Fatima evaluated the expression StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction, when m = negative 2 and n = 4. Her work is shown below.

StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction = 4 m Superscript negative 2 Baseline n Superscript negative 3 Baseline = 4 (negative 2) Superscript negative 2 Baseline (4) Superscript negative 3 Baseline = StartFraction 1 Over 64 EndFraction times StartFraction 1 Over 64 EndFraction = StartFraction 1 Over 4,096 EndFraction

What was Fatima’s error?
She subtracted the exponents incorrectly when simplifying the expression.
She substituted the wrong values for the variables.
She applied the exponent Negative 2 to 4 (negative 2) instead of applying the exponent to just Negative 2.
She found an incorrect value for (Negative 8) Superscript negative 2 since the value should be negative.

The sample space is a combination of these two dice as we have shown in the attachment

This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.

The question has two dice. These dice are made up of numbers from 1 to 6  each.

Die A = {1,2,3,4,5,6}

Die b = {1,2,3,4,5,6}

The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.

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The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

In order to find the measure of LM, we will take the ratio of the sides of the similar triangles.

Using the equation as shown

DF/EF = LK/LM

DF/LK = EF/LM

Substitute the measure of the sides

9/13.5 = 14/LM

Hence the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

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If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

In accordance with the statement, Susan's calculator performs the following operation by pressing the "cubing" key:

x → x³

If we need to display a number that is greater than 10⁹, then we need to press the "cubing" key as many as needed. By algebra we have the following property for a power:

[tex](x^{m})^{n} = x^{m\cdot n}[/tex]     (1)

Since we have a "cubing" key and we are supposed to make consecutive operation, we derive the following operation:

x → [tex]x^{3^{i}}[/tex], where i is the number of consecutive "cubing" operations.

If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

The statement presents typing mistakes, correct form is shown below:

Susan's calculator has a key that replaces the number displayed with its cube. If a³, is displayed, how many time must Susan press the "cubing" key to display a number that is greater than 10⁹.

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Answer:

$2.40

Step-by-step explanation:

$9.60/4 = $2.40

Answer:

Step-by-step explanation:

[tex]\frac{9.60}{4} =$ 2.40[/tex]

The length of AL in the triangle is 12cm.

From the information given, angle C = 90° and BAC is given as 2ABC.

In this case, the length of angle BC is given as 24cm. Therefore, the length of AL will be:

= 24/2

= 12..

Therefore, AL = 12cm

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For the function f(x) = -3|x - 2| - 1, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = -3|x - 2| - 1

-3|x - 2| = 1

|x - 2| = -1/3

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = -3|0 - 2| - 1 = -6 - 1 = -7.

The y-intercept is of y = -7.

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Answer:

Answer is in the 2nd attachment

Step-by-step explanation:

the first attachment is the work done.

Answer:

a ≈ 4.9

Step-by-step explanation:

using the Cosine Rule in Δ ABC

a² = b² + c² - (2bc cosA )

   = 16² + 18² - (2 × 16 × 18 × cos15° )

   = 256 + 324 - (576cos15° )

   = 580 - 576cos15

   = 23.6267 ( take square root of both sides )

a = [tex]\sqrt{23.6267}[/tex]

   ≈ 4.9 ( to the nearest tenth )

Answer:

The inverse is  -1/7(x+4)

Step-by-step explanation:

We have the function

y = -7x-4

To find the inverse, exchange x and y

x = -7y -4

Solve for y

Add 4 to each side

x+4 = -7y -4+4

x+4 = -7y

Divide each side by -7

-1/7(x+4) = -7y/-7

-1/7(x+4) = y

The inverse is  -1/7(x+4)

The triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.

The area of a plane figure is the space occupied within its boundary.

The area of a triangle is given as,

a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.

In the question, we have been given a triangle with a base of 14, sides 12 and 6, and a height of 5.

We are asked to determine the area of this triangle.

To determine the area of the triangle, we will use the formula:

a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.

Now, we are given that the base is 14 and the height is 5, thus substituting b = 14, and h = 5, in the above formula, we get:

a = (1/2)(14)(5) sq. units.

or, a = 35 sq. units.

Comparing this with the given options, we can choose the third option.

