x=√7

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The system of equations y=2x -3.5 and x- 2y = -14 has a solution as (7, 10.5)

The solution to the system of equations can be calculate as follows:

y = 2x - 3.5 …. (1)

x - 2y = -14 …. (2)

Let's solve the system of linear equations using the elimination method.

Add two to equation (1).

2y = 4x - 7

- 4x + 2y = -7 …. (3) (3)

By incorporating equation (2) and (3)

- 3x = - 21

multiplying both sides by 3

x = 7

Change the value of x in the equation (1)

y = 2 (7) - 3.5

By additional computation

y = 14 - 3.5

y = 10.5

Consequently, the answer is (7, 10.5).

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Answer:

-27

Step-by-step explanation:

f(a) = -3a + 3

f(10) = -3(10) + 3

= -30 + 3

= -27

Answer:

B) 800 cm^2

Step-by-step explanation:

A=2(wl+hl+hw)

800 = 2(10x15 + 10x10 + 10x15), which is B

Answer:

800 cm^2

Step-by-step explanation:

rob has 8 dimes and 17 nickels in $1.65

There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.

Let n represent nickels & d dimes

given: n + d = 25 #1 (number of coins)

given: .05n + .10d = 1.65 #2 (amount in dollars)

n = 25 - d #3 (rewrite of #1)

.05(25 -d) + .10d = 1.65 (substitute #3 in #2)

1.25 - .05d + .10d = 1.65 (multiply out the left side)

.05d = .40 (collection of like terms)

d = 8 (divided both sides by.05)

n + 8 = 25 (substitute answer for d in #1)

n = 17 (subtract both sides by 8)

There are 8 dimes and 17 nickels.

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Answer:

x=y-4

Step-by-step explanation:

If Samir has skated y laps around the rink, then Kai has skated y - 4 laps around the rink.

So the expression that shows how many laps Kai has skated around the rink is: x=y-4

Answer:

Step-by-step explanation: patience. wyd here.

but the answer is x=y-4

Explanation: To solve this question we just need to substitute the x and y values from each point into the equation, if the equality is true it means the point is on the graph but if the equality is wrong it means the point is not on the graph of the equation.

Step 1: Let's substitute the values for each of the points and calculate as follows

Final answer: So the points on the graph are (0,-2) and (8,2).

Answer:

30 feet

Step-by-step explanation:

20×1.5=30

Answer:

B) 30

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x = - 1, x = 2

Step-by-step explanation:

Given

x + (x + 1) + (x + 2) = (x + 1)² ← expand using FOIL , then

x + x + 1 + x + 2 = x² + 2x + 1 , that is

3x + 3 = x² + 2x + 1 ( subtract 3x + 3 from both sides )

0 = x² - x - 2 ← in standard form

0 = (x - 2)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 2 = 0 ⇒ x = 2

Answer:

70

Step-by-step explanation:

GCF(x,y)*LCM(x,y)=xy

10*280=40n

2800=40n

70=n

n=70

\((2x + 15) + (10x + 45) = 180\)

\(12x + 60 = 180\)

\(12x = 180 - 60\)

\(12x = 120\)

\(x = \frac{120}{12}\)

\(\boxed{x = 10}\)

.

\(5x + 60 + 40 = 180\)

\(5x + 100 = 180\)

\(5x = 180 - 100\)

\(5x = 80\)

\(x = \frac{80}{5}\)

\(\boxed{x = 16}\)

.

\(4x + 80 + 100 + 120 = 360\)

\(4x + 300 = 360\)

\(4x = 360 - 300\)

\(4x = 60\)

\(x = \frac{60}{4}\)

\(\boxed{x = 15}\)

Answer:

18. x = 10

19. x = 16

20. x = 15

My friend consumed 8 donuts in one sitting. 8 donuts is a lower bound on how many donuts he is physically capable of eating in one sitting option A.

