8 (a) The formula for the area of a trapezium is A = = h(c + d)
(* Find an expression for c in terms of A, hand d.

We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

The value of x and z are [tex]4^\circ, 96^\circ[/tex].

Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.

We know the measure of the triangle are equal in Pair.

So we have got the equation as -

[tex]10x+44=13x+32[/tex]

⇒[tex]13x-10x=44-32[/tex]

⇒3x=12

⇒x=4.

We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].

Now angles around a point add to [tex]360^\circ[/tex].

So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.

Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]

⇒[tex]2z=192^\circ[/tex]

⇒ [tex]z=96^\circ[/tex],

Hence we have got the value of x and z i.e. 4 and 96.

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Answer:

5/13

Step-by-step explanation:

[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]

The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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Answer:4

Step-by-step explanation:

We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

What do you mean by  Annexation?

International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.

According to the question,

We have the given data:

A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.

The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.

This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.

Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

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The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.

This is calculated by probability of independent events.

We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.

So, P(A and B occurring together )= P(A)P(B) if A and B are independent.

And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)

This is because, being the probability of independent events , they are multiplied.

so, the total probability is 6.5.4.3.2.1/6^6 = 1.54

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The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

What is a rectangular Prism ?

A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.

A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.

It is given that length of the rectangular prism has length of 2 cm more than  the width and 3 cm less than the depth

Let the depth be x cm

and width be y cm

Then the length will be y+2 cm and x-3 cm

y+2 = x- 3

x = y+5

A rectangular prism is a cuboid with six faces

Volume of a rectangular prism can be written as

length * width * depth

= (y+2) *x*y

= (y+2)* (y+5)*y

= (y²+2y)(y+5)

= y³ +5y²+2y²+10y

= y³ +7y² +10y cm³

Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

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Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Original selling price = $171.59

Price during sales = $148.37

Then, the percentage markdown will be,

% markdown = (171.59 - 148.37)/171.59 × 100

= 23.22/171.59 × 100

% markdown = 13.53%

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Answer:

Here is answer

Step-by-step explanation:

To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.

Let's start by factoring each of the given polynomials:

ax² - (a² + ab)x+ a²b = a(x - b)x

bx² - (b² + bc)x+ b²c = b(x - c)x

cx² - (c² + ac)x + c²a = c(x - a)x

The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.

Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.

The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.

Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.

From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.

It should be noted that this will be illustrated through tye lowest common multiple.

Multiples of 6 = 6, 12, 18, 24

Multiples of 8 = 8, 16, 24

Therefore, they'll meet at the 24th house.

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Answer:

Step-by-step explanation:

g(x) = (-x)1/2

Answer: B

Step-by-step explanation:

A - Nope.

B - Possibility.

C. Nope. (2.23606797)

D. Nope.

When facing questions like this, it can be easier to use the process of elimination.

The answer of the function  f(x)=7(3-x)+5 is -7x + 26.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

Given the function;

f(x)=7(3-x)+5

To simplify the function:

First, solve parenthesis,

f(x)=21 - 7x +5

Taking, constant with constant term,

f(x) = -7x + 26

Therefore, the answer is  -7x + 26.

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The equation that gives the relationship between cost (c) and area (a) is c = 2a

A variation is a relation between a set of values of one variable and a set of values of other variables

Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet

We can write:

c α a

c = ka

where k is the constant of proportionality

since c = $3,000 and a = 1500

c = ka

3000 = 1500k

k = 3000/1500

k = 2

Thus, the equation of the relationship is c = 2a

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The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .

total length of four-bit strings = 16

Let S represent the collection of all four-bit bit strings.

Let A represent the occurrence of a randomly generated string beginning with 1.

Let B represent the scenario where a string created at random contains two consecutive 0s.

S has 8 strings that begin with the letter "1."

P( A ) = 8 / 16 = 1 / 2

Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100

P(A ∩ B)  = 3 / 16

Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,

3/16 / 1/2

= 3 / 8

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The probability of experiencing only nausea is 0.06.

Using Venn Probabilities, it is found that there is a 0.45 = 45% probability of experiencing neither of the side effects.

What is a Venn probability?

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

P(N∪D) = P(N) + P(D) - P(N∩D)

In this problem, the probabilities given are:

P(N)= 0.2 , P(D)= 0.45 , P(N∩D) = 0.14

The "at least one" probability is:

P(N∪D) = 0.20 + 0.45 - 0.14 = 0.51

Hence, the "neither" probability is:

1 - P(N∩D) = 1 - 0.51 = 0.49

The probability of experiencing only nausea = P(nausea) - P(both side effects)

                                                                           =0.20 - 0.14

                                                                            =0.06

0.49 = 49% probability of experiencing neither of the side effects.

The probability of experiencing only nausea is 0.06.

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Answer: 19 feet

Step-by-step explanation:

The area, 266, divided by the width, 14, equals to 19 feet.

Answer:

-48y+24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠)

=-6(8y+-4)

=-48y+24

Answer:

-48y + 24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠) =

= −6⁢(⁠8y - 4)

= -48y + 24

Answer: $23.40

Step-by-step explanation:

To find out how much Olivia spent on the bracelet, we need to subtract the cost of the sunglasses from the total amount spent. In this case, that would be $39.75 - $16.35 = $<<39.75-16.35=23.40>>23.40. Therefore, Olivia spent $23.40 on the bracelet.

Answer:0.41

Step-by-step explanation:

Answer:

1. 4

2. rise = 2; run = 1; slope = 2

3. y = 2x + 4

Step-by-step explanation:

1. Look at the graph. On the y-axis, the line passes through 4. The line crosses the y-axis at 4, so 4 is the y-intercept, and b = 4 in the equation y = mx + b.

2. Choose any two points on the line. I choose the y-intercept, (0, 4) and point (-1, 2).

slope = rise/run

We need to go from point (-1, 2) to point (0, 4) by only moving vertically and horizontally. Start at (-1, 2). Go up 2 units. That is a ris of 2. Now go right 1 unit to arrive at point (0, 4). that is a run of 1.

slope = rise/run = 2

3. We have b = 4, and m = 2.

y = mx + b

y = 2x + 4

Answer:

SSS, SAS, ASA, AAS

Step-by-step explanation:

s = sides

a = angle

Answer:

50x + 9500 ≤ 27500

x ≤ 360

Step-by-step explanation:

50x + 9500 ≤ 27500  Subtract 9500 from both sides

50x + 9500 - 9500 ≤ 27500 - 9500

50x ≤ 18000  Divide both sides by 50

[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]

x ≤ 360

For a system with equations y = f(x) and y = g(x), the graph of the system will be just a coordinate plane with the two functions graphed on it.

What is functions graphed?

What Does Graphing Functions Mean? Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function. As an illustration, the graph below depicts the linear function f(x) = -x+ 2.

From this, we can see that the correct option is the first one:

"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."

Also a graph of the system can be seen at the end of this answer.

Here our system is:

y = 3

x + y = 4

The first one is a horizontal line at y = 3.

The second can be rewritten as:

y =  -x + 4

So this is a line with a negative slope, that passes through the points (0, 4) (when you evaluate in x = 0, you get y = 4) and (4, 0) (when you evaluate in x = 4, you get y = 0)

Then the correct option is the first one:

"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."

The graph can be seen below

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Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.

y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.

where m is the slope and m = y/x

Take notice that tanФ = y/x.

This tanФ is often referred to as the line's slope.

The given equation is of the form [tex]ax+by=c[/tex]

On comparing we can say that a is -8 and b is -6

So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]

The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]

Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]

Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

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