Thus, the triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.

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The simplification that represents ∛7=[tex]7^{1/3}[/tex] is [tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

The simplification that accurately explains the statement ∛7 = [tex]7^{1/3}[/tex] is as follows;

Therefore, the simplification is as follows

[tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

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The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.

The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.

(20 – 10) < S <(20+ 10) ; 10< S < 30

Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

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Answer:

The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.

Step-by-step explanation:

A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(a, b),(c, d),(e, d)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {a, c, e}.

The set of the second components of each ordered the range.

From the relation, the range is {b, d, d}.

The given relation is a function. But it is not a one-to-one function.

Answer:

infinite if you say that you have to find 2 or 3 solution so we can find by putting x value like 0 ,2,1 or also you can put y value

Answer:

Given a map of San Francisco, Las Vegas and Los Angeles on which triangles are drawn.

We find that the distance from Los Angeles to San Francisco is  351 miles.

Step-by-step explanation:

Step 1 of 2

In similar triangles, the corresponding sides are proportional.

We know that the distance between Los Angeles and Las Vegas is 270 miles and on the map it is 1 inches.

We need to form a proportion to find the distance between Los Angeles and San Francisco if on the map it is 1.3 inches.

Let the distance between Los Angeles and San Francisco be x .

[tex]\begin{aligned}&\frac{\text { miles }}{\text { inches }}=\frac{\text { miles }}{\text { inches }} \\&\frac{x \text { Miles }}{1.3 \text { inches }}=\frac{270 \text { Miles }}{\text { linch }} \\&\text { Multiplying both sides by } 1.3 \text { we get, } \\&x=270 \times 1.3 \text { Miles } \\&x=351 \text { Miles }\end{aligned}[/tex]

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

[tex]\frac{x \text { Miles }}{\text { 1.3inches }}=\frac{270 \text { Miles }}{1 \text { inch }}$$[/tex]

We found x=351 Miles hence,

[tex]$$\begin{aligned}&\frac{351}{1.3}=\frac{270}{1} \\&270=270 \\&\text { Here, } L H S=\text { RHS }\end{aligned}$$[/tex]

Hence, our answer is correct.

The larger angle is 55 deg at the larger angle.

We have to know which angles are called Complementary Angles...

if we add two angles and the total will be equal to 90 deg

let's say one angle is x and  another angle is  y

as they are complementary angles from the definition we can write the equation x + y =  90

one angle is 20 deg more  than another one  so from the above condition  we write x = 20 + y

Substitute the value of x  in the first eaquation we get, 20 + y + y =  90

Then,  20 + 2y =  90

subtracting 20 from both sides,

 2y  =  90-20 = 70  

 dividing both sides by 2,

2y/ 2 = 70 / 2

 y  =  35

 So we got one angle is 35 deg

another angle is  35 + 20 = 55 deg.

Our answer is 55 deg the larger angle.

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The interval on the number line is (-∞, 2) U [3, ∞)

From the number line, we have the following inequalities

x < 2 and x ≥ 3

In inequalities, < and > are represented by brackets i.e. ( and )

While ≤ and ≥ are represented by square brackets i.e. [ and ]

So, we have:

x < 2 and x ≥ 3 = 2) and [3

The intervals must be closed and opened with infinity symbols.

So, we have:

x < 2 and x ≥ 3 = (-∞, 2) and [3, ∞)

Replace and with U

x < 2 and x ≥ 3 = (-∞, 2) U [3, ∞)

Hence, the interval on the number line is (-∞, 2) U [3, ∞)

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Answer:

H)

Step-by-step explanation:

First, Length XY is 20 centimeters. Since YZ = 3/5 XY, [tex]\frac{3}5\times20=12[/tex]

YZ = 12 + 20 = 32 cm, hence H)

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Answer:

ab=48

Step-by-step explanation:

96/2=48

Answer:

x/3

Step-by-step explanation:

x+1 will always be an odd integer, since x is an even integer because the pattern of integers is odd, even, odd, even, odd... and so on, in intervals of 1.

