Use unit rates to determine the better buy and provide the unit price for your answer. Round your answer to the nearest hundredth, if necessary.
$4.05 for 150 index cards
$1.17 for 30 index cards

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Explanation:

sigma = 120 = population standard deviation

n = 25 = sample size

sigma/sqrt(n) = standard deviation of the xbar distribution

sigma/sqrt(n) = 120/sqrt(25) = 24

The standard deviation of the sampling distribution of the mean for this sample is 24. Rephrased, the standard deviation of the xbar distribution is 24.

To get the variance, we square the standard deviation

variance = (standard deviation)^2

variance = 24^2

variance = 576

Keep in mind this is the variance of the xbar distribution, and not the original underlying distribution it came from.

There is strong positive association between the variables.

The strength of the linear link between two variables is assessed using correlation coefficients. A correlation coefficient with a value over zero denotes a positive link, whereas one with a value below zero denotes a negative relationship. A statistical indicator of how strongly two variables are linearly related is the correlation coefficient. From -1 to 1, its values are possible. A correlation coefficient of -1 indicates a perfect negative, or inverse, correlation, in which the values in one series rise as the values in the other fall, and the other way around. A value of 1 indicates a direct link that is 100 percent positive. There is no linear link when the correlation coefficient is zero.

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Answer:

Manny.

Step-by-step explanation:

Because they split cleaning on Thursday and Manny finished first, then on Friday Manny will clean more stalls because they are faster.

a. Natasha says her answer is 11.75. Therefore, she is correct.

b. The possible error that was made was that Jorge shifted the decimal backward.

A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio. A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent a numerical value for a whole plus some fraction of a whole.

From the information, it should be noted that Natasha and Jorge were asked to find the quotient to the decimal division problem 18.8÷1.6.

a. It should be noted that the division of the decimals will be:

= 18.8 ÷ 1.6

= 11.75

This can easily be done with a calculator.

b. One can easily know who is correct through the use of a calculator or mentally. The fact that Jorge got 1.175 is incorrect.

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(3x+2)(x+2)

Step-by-step explanation:

How to solve your problem

3x² + 8x + 4

1. Grouping

Use the sum-product pattern

3x² + 8x + 4

3x² + 6x + 2x + 4

2. Common factor from the two pairs

3x² + 6x + 2x + 4

3x(x+2)+2(x+2)

3. Rewrite in factored form

3x(x+2)+2(x+2)

(3x+2)(x+2)

Solution

(3x+2)(x+2)

Answer:

(x+2) x (3x+2)

He doesn't have enough storage space remaining to add a rock playlist that uses that uses 0.4 gigabytes

From the information, Morgan's phone can hold 4 gigabytes of music. He also already has three oldies playlists that take up 1.2 gigabytes each.

A rock playlist is 0.8 gigabytes. Therefore, the space remaining will be:

= Total gigabytes - Space used

= 4 gb - (1.2 × 3)

= 4gb - 3.6gb

= 0.4gb

Since the Rock music is 0.8 gigabytes, there no enough space.

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The volume V of the described solid S is 3.48 π and this can be described by performing the integration and using the given data.

Given: The base of S is the region enclosed by the parabola [tex]$y=2-3 \mathrm{x}^2$[/tex] and the x-axis.

Cross-sections perpendicular to the y-axis are squares.

To determine the x-intercept by substituting (y = 0) in the given function.

[tex]$&0=2-3 \mathrm{x}^2 \\[/tex]

[tex]$&x^2=\frac{2}{3} \\[/tex]

[tex]$&x=\pm \sqrt{\frac{2}{3}}[/tex]

The volume of solid S is given by: [tex]$\mathrm{V}=\pi \mathrm{r}^2 \mathrm{~h}$[/tex]

where [tex]$\mathbf{r}=\mathbf{y}\sqrt{x}[/tex] and h = dx.

[tex]$&\mathrm{dV}=\pi\left(2-3 \mathrm{x}^2\right)^2 \mathrm{dx} \\[/tex]

[tex]$&\mathrm{dV}=\pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx}[/tex]

Now, integrate the above expression.

[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]

[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]

Simplify the above expression, we get

[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]

[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]

Simplify the above expression.