An element of K that is bigger than or equal to each member of S is referred to as an upper limit or majorant of a subset S of some preordered set (K, ) in mathematics, notably in order theory. In addition, each element of K that is smaller than or equal to each element of S is characterised as a lower limit or minorant of S.

A set that has an upper (or lower) bound is referred to as being majorized (or minorized), bounded from above, or minorized by that bound. In the mathematical literature, sets that have upper (or lower, respectively) limits are referred to as being bounded above (or below).

Friend consumed 8 doughnuts. So it is

lower bound on how can eat in a sitting.

Many donuts he lower bound is the lowest quantity in a set, as in our.

example, we definitely know he can eat 8 of them. We don't know how many more can be eat (upper bound) or is it exact amount be can eat.

Hence option (a) is correct.

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3\(x^4\) + 1 is equivalent to \(x^{(4/2)}\) in terms of asymptotic growth rate. The value of 3\(x^4\) + 1 is O(\(x^{(4/2)}\)) and \(x^{(4/2)}\) is O(3\(x^4\) + 1).

To show that 3\(x^4\) + 1 is O(\(x^{(4/2)}\)), we need to find a constant C and a value of x such that:

|3\(x^4\) + 1| <= C|\(x^{(4/2)}\)|

For x >= 1, we can say that:

3\(x^4\) + 1 <= 4\(x^4\)

Taking the square root of both sides, we get:

sqrt(3\(x^4\) + 1) <= 2x²

Thus, we can choose C = 2 and x0 = 1, and we have:

|3\(x^4\) + 1| <= 2|\(x^{(4/2)}\)| for all x >= 1

Therefore, 3\(x^4\) + 1 is O(\(x^{(4/2)}\)).

To show that \(x^{(4/2)}\) is O(3\(x^4\) + 1), we need to find a constant C and a value of x such that:

|\(x^{(4/2)}\)| <= C|3\(x^4\) + 1|

For x >= 1, we can say that:

\(x^{(4/2)}\) <= x²

Thus, we can choose C = 1 and x0 = 1, and we have:

|\(x^{(4/2)}\)| <= |3\(x^4\) + 1| for all x >= 1

Therefore, \(x^{(4/2)}\) is O(3\(x^4\) + 1).

Since both 3\(x^4\) + 1 is O(\(x^{(4/2)}\)) and \(x^{(4/2)}\) is O(3\(x^4\) + 1).

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Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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The appropriate inference method to test for a difference between the average IQ scores of identical twins raised by birth parents and in a foster home is paired t-test.

A paired t-test is used when comparing two sets of observations that are paired or matched in some way, such as in the case of identical twins. In this scenario, the twins are matched based on their genetic makeup, and their IQ scores are compared based on their different upbringing environments (birth parents vs. foster home). The paired t-test allows us to analyze the difference between the paired observations (IQ scores) and determine if there is a statistically significant difference between the two groups.

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By the application of the exponential function to the problems we have;

1)  $16187

2) $1346

3)  6774

4) $5670

5)  $ 7233

6) 4%

We have to know that the value of the car can be obtained by the use of the function;

P = Poe^-rt

P = Value at time t

Po = initial value

r = rate of depreciation

t = time taken

P = 44,000e^-0.25*4

P = $16187

2) P= Poe^-rt

P = 1580e^-0.02 * 8

P = $1346

3) P =  Poe^rt

P = 6348e^0.013 * 5

P = 6774

4) A = P(1 + r/n)^nt

A = 5,000( 1 + 0.036/12)^12 * 3.5

A = $5670

5) A = P(1 + r/n)^nt

A = 6,013.53( 1 + 0.0185/4)^4 *10

A = $ 7233

6)  A = P(1 + r/n)^nt

6,520.02 = 4,848(1 + r/2)^6 * 2

6,520.02/ 4,848 = (1 + r/2)^6 * 2

1.34 = (1 + r/2)^12

ln 1.34 = 12ln (1 + r/2)

ln (1 + r/2) = ln 1.34/12

ln (1 + r/2) = 0.024

1 + r/2 = e^0.024

1 + r/2 = 1.02

r/2 = 1.02 - 1

r/2 = 0.02

r = 2 * 0.02

r = 0.04

r = 4%

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Answer:

\(volume = 10\pi m^3\)

Step-by-step explanation:

Volume of a prism = Base Area x height

Base is a quarter of a circle.

