Manny's grocery store has a rectangular logo for their business that measures 1.9 meters long with an area that is exactly the maximum area allowed by the building owner.


Create an equation that could be used to determine L, the unknown side length of the logo.

25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes

what is percent  ?

A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".

In the given question,

Let's assume that there are 100 people in Math town.

60% of them are males, so there are 60 males and 40 females.

Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.

28% of the entire population have brown eyes, so there are 28 people with brown eyes.

To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:

28 - 18 = 10

So, there are 10 females with brown eyes.

Out of the 40 females in Math town, what percentage have brown eyes?

10 brown-eyed females out of 40 females is:

10/40 = 0.25 or 25%

Therefore, 25% of the females in Math town have brown eyes.

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Answer:

x = [tex]\frac{53}{40}[/tex]

Step-by-step explanation:

18 7/8 + __ = 20 1/5

18 7/8 = 151/8

20 1/5 = 101/5

[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]

x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]

x = [tex]\frac{53}{40}[/tex]

So, the answer is [tex]\frac{53}{40}[/tex]

Answer:

Step-by-step explanation:

1

The evaluation of the functions using piecewise function gives:

f(-9) =  8

f(0) =  2

f(6) =  7

f(-6) =  4

f(3) =  4.5

f(9) = -6

To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:

For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:

f(-9) =  (-4/3)*(-9) - 4

f(-9) =  8

For f(0), x = 0. Thus, -6 x ≤ 6. So  use f(x) = (5/6)x + 2 to evaluate f(0). That is:

f(0) = (5/6)*0 + 2

f(0) =  2

For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:

f(6) = (5/6)*6 + 2

f(6) =  7

For f(-6), f(x) = (-4/3)x - 4:

f(-6) = (-4/3)*(-6) - 4

f(-6) =  4

For f(3), f(x) = (5/6)x + 2:

f(3) = (5/6)*3 + 2

f(3) =  4.5

For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:

f(9) = -2*9 + 12

f(9) = -6

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Answer:

The odds that are less generous are 19:1, 14:1, and 15:1.

Step-by-step explanation:

You have to see which numbers are greater than 11.

The calculated degrees of freedom for the t-test is 18

The degrees of freedom (df) for an independent t-test with two samples can be calculated using the following formula:

df = (n1 + n2) - 2

Where n1 is the sample size of the first group and n2 is the sample size of the second group.

In this case, the first sample has N = 8 and the second sample has N = 12.

Therefore, the degrees of freedom for the t-test will be:

df = (8 + 12) - 2

df = 18

So the t-test for this experiment will have 18 degrees of freedom.

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The area of the triangle is 87.6 cm².

The area of the triangle can be found as follows:

Therefore,

area of a triangle = 1 / 2 bh

where

Therefore,

b = 17 cm

h = 10.3 cm

Hence,

area of a triangle = 1 / 2 × 17 × 10.3

area of a triangle = 1 / 2 × 175.1

area of a triangle = 87.55

area of a triangle = 87.6 cm²

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The value of x and y are -3 and 3 respectively as shown in the graph

An equation is an expression that shows how numbers and variables using mathematical operators.

Given the equation:

2x - 3y = -13      (1)

Also:

4x + 2y = -2    (2)

From equation 2:

4x + 2y = -2

2y = -4x - 2

y = -2x - 1

substitute y = -2x - 1 in equation 1:

2x - 3(-2x - 1) = -13

2x + 6x + 3 = -13

8x = -16

x = -2

Put x = -2 in eqn 2:

4(-2) + 2y = -2

-8 + 2y = -2

2y = 6

y = 3

The value of x and y are -3 and 3 respectively

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Answer:

range = 22

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest value = 25 , smallest value = 3

range = 25 - 3 = 22

By adding the formed equations, Schuyler will receive $7.05 in change.

What is addition?

Addition is a basic arithmetic operation in mathematics that involves combining two or more numbers to form a sum.

