-7(-1 - 4d) simplified

X=2

Answer:

Both cards would have equal value when both have purchased 2 Pizzas each

Step-by-step explanation:

since the number of pizzas purchased is X

70-(20*X) =X*15

-20X-15X=-70

-35X = -70

X =2

Answer:

a) 5, 8, 11

b) 32

Step-by-step explanation:

a)

First term: 3(1)+2=3+2=5

Second term: 3(2)+2=6+2=8

Third term: 3(3)+2=9+2=11

b)

Tenth term: 3(10)+2=30+2=32

Hope this helps!

Answer:

  [-4, 2]

Step-by-step explanation:

You want the range of the graph shown.

The range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...

  [-4, 2] . . . . or -4 ≤ y ≤ 2

Answer:

257k-392=153

Step-by-step explanation:

Answer:

257k-392=153

the product of 257 and k means you are multiplying 257 and k. 392 is subtracted from that product so you put that subtraction sign after the multiplication problem. The same as means the answer is equal to 153.

The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

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Answer:

66 percent

Step-by-step explanation:

⅔ are shaded which is 0.6 recurring which as a percentage is 66 percent. may have to say 66.6

The function h(x) is given as:h(x) = {e^(-x/3), if x < -1e^(x/5), if -1 <= x < 0 101, if x = 0 1, if x > 0Now, the definite integral of h(x) between -2 and 5 is to be evaluated.

Let F(x) be the indefinite integral of h(x). Then, we have:F(x) = { -3e^(-x/3) + C1, if x < -1 5e^(x/5) + C2, if -1 <= x < 0 101x + C3, if x = 0 x + C4, if x > 0where C1, C2, C3, C4 are constants.Now, evaluating the definite integral ∫_-2^5 h(x) dx, we get; ∫_-2^5 h(x) dx = F(5) - F(-2) = [5 + C4] - [-3e^(2/3) + C1]Therefore, the value of the definite integral is 5 + 3e^(2/3) + C1 - C4.The constant values depend on the value of x for which F(x) is defined. However, since no limits are provided, the constant values cannot be calculated.

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Answer: B  is the answer

Step-by-step explanation:

Ur answer sir :)

1) 6⁴

2) t²

3) b⁴

4) 5²× 7³

5) 2²× a²

6)a³× c⁴× d

Answer:

11

Step-by-step explanation:

QS = QR + RS ➡ 19 = -1 + x + 2x - 7 add like terms

19 = 3x - 8

27 = 3x

9 = x

RS = 2x - 7 so 2×9 - 7 = 11

Answer: need photo

Step-by-step explanation:

Answer:

3 teaspoons

Step-by-step explanation:

Answer:

3 tbs

Step-by-step explanation:

Therefore, the length of each side of the original square is 5 cm.

Area is a measure of the size of a two-dimensional surface or region. It is the amount of space enclosed by a boundary in two dimensions. In simple terms, area is the size of a flat surface, such as the floor, a wall, or a piece of paper. It is usually measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or acres.

Here,

Let x be the length of each side of the original square.

When the length of each side is increased by 10 cm, the new length is x + 10, and the area of the new square is (x + 10)².

According to the problem, the increase in area is 200 cm², so we can set up the equation:

(x + 10)² - x² = 200

Expanding the left side of the equation, we get:

x² + 20x + 100 - x² = 200

Simplifying, we get:

20x + 100 = 200

Subtracting 100 from both sides, we get:

20x = 100

Dividing both sides by 20, we get:

x = 5

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Thus, the composite function are -

a) (g ∘ f)−1(x) = -x - 4.
b) g−1(x) = -x.
c) f −1(x) = x - 4.
d) (f −1 ∘ g−1)(x) = -x - 4.

a) To find (g ∘ f)−1, we first need to find g ∘ f. This means we need to plug function f(x) into g(x) and simplify:
(g ∘ f)(x) = g(f(x)) = g(x + 4) = -(x + 4)

Now we need to find the inverse of this function, which means solving for x:
-(x + 4) = y
x + 4 = -y
x = -y - 4
So, (g ∘ f)−1(x) = -x - 4.

b) To find g−1, we need to solve for x in the equation g(x) = -x:
g(x) = -x
x = -g(x)
So, g−1(x) = -x.

c) To find f −1, we need to solve for x in the equation f(x) = x + 4:
f(x) = x + 4
x = f(x) - 4
So, f −1(x) = x - 4.

d) To find f −1 ∘ g−1, we need to plug g−1(x) into f −1(x) and simplify:
f −1 ∘ g−1(x) = f −1(-x) = -x - 4.
So, (f −1 ∘ g−1)(x) = -x - 4.