x/2 will sometimes be an odd integer. Because x/2 will always be an integer, since x is an even integer, meaning it is divisible by 2. So by definition any integer, even or odd, multiplied by 2 will give you an even integer. For example 3*2 = 6, 5*2 =10, 7*2=14. These are all even integers, and when you divide by 2, you'll get an odd integer

So let's look at x/3. 1*3 = 3, 3*3 = 9, 5*3 = 15, 7*3 = 21. See how it always results in another odd integer? Well this is because you essentially have (odd + odd + odd), the odd+odd will result in an even, which is explained in the previous question, but then adding another odd number to an even number, will result in an odd. This means that any time you multiply an odd integer by 3, you will always get an odd result, meaning no even integer can be divided by 3 to get an odd integer.

Answer:

Y

Step-by-step explanation:

Given equation: f(x) = ∛(x - 2)

Find the y-intercept, [set x = 0]

f(x) = ∛(0 - 2)

f(x) = ∛-2 = -1.26

y-intercept: (0, -1.26)

Find the x-intercept, [set y = 0]

0 = ∛(x - 2)

x - 2 = 0

x = 2

x-intercept: (2, 0)

Graph Y shows this characteristics by passing points (2, 0) and (0, -1.26).

Graph Y shown:

The graph that shows y=3⌈x⌉ + 1 from the given options is the Third graph as shown attached.

The third graph shows the function and this can be tested as follows:

When x = 2, y = 7:

y = 3x + 1

= 3 x 3 + 1

= 7

When x = 3, y = 10:

y = 3 x 3 +1

= 10

When x = 1, y = 4

y = 3 x 1 + 1

= 4

This shows that the line on the third graph is well represented by the function, y=3⌈x⌉+1.

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No, we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.

Given mean=1900, standard deviation=65, sample size=150, sample mean=1902, level of significance=0.01.

The hypothesis are:

[tex]H_{0}:\\[/tex]μ=1900

[tex]H_{1}:[/tex]μ>1900

We have to use z test as the sample size is large and we know the population standard deviation.

z=(x-μ)/σ/[tex]\sqrt{n}[/tex]

z=(1902-1900)/65/[tex]\sqrt{150}[/tex]

z=0.38

finding the p value:

p value=P(Z>z)

=P(Z>0.38)

=1-P(Z<0.38)

from the z table we get;

P(Z<0.38)=0.6480

Therefore p value=1-0.6480

=0.3520

If the p value is less than 0.01 then we reject the [tex]H_{0}[/tex] otherwise we will reject the null hypothesis.

In this problem we also reject the null hypothesis.

Hence  we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.

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Question is incomplete. It should includes:

 mean=1900,

standard deviation=65,

sample size=150,

sample mean=1902,

level of significance=0.01.

The area of the composite shape is 136 square cm

The area of the composite function is expressed as;

Area = area of triangle + area of rectangle

Area of the composite shape = (1/2* 4 * 5) + (7*18)

Area of the composite shape = 10 + 126

Area of the composite shape = 136 square cm

Hence the area of the composite shape is 136 square cm

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Answer:

(-5,7) (5,-7)

Step-by-step explanation:

When you are told to lable, show or name the points that lie on a horizontal line, it basically means that; when a line is drawn, it passes through the selected points without changing the direction when joined together (horizontally).

From the above problem, (-5,7) and (5,-7) lie in the same horizontal line.

For (7,-5) and (-7,5) lie in the same vertical line.

Thereforeour, the answer is (-5,7) (5,-7).

The secondary use of data from the 2000 census classification system to identify disparities in mental healthcare.

The 2000 Census classification system helps our communities choose where to build everything from homes to hospitals to schools and shops. It also reveals who we are as a country and where we are headed. It aids in the government's decision-making about the allocation of cash and assistance to cities and states.

The government-wide 2000 Standard Occupation Classification (SOC) system served as the foundation for the 2000 Census classification system, while the 1980 SOC was used for the 1990 Census.

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Answer:

If compounding = rs 11547.36

If not compounding = rs 11484

[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]

[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]

[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]

[tex]10y {}^{2} + 90y + 200 = 0[/tex]

[tex]y {}^{2} + 9y + 20 = 0[/tex]

[tex](y + 4)(y + 5) = 0[/tex]

[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]

[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]

[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]