To find the total cost of the almonds and walnuts, we need to calculate the cost of each separately and then add them together.

The cost of 0.4 pound of almonds is:

0.4 x $9.95 = $3.98

The cost of 0.6 pound of walnuts is:

0.6 x $14.95 = $8.97

The total cost of the almonds and walnuts is:

$3.98 + $8.97 = $12.95

Schuyler gives the cashier $20, so the amount of change she will receive is:

$20 - $12.95 = $7.05

Therefore, Schuyler will receive $7.05 in change.

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Matching each function with the transformation that took place gives:

g(x) = -(x - h)ⁿ: Reflection across the x-axis

j(x) = axⁿ + k: Translation of k units up

m(x) = (x + h)ⁿ - k: Translation of h units to the left

Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.

In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.

Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.

Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.

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The value of  p-value is (a)   0.0025. (b). The decision regarding the null hypothesis is to  Reject the H0 (c.) Yes there is a difference in the mean given by the two offices.

Recall that The p-value or probability value is a number, calculated from a statistical test, that describes how likely your results would have occurred if the null hypothesis were true.

The first thing is to find the difference between the set of data

30 - 26 = 4

22 - 19 = 3

25 - 20 = 5

19 - 15 = 4

26 - 19 = 7

The find the average of the set of scores

24.4 , 19.8, 1.52

Hypothesis formulation

H0: µ1 = µ2

Ha: µ1 ≤ µ2

Decide the test statistic and the level of significance:

alpha = 0.05

df = 5 - 1 = 4

The upper critical value at the level of significance = 2.7764

And the lower critical value at the level of significance = -2.7764

The decision rule

Reject H0 if |t| > 2.7764

Test statistics calculating

bar x1 - bar x2 =

24.4 - 19.8 = 4.6

standard error = s / √n

= 0.6798

t statistic = 4.6 / 0.6798

= 6.767

The decision would be given that 6.7670 > 2.7764, we would have to reject the null hypothesis and accept the alternate hypothesis.

The p value is given as 0.0025. This is the probability of rejecting the true H0

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The expression for the velocity is v(t) = 30m/s

(a) x(t) = 30t

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 30t, we have:

v(t) = d/dt (30t)

= 30

So the expression for velocity is v(t) = 30 m/s.

(b) x(t) = 7sin(30)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 7sin(30), we have:

v(t) = d/dt (7sin(30))

= 7cos(30) * d/dt (30t)

= 3.5cos(30)

So the expression for velocity is v(t) = 3.5cos(30) m/s.

(c) x(t) = ecos(701)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = ecos(701), we have:

v(t) = d/dt (ecos(701))

= -e sin(701) * d/dt (701t)

= -701e sin(701t)

So the expression for velocity is v(t) = -701e sin(701t) m/s.

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The regular price of the running shoes is $80.

Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.

Given that the sales price is $64, we can set up the equation:

0.8P = $64

To find the regular price P, we divide both sides of the equation by 0.8:

P = $64 / 0.8

P = $80

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The amplitude and period of each function are calculated and listed below

The amplitude and period of each function can be determined using their standard form:

y = A sin (Bx + C) or y = A cos (Bx + C)

where |A| is the amplitude, B is the frequency (or angular frequency), and 2π/B is the period.

Let's apply this formula to each function:

y = cos(2x)

Amplitude = 1

Period = 2π/2 = π

y = -sin(2x)

Amplitude = 1

Period = 2π/2 = π

y = -3sin(3x)

Amplitude = 3

Period = 2π/3

y = (1/2)cos(4x)

Amplitude = 1/2

Period = 2π/4 = π/2

y = 10sin(1/2x)

Amplitude = 10

Period = 2π/(1/2) = 4π

y = 5cos(1/4x)

Amplitude = 5

Period = 2π/(1/4) = 8π

y = (-1/3)cos(1/3x)

Amplitude = 1/3

Period = 2π/(1/3) = 6π

y = 4sin(-2x)