In summary:
a) (g ∘ f)−1(x) = -x - 4.
b) g−1(x) = -x.
c) f −1(x) = x - 4.
d) (f −1 ∘ g−1)(x) = -x - 4.

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The axiom AABC and ADEF shown in the figure are congruent by SAS axiom.

The SAS (Side-Angle-Side) axiom, also known as the SAS postulate or SAS congruence criterion, states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In other words, if you have two triangles with the same angle between two sides of equal length, then those triangles are congruent.

This can be written mathematically as:

If triangle ABC is congruent to triangle DEF by SAS axiom, then:

AB = DE

AC = DF

angle BAC = angle EDF

angle ABC = angle DEF

angle ACB = angle DFE

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Answer:

V = x³ + 11x² + 12x

Step-by-step explanation:

calculate the volume (V) using the formula

V = lwh ( l is the length, w the width and h the height )

here l = 2x + 3 , w = x , h = x + 4 , then

V = (2x + 3)(x)(x + 4)

  = x(2x + 3)(x + 4) ← expand the factors using FOIL

  = x(2x² + 8x + 3x + 12)

  = x(2x² + 11x + 12) ← distribute terms in parenthesis by x

  = 2x³ + 11x² + 12x

The mass of the decoration is 200 kg and for each passenger car is 550 kg

From the question, we have the following parameters that can be used in our computation:

These can be represented as

(6, 3500) and (4, 2400)

The slope of the above points represent the mass of each passenger car

This is calculated as

Slope = Difference in mass/Difference in number of cars

So, we have

Slope = (3500 - 2400)/(6 - 4)

Evaluate

Slope = 550

When there are no passenger cars in the train, we have

(0, Mass of decoration)

Using the slope formula, we have

Slope = (Mass of decoration - 3500)/(0 - 6)

So, we have

Slope = (Mass of decoration - 3500)/(-6)

This gives

(Mass of decoration - 3500)/(-6) = 550

Cross multiply

Mass of decoration - 3500 = -3300

Add 3500 to both sides

Mass of decoration = 200

Hence, the mass of decoration is 200 kg

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Answer:

12^12

Step-by-step explanation:

Answer:

$539.94

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r/m)^mn

FV = Future value  

P = Present value = $400

R = interest rate = 2.5/ 365

N = number of years = 12 x 365

$400 x ( 1 + 0.025/365)^4380 = $539.94

a. To find the z score for a given confidence level, you can use the `qnorm()` function in R. The `qnorm()` function takes a probability as an argument and returns the corresponding z score. To find the z score for a 95% confidence level, you can use `qnorm(1-.025)`:

```R
z <- qnorm(1-.025)
```

This will give you the z score for a 95% confidence level, which is approximately 1.96.

b. To create a vector `x` with 50 numbers from a normal distribution with mean 30 and standard deviation 2, you can use the `rnorm()` function:

```R
x <- rnorm(50, mean = 30, sd = 2)
```

To calculate the confidence interval for this data, you can use the formula:

```R
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
```

This will give you the lower and upper bounds of the 95% confidence interval. You can check whether the interval covers the true mean of 30 by seeing if 30 is between the lower and upper bounds:

```R
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
 print("The interval covers the true mean.")
} else {
 print("The interval does not cover the true mean.")
}
```

c. To repeat the above experiment 200 times and calculate the percentage of intervals that cover the true mean, you can use a for loop:

```R
count <- 0
for (i in 1:200) {
 x <- rnorm(50, mean = 30, sd = 2)
 CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
 lower <- CI[1]
 upper <- CI[2]
 if (lower <= 30 && upper >= 30) {
   count <- count + 1
 }
}
percentage <- count / 200
```

This will give you the percentage of intervals that cover the true mean.

d. To write a function that takes a confidence level as an input and returns the percentage of intervals that cover the true mean, you can use the following code:

```R
calculate_percentage <- function(CL) {
 z <- qnorm(1-(1-CL)/2)
 count <- 0
 for (i in 1:200) {
   x <- rnorm(50, mean = 30, sd = 2)
   CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
   lower <- CI[1]
   upper <- CI[2]
   if (lower <= 30 && upper >= 30) {
     count <- count + 1
   }
 }
 percentage <- count / 200
 return(percentage)
}
```

You can then use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability:

```R
CL <- c(.8, .85, .9, .95, .99)
percentage <- sapply(CL, calculate_percentage)
matrix <- cbind(CL, percentage)
```

This will give you a matrix with the theoretical CL in the first column and the empirical coverage probability in the second column.

