8. What is the measure of an angle if it is 285 less
than four times its own complement?

Answer:

70

Step-by-step explanation:

the distributive property distributes the multiplier into both of the numbers inside

so you can look at it as (10 x 4) + (10 x 3)

10 x 4 is 40

10 x 3 is 30

when you add them together you get 70

Answer: 70

When using distributive property you will need to multiply the numbers inside the parentheses by the number outside the parentheses.

Step-by-step explanation:

10(4+3)

10x4=40

10x3=30

(40+30)=70

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

The safe moment capacity of the prestressed beam is approximately 2663.375 kNm.

To determine the safe moment capacity of the prestressed beam, we need to consider the compressive and tensile stresses in the concrete. Given the dimensions of the beam (300mm x 600mm), the effective depth can be calculated as the distance from the centroid to the extreme fiber.

Effective depth (d) = 600mm - (200mm + 300mm/2) = 550mm

Next, we can calculate the lever arm distance (a) using the effective depth:

Lever arm (a) = d/3 = 550mm/3 = 183.33mm

Now, let's calculate the compressive stress (σ_c) in the concrete:

σ_c = Prestressing Force/Area

    = 1110kN / (300mm x 600mm)

    = 6.17 MPa

Since the compressive stress (6.17 MPa) is below the allowable stress in compression (13.5 MPa), we can assume that the beam remains uncracked in compression.

To determine the safe moment capacity (M), we can use the formula:

M = (σ_c * A * d) - (σ_t * A_t * a)

where:

A = Cross-sectional area of the beam (300mm x 600mm)

σ_t = Allowable stress in tension (1.4 MPa)

A_t = Tensile force due to prestressing (Initial force - Final force)

    = (1110kN - 880kN)

    = 230kN

Substituting the values into the formula:

M = (6.17 MPa * 300mm x 600mm * 550mm) - (1.4 MPa * 230kN * 183.33mm)

 = 6.17 * 0.3 * 0.6 * 0.55 * 550 - 1.4 * 230 * 0.18333

 = 2663.375 kNm

Therefore, the safe moment capacity of the prestressed beam is approximately 2663.375 kNm.

To determine the superimposed live load that the beam can carry, we need to consider the appropriate load factors and the span length. The specific load factors depend on the design code and requirements. Once the load factors are determined, the superimposed live load can be calculated based on the safe moment capacity and the span length.

It is important to note that this is a simplified calculation, and a more detailed analysis should be conducted by a qualified structural engineer to ensure the structural integrity and safety of the condominium.

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To compute the correlation between two ordinal-level variables, you should use Spearman's rank correlation coefficient.

Spearman's rank correlation coefficient is a non-parametric statistical measure that is used to assess the association between two ordinal-level (ordinal or ranked) variables.

This type of correlation calculates the correlation between the ranks of the data rather than the actual values, making it suitable for ordinal data where the difference between the levels is not well defined.

The coefficient ranges from -1 to 1, where a value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation.

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The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.

To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.

To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.

Converting the fractions to have a denominator of 12, we get:

James: 2/3 = 8/12

Gilbert: 11/12 (already in terms of 12)

Matthew: 5/6 = 10/12

Simon: 7/12 (already in terms of 12)

Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).

To find the difference between these two times, we subtract the slowest time from the fastest time:

8/12 - 11/12 = -3/12 = -1/4

Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.

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Answer:

the first option

Step-by-step explanation:

f(c)= 1/3p + 5/3

Answer:

(0,2)

Step-by-step explanation:

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Statistical procedures that summarize and describe a series of observations are called descriptive statistics.

Descriptive statistics involve various techniques and measures that aim to summarize and describe the key features of a dataset. These procedures include measures of central tendency, such as the mean, median, and mode, which provide information about the typical or average value of the data. Measures of dispersion, such as the range, variance, and standard deviation, quantify the spread or variability of the data points.
In addition to these measures, descriptive statistics also involve graphical representations, such as histograms, box plots, and scatter plots, which provide visual summaries of the data distribution and relationships between variables. These graphical tools help in identifying patterns, outliers, and the overall shape of the data.
Descriptive statistics play a crucial role in providing a concise summary of the data, enabling researchers and analysts to gain insights, make comparisons, and draw conclusions. They form the foundation for further statistical analysis and inferential techniques, which involve making inferences about a population based on a sample.

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Answer:

x = ± √ 22 − 3

Step-by-step explanation:

Answer:

the zero of a function is what value you can plug in and get 0 as the answer.

having a multiplicity of 3 means that the zero is there 3 times so if your zero is 2 with multiplicity 3 then (x-2)^3 is what it looks like

Step-by-step explanation:

perimeter is the length of all sides added up so we add the expressions

(2x + 1) + (3x - 5) + (4x) = 9x-4

9x - 4 = 23

now work backwards

add 4 to 23 to get rid of -4

9x = 27

now divide by 9 to get x

x = 3

I'm doing this right now too :)

You start by writing the original numbers given into a proportion, which would be

miles          

_____      

hours

Then you have to convert the top unit, miles, into feet. You have to use the rate 1mile:5280 feet. You write that as a proportion too.

miles        1

_____ =  ___

hours      5280

Next, you have to add a conversion rate for changing the hours into seconds. You'd use the rate 1 hour: 60 seconds.

miles        1          60

_____ =  ___  =  ____

hour        5280      1

Then you'd cross multiply to solve.

Hope I helped! Please mark me brainliest

Each member of the club needs to pay £ 4.895 to cover the cost of hiring the buses.

A youth club's 143 members and eight leaders ride a bus to a bowling alley.

The buses for hire by the beezer bus company hold 32 passengers each.

The cost of each bus to hire is £140.