Amplitude = 4

Period = 2π/(-2) = -π

y = -2sin(2πx)

Amplitude = 2

Period = 2π/(1) = 2π

y = -3sin(πx)

Amplitude = 3

Period = 2π/π = 2

y = 1 + (1/2)cos(πx)

Amplitude = 1/2

Period = 2π/π = 2

y = -2 + cos(4πx)

Amplitude = 1

Period = 2π/(4π) = 1/2

The graphs of the functions are added as attachment

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The one to one functions in the options includes

A one-to-one function, also known as an injective function, is a type of function in mathematics where every element in the domain maps to a unique element in the range.

So we can say that, each input value corresponds to exactly one output value, and no two distinct input values have the same output value.

Graphically, one-to-one functions pass the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once.

Applying the horizontal line test shows that the one-to-one function are: Graph 1, 4 and 6

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A registered investment account, or RRSP, enables you to put money aside for retirement while delaying taxes on investment gains.

An annuity is a financial product that provides regular payments over a specified period of time in exchange for a lump sum of money. It's often used as a retirement income source and comes in different types such as fixed, variable, immediate, and deferred annuities. It's important to understand the terms, fees, and charges before purchasing an annuity.

Registered Retirement Savings Plan is the full form of RRSP.

In Canada, both workers and independent contractors can save and invest during their retirement through Registered Retirement Savings Plans (RRSP).

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Here is an example of how to create an object model, UML diagrams, and contract obligations in general.

Let's have a look at a basic "Bank Account" system, where a customer may deposit money, withdraw it, and see the amount of their account. The following classes would be represented in the UML class diagram for this system:

Bank Account Client

The following characteristics would be included in the Bank Account class:

string Account Number

stability: float

and the subsequent techniques:

deposit(float amount) = None

withdrawal(float :amount) = None

float: check Balance()

The following characteristics would apply to the Customer class:

string name

list of accounts[Bank Account]

and the subsequent techniques:

account: Bank Account; add account(account) -> None

account: Bank Account; remove  Account(account: None)

Bank Account: get  Account(Account number: string)

For the Bank Account class, the design by contract obligations would be:

Pre-conditions:

amount > 0

withdraw(amount): amount > 0 and balance >= amount

Check Balance(): None

Post-conditions:

deposit(amount): balance += amount

withdraw(amount): balance -= amount

Check Balance(): return balance

The design by contract responsibilities for the Customer class would be:

Pre-conditions:

Add account(account): account not in accounts

Post-conditions:

Add account(account): accounts. append(account)

remove (account): accounts.

get account (account number): return the Bank Account object with the given account Number.

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Answer: 12

Step-by-step explanation: 2 x 6 = 12 = the third side

Answer: 5

Step-by-step explanation:

the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color.

How to solve the question?

To find the least number of rows, we need to determine the greatest common divisor (GCD) of 56 and 120, since each row must have the same number of blocks. We can use the Euclidean algorithm to find the GCD:

120 = 2 x 56 + 8

56 = 7 x 8 + 0

Therefore, the GCD of 56 and 120 is 8. This means that each row must have 8 blocks, and there will be a total of (56+120) = 176 blocks to be arranged.

Since each row can have either only yellow or only black blocks, we need to determine which color will have the greater number of rows. To do this, we can divide the total number of blocks by the number of blocks in each row:

Yellow blocks:

Number of rows = 56 ÷ 8 = 7 rows

Black blocks:

Number of rows = 120 ÷ 8 = 15 rows

Since there are more black blocks, we will use 15 rows of black blocks. Each row will have 8 blocks, so there will be a total of (15 x 8) = 120 black blocks.

We can then use the remaining 56 yellow blocks to create rows of only yellow blocks. Each row will have 8 blocks, so there will be a total of (56 ÷ 8) = 7 yellow rows.

Therefore, the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color

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1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.

2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.

The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,

z = (15 - 20) / 5 = -1

Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.