              \(Area \ of \ circle = \pi r^2\\\\r = 2m\\\\Area \ of \ quarter \ of \ a \ circle = \frac{1}{4} \pi r^2 = \frac{1}{4}\pi \times 4 = \pi m^2\)

Base Area = π square meters.

Therefore ,

          \(Volume = Base Area \times height = \pi \times 10 = 10\pi m^3\)

Answer:5,482

Step-by-step explanation:

Answer:

I got 11

Step-by-step explanation:

Answer:

12.25 cm^2

Step-by-step explanation:

Draw a segment from the bottom of the 1.5-cm vertical side to the bottom side of the entire polygon.

Now you have two rectangles.

The left rectangle has dimensions 3.5 cm by 1.5 cm.

The right rectangle has length 5 cm - 1.5 cm = 3.5 cm and width 3.5 cm - 1.5 cm = 2 cm.

The total area is the sum of the areas of the two rectangles.

area of rectangle = length * width

total area = 3.5 cm * 1.5 cm + 3.5 cm * 2 cm

total area = 5.25 cm^2 + 7 cm^2

total area = 12.25 cm^2

Answer:

y=2x-2

Step-by-step explanation:

m= slope= rise/ run. 2/1=2

Y intercept is -2, so the linear equation equals y=2x-2

Hi there!

The answer is True.

(For Proof and explanation, please check the attached picture)

\(Have \: a \: great \: day! \: :)\)

The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.

Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0

Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x

Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).

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Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

The maximum area that the 60 m can enclose is 225m², the dimensions of the maximal region are 15m x 15m, and the height as an fcn of the base is 30 - b.

Let the base of the rectangular region be "b",

and the height be "h" and,

it is given that the perimeter of the rectangular region = 60m

(a) write height as an fcn of base

by using the formula of the perimeter of a rectangle,

2(h+b) = 60m

we can write, h = 30 - b

⇒Area of the rectangular region

area(A) = height × base

substituting the value of h.

= (30 - b) × b

thus, A(b)= 30b - b²

to find the maximum area that the 60 m can enclose

\(\frac{dA(b)}{db}\) should be equal to 0.

substituting the value of A(b).

30 - 2b = 0

thus, b = 15

maximum area = 30b - b²

substituting the value of b.

= (30 × 15) - 15²

thus, maximum area = 225m².

dimensions of the maximum region,

for maximum area height = base = 15m

thus, the dimensions of the maximum rectangular region are 15m x 15m.

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Answer:

(a.) B: 8,000

(b.) C: 800

(c.) A. 10 times

Step-by-step explanation:

8762 has 3 digits after the 8. 8,000 has 3 digits after the 8

851 has 2 digits after the 8. 800 has 2 digits after the 8.

8,000 ÷ 800 = 10

Another way to do it is: 8000 has 3 zeros and 800 has 2 zeros.

3 - 2 = 1. 10 has 1 zero.

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Answer:

How much the tree grew a week

Step-by-step explanation:

The equation of the function y = a( x - h )^3 + k after the transformations resulted to

The given function is y = a( x - h )^3 + k

Shifting left or right affects the x values only, shifting left 2 units means adding to the x, to get to

y = a( x - h + 2 )^3 + k

vertically compressed by a factor of 1/2 means multiplying the equation by a factor of half to get

y = a/2 ( x - h + 2 )^3 + k

Reflection across the x-axis (flipped) will be effective when a negative sign is attached to the equation

y = -a/2 ( x - h + 2 )^3 + k

Moving up 3 units means adding 3 to the equation

y = -a/2 ( x - h + 2 )^3 + k + 3

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