There are eight leaders and 143 members.

Therefore, there are a total of 143 + 8 = 151 passengers.

So, the number of buses required will be:

= 151 / 32 =  4.7 ≈ 5 buses

Therefore, the cost of hiring 5 buses will be:

= 5 × £140 = £ 700

As the eight leaders will not ay.

Therefore, the amount each member needs to pay is:

= £ 700 / 143

= £ 4.895

Each member of the club needs to pay £ 4.895 to cover the cost of the buses.

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Answer:

Slope = 2

Step-by-step explanation:

5-3

over

2-1 is

2 over 1 which is slope of 2

Answer:

A-  75,000+4,800n=80,000+3,900n

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I took the quiz.

The dot plot of the data values is added as an attachment

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

85,88,75,100,90,90,88,72,72,79,88,85

Next, we create a frequency table

So, we have

Values   Frequency

72             2

75             1

79             1

85            2

88            3

90           2

100          1

Total      12

Using the frequency table above, we create the dot plot

See attachment for the dot plot

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First, let's calculate the Profit functions which is P(x)=R(x)-C(x)

Let's continue simplifying the function

The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number

Domain=(-∞,∞)

Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.

And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.

Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):

The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.

The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.

According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function

As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.

First blank: Dividing the numerator and denominator of 16/24 by 8 gives the unknown to be 2.

Second blank: Dividing the numerator and denominator of 16/24 by 4 gives the unknown to be 4.

Third blank: Dividing the numerator and denominator of 16/24 by 2 gives the unknown to be 12.

Answer:

Must save 8 weeks or more to purchase the bike.

Step-by-step explanation:15*w >= 120 where W is the number of weeks.

w >= 120/15 = 8

You need to save $15 every week for the next 8 weeks in order to purchase the bike.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is that you save $15 per week to purchase a bike that costs $120.

Assume that you need [w] weeks to save $120 for the bike.

Amount earned per week [A] = $15

Amount earned in [w] weeks [W] = $15w

Money needed [R] = $120

The inequality can be written as -

[W] ≥ [R]

We can write it as -

15w ≥ 120

Solving the inequality, we get -

15w/15 ≥ 120/15

w ≥ 8

Therefore, you need to save $15 every week for the next 8 weeks in order to purchase the bike.

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Answer:

x=1

Step-by-step explanation:

3(x)+1    substitute 1 in for x

3(1)+1=4

10(x)-6    substitute 1 in for x

10(1)-6=4

4=4

(sorry if that doesn't make any sense)

Answer: The answer is ⠀ ⠀ ⠀, hope this helps! :))

Step-by-step explanation:

For the statement 8 to the power of 24, we get the expression as 2 ⁷².

We are given a statement:

8 to the power of 24

We need to form an expression for the same.

We can write the expression as:

8 ²⁴

This can also be written as:

8 = 2 × 2 × 2

So, we get that:

( 2 ³) ²⁴

Since we know the property of exponents, we will use it here.

We get the result as :

= 2 ⁷²

Therefore, for the statement 8 to the power of 24, we get the expression as 2 ⁷².

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The amount that Roxana has left is $7560.

Total Amount = $12000

She spent 12% on meat and 25% on vegetables.

Therefore, the amount left will be:

= (100 - 12% - 25%) × 12000

= 63% × 12000

= 63/100 × 12000

= 0.63 × 12000

= $7560

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\(\\ \sf\longmapsto Time\:period=\dfrac{Time\:taken}{No\:of\; oscillations}\)

\(\\ \sf\longmapsto Time\:taken=No\:of\: oscillations (Time\: period)\)

\(\\ \sf\longmapsto Time\:taken=20(0.5)\)

\(\\ \sf\longmapsto Time\:taken=10s\)

\(\begin{gathered} {\underline{\boxed{ \rm {\red{Time \: period \: = \: \frac{Time \: \: taken}{Number \: of \: oscillations} }}}}}\end{gathered}\)

\(\begin{gathered} {\underline{\boxed{ \rm {\purple{Time \: taken \: = \: Number \: of \: oscillations \: (Time \: period)}}}}}\end{gathered}\)

\( \large \rightarrow \: {\rm {{{\color{orange}{Time \: taken \: = \: 20 (0.5)}}}}} \)

\(\large \rightarrow \: {\rm {{{\color{orange}{Time \: taken \: = \: 10s}}}}} \)

b + d ≥ 9 this inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities, indicating whether they are equal or not, and in what direction they differ. An inequality is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).

The inequality that represents the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Ryan can work in a given week is:

b + d ≥ 9

This inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.

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Answer:

Negative

Step-by-step explanation:

Hello There!

The points on the scatter plot show some sort of correlation as they are grouped closely enough to create a trend line ( a line drawn where most points are at. )

If you were to draw a line through the points, the line would have a negative slope as  most of the points go down from left to right indicating that the correlation is negative

The probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.02712.

Probability of natural occurrences = 0.82Probability of outside factors = 0.18To find the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors, we have to consider two possibilities:

The first two patients are due to natural occurrences, or the first two patients are due to outside factors.If the first two patients are due to natural occurrences, the probability of the third patient being the first due to outside factors is:0.82 x 0.82 x 0.18 = 0.12272

If the first two patients are due to outside factors, the probability of the third patient being the first due to outside factors is:0.18 x 0.82 x 0.82 = 0.12272

Therefore, the total probability of the third patient being the first due to outside factors is the sum of these two probabilities:0.12272 + 0.12272 = 0.24544But, we have counted the case where all three patients have outside factors twice, so we need to subtract that probability once:0.24544 - 0.01836 = 0.22708

Therefore, the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.22708 or approximately 0.02712.

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