[tex]$$\mathrm{V}=\pi\left[\left(9 \frac{\left(\sqrt{\frac{2}{3}}\right)^5}{5}-\frac{\left(\sqrt{\frac{2}{3}}\right)^3}{3}+4\left(\sqrt{\frac{2}{3}}\right)\right]\right.$$\alpha[/tex]

Now, simplify the above expression by using the arithmetic operations.

V ≈ 3.48 π

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Explanation

Step 1

as the triangles are similar

Step 2

solve for x

so, the anwer

Given -

-4x + 5y = -2

To Find -

Value of x and y

Step-by-Step Explanation -

At x = 0

-4(o) + 5y = -2

y = -2/5

At y = 0

-4(x) + 5(0) = -2

-4x = -2

x = 1/2

Final Answer -

Graph:

The liters of gas that Alonso need to fill his gas tank is 71.92279 liters.

It was stated that Alonso's car holds a maximum of 19 gallons of gas.

It is important to note that 1 gallon = 3.78541 liters.

Therefore, the number of liters will be calculated by multiplying the value. This will be:

= 19 × 3.78541

= 71.92279 liters.

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Answer:

-3

Step-by-step explanation:

N/A

Answer:

Never True

Step-by-step explanation:

The equation is not balanced.

Answer: 84.

Step-by-step explanation: If you add the width 5cm and 2cm, it gives you 7cm, then length x width so 12x7= 84(cm).

If I am wrong, I am truly sorry, I haven't done area in a long time.

Answer:

see explanation

Step-by-step explanation:

assuming you require the measure of the numbered angles.

∠ 5 and 148° are vertically opposite angles and are congruent , so

∠ 5 = 148°

∠ 6 and 148° are a linear pair and sum to 180° , that is

∠ 6 + 148° = 180° ( subtract 148° from both sides )

∠ 6 = 32°

∠ 6 and ∠ 7 are vertically opposite angles and are congruent , then

∠ 7 = 32°

∠ 3 and ∠ 6 are same- side interior angles and sum to 180° , that is

∠ 3 + 32° = 180° ( subtract 32° from both sides )

∠ 3 = 148°

∠ 1 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 1 = 148°

∠ 1 and ∠ 2 are a linear pair and sum to 180° , so

∠ 2 + 148° = 180° ( subtract 148° from both sides )

∠ 2 = 32°

∠ 2 and ∠ 4 are vertically opposite angles and are congruent , then

∠ 4 = 32°

In summary

∠ 1 = 148° , ∠ 2 = 32° , ∠ 3 = 148° , ∠ 4 = 32° , ∠ 5 = 148° , ∠ 6 = 32° , ∠ 7 = 32°

Answer:

The answer is A

Step-by-step explanation:

y=-0.5x + 225

This is because every month 50 cents which can be written as 0.5 is taken off the account so it would be negative. Since X =  the number of months, you would multiply it by 0.5, hence -0.5x. Since 225 is the orginial balance you would add that.

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perpendicular gradients are egual to -1 when multiplying them which means

Step-by-step explanation:

.Ma×Mb=-1

Ma=-1/Mb

The order of the color of the 39th skittle is: yellow

By adding numbers to the given sequence and examining the repetition, order-based issues in mathematics can be addressed. Once the proper order number has been determined, numbering the other objects will be a breeze.

The answer is a bag of Skittles in the following color order: red, orange, brown, yellow, green, and blue.

The hue of the 39th skittle that they consumed is:

There are six hues in all.

Red is repeated once again after number 6. The order for the red is as follows:

[1, 6,12,18,24,30,36]

39 is yellow, 38 is brown, and 37 is orange.

Consequently, the 39th skittle is colored in the following order: yellow

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Equations f(x) = g(x) is proved with x be (C) 4.

So, to get f(x) = g(x):

Solve for 'x' as follows:

Now, but 'x = 4' in both equations to check that LHS = RHS:

The sketch of equations "f(x) = 2x + 1" and "g(x) = 3x -3" is attached below with the value of coordinate x = 4.

So, value of x = 4.

Therefore, equations f(x) = g(x) is proved with x be (C) 4.

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Answer:4.5

Step-by-step explanation:4.5

For students who earned a score of 21 or higher on the quiz

The cumulative frequency = 16

The relative frequency  = 32%

The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.

To get relative frequency, we will take this cumulative number and divide by the total number of students. number of 21 or more / total number of students = 16 / 50 = 0.32 or 32%.

The cumulative frequency of students who earned a score of 21 or higher on the quiz is =16.