(b) Similarly, we have

z = (30 - 20) / 5 = 2

Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.

(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:

z1 = (18 - 20) / 5 = -0.4

z2 = (25 - 20) / 5 = 1

Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.

2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,

a = μ + σ * z = 0 + 1 * 1.645 = 1.645

(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,

b = μ + σ * z = 0 + 1 * (-1.645) = -1.645

(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,

c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.

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Therefore, The dilated image's vertices are as follows:B'(2 , 3)   C'(3 , 3)     D'(1 , 3)

It is not necessary for the dilation's center to be inside the form. It might be the polygon's vertices. The preimage is still a square in this case, but the center of the dilatation is at the top-left vertex, which is shared by both of the dilated pictures (one smaller and one larger).

To get the vertices of the dilated image, multiply each vertex's coordinate by a factor of three.

B(6,9)⇒B'(1/3×6,1/3×9) = B'(2 , 3)

C(9,9)⇒C'(1/3×9 , 1/3×9) = C'(3 , 3)

D(3,9)⇒D'(1/3×3 ,1/3×9) = D'(1 , 3)

The dilated image's vertices are as follows:

B'(2 , 3)   C'(3 , 3)     D'(1 , 3)

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Answer:

To determine the classification of a triangle based on its side lengths, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

For this particular triangle with side lengths 6 cm, 10 cm, and 12 cm, we can apply the Pythagorean theorem to determine whether the triangle is acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is equal to 90 degrees).

Using the Pythagorean theorem, we find:

6^2 + 10^2 = 136

12^2 = 144

Since 136 is less than 144, we know that 6 cm, 10 cm, and 12 cm are the side lengths of a triangle that is obtuse (one angle is greater than 90 degrees), because the longest side (the hypotenuse) is greater than the sum of the squares of the lengths of the other two sides.

Therefore, the correct answer is: obtuse, because 6^2 + 10^2 < 12^2.

Answer:

the volume of the cylinder is 904.32 m³

Step-by-step explanation:

Answer: To find d(L(x))/dx, we need to differentiate L(x) with respect to x using the derivative rules.

d(L(x))/dx = d/dx (sinx - cosx)

= cosx + sinx

Therefore, the correct answer is option A, cosx+sinx.

Step-by-step explanation:

Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.

Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.

Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.

Step-by-step explanation:

Recall the general equation for a line in slope-intercept form:

[tex]y=mx+b[/tex]

where:

[tex]\text{y = y-coordinate}[/tex]

[tex]\text{m}=\bold{slope}[/tex]

[tex]\text{x = x-coordinate}[/tex]

[tex]\text{b = y-intercept}[/tex]

In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:

[tex]-4x+y=0[/tex]

[tex]-4x +4x+y=0+4x[/tex]

[tex]\implies y=4x+0[/tex]

Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.

If you were to graph the line, you would see the intersection at (0,0):

graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]

In the ratio, the odds that are less generous is C) 19:1 and D)18:1.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here odds for bets are 11:1.

That means if for every $1  you bets, you may wins $11.

There are [tex]\frac{1}{1+11}=\frac{1}{12}=8.33\%[/tex] chance of this happens.

If the friends thinks odds are too generous , then the odds that less than generous are,

=> for 4:1 then [tex]\frac{1}{1+4}=\frac{1}{5}= 20\%[/tex]

=> For 6:1 then [tex]\frac{1}{6+1}=\frac{1}{7}= 14\%[/tex]

=> For 19:1 then [tex]\frac{1}{19+1}=\frac{1}{20}=5\%[/tex]

=> For 18:1 then [tex]\frac{1}{18+1}=\frac{1}{19}=5.2\%[/tex]

Hence the odds that are less generous is C) 19:1 and D)18:1.

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Answer:

  (b)  $21,495.64

Step-by-step explanation:

You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.

The value of an account earning interest at annual rate r compounded continuously is ...

  A = P·e^(rt)

where P is the initial account value, and t is the number of years.

In this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...

  A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B

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