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Answer:

A = 12.5 and P = 16.2

Step-by-step explanation:

A = 5 x 5/ 2

A = 12.5

To find right hypotenuse

= √25 + 9 = √34

To find right hypotenuse

= √25 + 4 = √29

P = 5 + √34 + √29

P = 5 + 5.8 + 5.3

P = 16.1 (roughly 16.2)

Answer:

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Identity:

An identity is an equality which is true for all values of a variable in the equality.

(a + b)³ = a³+ b³+ 3ab(a + b)

In an identity the right hand side expression is called expanded form of the left hand side expression.

---------------------------------------------------------------------------------------------------

Solution:

(i) (2x + 1)³

Using identity

(a + b)³ = a³+ b³+ 3ab(a + b)

(2x + 1)³

= (2x)³ + 1³ + (3×2x×1)(2x + 1)

= 8x³+ 1 + 6x(2x + 1)

= 8x³ + 1 + 12x² + 6x

(ii) (2a – 3b)³

Using identity,

(a – b)³ = a³–b³ – 3ab(a – b)

(2a – 3b)³ = (2a)³– (3b)³ – (3×2a×3b)(2a – 3b)

=8a³–27b³–18ab(2a –3b)

= 8a³–27b³–36a²b + 54ab²

(iii) [3x/2  + 1]³

Using identity,

(a + b)³ = a³+ b³+ 3ab(a + b)

[3x/2 +1]³

=(3x/2)³+1³+ (3×(3x/2)×1)(3x/2+ 1)

=27x³/8+1+9/2x×(3x/2+1)

= 27x³/8 + 1 + 27/4 x² + 9/2x

= (27/8)x³ + (27/4) x² + 9/2 x + 1

(iv) [x–2/3 y]³

Using identity,

(a - b)³=a³-b³-3ab(a-b)

(X+ 2/3y)³

= (x)³–(2/3 y)³– (3×x×2/3 y)(x – 2/3 y)

= x³– 8y³/27–2xy(x – 2/3 y)

= x³– (8/27)y³–2x²y+ 4/3xy²

=========================================================

Hope this will help you....

Step-by-step explanation:

Answer:

1) first book can be at any of 4 places

2) Second book can be on any of leftover 3 places

3) Similarly third book on 2 and forth on 1 place

total : 4 * 3*2 * 1 = 24 ways .

other way we have formula 4!/1! =24 , here ordering is important

It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.

example if you need to choose 2 friends for a party out of 4 friends ,

answer will be 4!/2!*2! = 6 groups. (Ordering doesn’t matter hence division)

hope it hleps

PLEASE MARK BRAINLIEST

The probability  of less than 15 questions in a randomly chosen maths test is 2.28%, rounded to two decimal places.

According to the empirical rule,

68% of the data falls within one standard deviation of the mean,

95% falls within two standard deviations of the mean,

And 99.7% falls within three standard deviations of the mean.

Since we want to find the probability of a math exam having fewer than 15 questions,

Which is more than one standard deviation below the mean,

we have to find the proportion of the data that falls outside of one standard deviation below the mean.

To do this, we first need to standardize the value of 15 using the formula ⇒ z = (x - mu) / sigma,

where x is the value we want to standardize,

mu is the mean, and sigma is the standard deviation.

In this case,

⇒ z = (15 - 20) / 2.5

       = -2.

Now, we can look up the proportion of data that falls beyond two standard deviations below the mean in a standard normal distribution table.

This is equivalent to finding the area to the left of z = -2,

which is approximately 0.0228.

Therefore, the probability of a randomly selected math exam having fewer than 15 questions is  2.28%, rounded to two decimal places.

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The secx equivalent of the two expressions are

tan²x = sec²x - 1

tan x =sec x * sin x

Generally, Equalities that utilize trigonometry functions and are true no matter what the values of the variables that are specified in the equation are what are referred to as trigonometric identities. There are many different trigonometric identities that may be found using the length of a triangle's side as well as the angle of the triangle.

a) Using the identity:

tan²x + 1 = sec²x

We can rearrange it to get:

tan²x = sec²x - 1

Therefore, in terms of secx:

tan²x = sec²x - 1

b) Using the identity:

tan x = sin x / cos x

We can rewrite it in terms of sec x as follows:

tan x = sin x / cos x

= (1/cos x) * sin x

= sec x * sin x

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Answer:

B.

Step-by-step explanation:

4x + 4x - 4x = 4x

24x ÷ 2 = 12x

3x • 4x = \(12x^2\)

15x - 3 = 15x - 3

Answer:

B. 24x/2

Step-by-step explanation:

12x

A. 4x + 4x - 4x = 8x - 4x = 4x

B. 24x/2  = 24/2 x = 12x

C. (3x)(4x) = 12 x^2

D. 15x - 3​ = 15x -3  ( no like terms