Total frequency is = 4+8+15+7+7+3+4+2=50.

So the relative cumulative frequency is

= 16 / 50

= 0.32 or 32%.

Hence , the relative cumulative frequency when students who earned a score of 21 or more is 0.32.

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Answer:

21 over 40 times t plus negative 22​

Step-by-step explanation:

3/4t - 5+ 2/5t - (5/8t + 17)

= 3/4t + 2/5t - 5 /8t - 5 - 17

= 21/40 t - 22

Answer:

Step-by-step explanation:

1) Find the table

To find the numbers on the table, just substitute the number for x

If x = 0

y=-4x+3

y=-4(0) + 3

y= 0 + 3

y= 3

If x = 1

y=-4x+3

y=-4(1)+3

y= -4 + 3

y= -1

You can see a pattern, each x makes it go down by 4.

So the following will be...

if x = 2 -> -5

if x = 3 -> -9

2) Now fill in the table with the points

(0, 3) (Taken from the table, the x and y)

(1, -1)

(2, -5)

(3, -9)

3) Afterward draw a line through it. You will get your graph.

There are 7040 yards in 4 miles.

A ratio indicates the number of times one number contains another.

Given, 5 miles = 8800 yards.

5 miles = 8800 yards

1 miles = 8800/5 yards

4 miles = (8800/5) × 4 yards

4 miles = 7040 yards.

Hence, there are 7040 yards in 4 miles.

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The remainder when the polynomial f(x) is divided by the x - 5 is 0.

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.

Consider the polynomial,

f(x) = x³ - x² - 17x - 15

The factor of the polynomial is x - 5.

So,

x - 5 = 0

x = 5

Substituting the value of x in the polynomial,

f(x) = x³ - x² - 17x - 15

f( 5 ) = 5³ - 5² - 17(5) - 15

f(5) = 125 - 25 - 85 - 15

f(5) = 125 - 125

f(5) = 0

Hence, the remainder is 0 when polynomial f(x) is divided by x - 5.

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Question: Simplify the expression 1 + 0.25 (8 + 12) - 0.3 × 2​

Solution:

Distributing 0.25 in the sum we obtain:

Performing each of the operations we obtain:

So the correct answer is

A) Hence,  proven that 3y²– 24y – 47 = 0

B) After solving the simultaneous equations y1 = −1.627314 or −1.6 and y2 = 9.627314  or 9.6.

Equations that are simultaneously solved and have two or more common variables are known as simultaneous equations (that is, simultaneously). Since the unknown variables in both equations, x and y, are the same, they can be solved simultaneously to find the values of the variables.

As an illustration, equations x + y = 5 and x - y = 6 are examples of simultaneous equations. Simultaneous equations can be resolved in a variety of ways, including graphically, by substitution, and by elimination.

a) Given that

x - 6y = 10

Lets solve for x

x = 10 + 6y

And 3y² = 4x + 7

Lets solve for x

x = (3y² - 7)/4

As x is equal lets cross multiply and we get

10 + 6y = (3y² - 7)/4

40 + 24y =  3y² - 7

47 + 24y = 3y²

0 = 3y² - 24y - 47

3y²– 24y – 47 = 0

B) To solve the simultaneous equations

Lets convert them to standard format

x - 6y = 10 already in standard format

3y² = 4x + 7

4x - 3y² = -7 in standard format

Now solve

⇒                 x - 6y = 10      (x4)

                   4x - 3y² = -7    (x1)

⇒                  4x - 24y = 40

                -   4x - 3y² = -7

                     0 + 3y²– 24y = 47

⇒ 3y²– 24y = 47

⇒ Putting the value in quadratic formula

⇒ y1 = −1.627314 or −1.6

⇒ y2 = 9.627314  or 9.6

A) Hence,  proven that 3y²– 24y – 47 = 0

B) After solving the simultaneous equations y1 = −1.627314 or −1.6 and y2 = 9.627314  or 9.6.

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The total number of ways in which different telephone numbers are possible in city  is  6561.

Permutation -

It relates to a mathematical process that determines the number of possible arrangements of a given set.

Now, according to the question:

The first three digits are fixed, we have to select the next four digits.

A total number of available telephone numbers is increased by selecting

Thus,

= 9×9×9×9

= 6561

Total number of ways in which different telephone numbers are possible in city are 6561.

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