Simplify the following expression.

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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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]

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 length of side CD is equal to 11 units.

Given coordinates of rectangle are A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5)

We are require to find the length of side CD.

Rectangle is a two dimensional figure whose two opposite sides are equal to each other. Distance between two coordinates is the equal to length of a side.

We know that the distance means how far two points are located.

Coordinates of  A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5).

Distance=[tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex] where ([tex]x_{1} ,y_{2} )(x_{2} ,y_{2} )[/tex] are the coordinates of two ends of a line.

CD=[tex]\sqrt{(-5-6)^{2} +(-4+4)^{2} }[/tex]

=[tex]\sqrt{11^{2}+0^{2} }[/tex]

=[tex]\sqrt{121}[/tex]

=11 units.

Hence the length of side CD is 11 units.

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Question is wrong as it should be :

Coordinates of rectangle A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5) and find the length of CD.

Answer:

Answer is in the 2nd attachment

Step-by-step explanation:

the first attachment is the work done.

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:

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:

ab=48

Step-by-step explanation:

96/2=48

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:

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.

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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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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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.

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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In statistics, the standard deviation deviation may be a measure of the quantity of variation or dispersion of a group of values. The margin of error may be a statistic expressing the number of sampling error within the results of a survey. The correlation could be a statistical measure of the strength of the connection between the relative movements of two variables.

Given nothing and that we need to explain standard deviation. margin of error, correlation coefficient .

Standard deviation

In statistics, the standard deviation may be a measure of the number of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be near the mean of the set, while a high variance indicates that the values are detached over a wider range.

Formula: [tex]\sqrt{(x-x bar)^{2}/N }[/tex]

where x bar is mean and N is size of population.

Margin of error

The margin of error may be a statistic expressing the quantity of sampling error within the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the results of a survey of the complete population.

Formula for M=z*s/[tex]\sqrt{n}[/tex]

here z is z value of Z score , s is variance , n is that the sample size.

Correlation coefficient

In statistics, the Pearson parametric statistic ― also called Pearson's r, the Pearson product-moment parametric statistic, the bivariate correlation, or colloquially simply because the coefficient of correlation ― could be a measure of linear correlation between two sets of information.

Formula=∑[tex](x_{i} -x bar)(y_{i} -y bar)/\sqrt{}[/tex]∑[tex](x_{i} -x bar)^{2}[/tex]∑[tex](y_{i}-ybar) ^{2}[/tex]

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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.

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:

Step-by-step explanation:

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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Answer:

4 ft

Step-by-step explanation:

Area = 30 square ft

base = 7.5 ft

          [tex]\sf \boxed{height \ of \ rectangle = \dfrac{Area}{base}}[/tex]

                                             [tex]\sf =\dfrac{30}{7.5}\\\\=\dfrac{30*10}{7.5*10}\\\\=\dfrac{300}{75}\\\\= 4 ft[/tex]

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 probability of selecting a heart or red Queen from the deck of cards is 1/2.

Total cards = 52

total red cards = 26

P(not selecting a red card)

= (52-26)/52

= 26/52

= 1/2

Total heart = 13

Total 2 = 4 (one for each club, diamond, heart, spade)

Total 2 of heart = 1

P(not selecting a 2 or heart) = (52 - 4 - 13 + 1)/52

= 36/52

= 9/13

Opportunity is the department of arithmetic concerning numerical descriptions of how probably an event is to arise, or how probably it's far that a proposition is genuine. The possibility of an occasion is a range of between zero and 1, where, more or less speaking, 0 shows the impossibility of the occasion and 1 indicates certainty.

The possibility is clearly how in all likelihood thing is to show up. each time we are uncertain about the final results of an event, we can talk about the probabilities of sure effects and how likely they're. The evaluation of activities governed via chance is known as statistics.

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Answer:

If compounding = rs 11547.36

If not compounding = rs 11484

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:

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:

$11.00

Step-by-step explanation:

1. To answer this question, we have to multiply 74.40 by 15%.

2. 15% = 0.15

3. 74.40 x 15 = 11.16