(b) The perimeter of a rectangular pool is 302 m. If the width of the pool is 54 m, what is its length?
Length of the pool:

The number of days to rent a car at either place and pay thesame amount is 11 days

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

Let the number of days to repay after a down payment be x and the y represent the total payment.

Therefore 61+24x= y equation 1

105+ 20x = y equation 2

subtract equation 1 from 2

105-61+20x-24x= 0

44-4x= 0

4x = 44

divide both sides by 4

x= 44/4

x= 11 days

therefore the number of days to rent a car at either places and pay thesame amount is 11 days

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Answer: To find the x-intercept of a line, we set y equal to 0 and solve for x. To find the y-intercept of a line, we set x equal to 0 and solve for y.

For the line 5x + 17y = -25, we set y equal to 0 to find the x-intercept:

0 + 17y = -25

17y = -25

y = -25/17

Since we set y equal to 0, the x-intercept is (0, 0).

For the line 6x - 7y = -21, we set x equal to 0 to find the y-intercept:

6x - 7y = -21

-7y = -21

y = 21/7

Since we set x equal to 0, the y-intercept is (0, 21/7).

Therefore, the x-intercept of the line 5x + 17y = -25 is (0, 0) and the y-intercept of the line 6x - 7y = -21 is (0, 21/7).

Simple random sampling is a sort of probability sampling in which a selection of participants is randomly chosen from a population by the researcher.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

Hence, In probability sampling, a sample is chosen from a population based on the randomization principle, also known as chance or random selection.

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Answer:

Step-by-step explanation:

5

Answer:

C

Step-by-step explanation:

A line perpendicular to the y-axis is a horizontal line

  Horizontal lines have  slope = 0

       answer C    y = 3   slope = 0

The statistician model makes sense to predict the calories in food items.

A mathematical model called a statistical model contains a collection of statistical presumptions about how sample data are produced (and similar data from a larger population). A statistical model simulates the process of creating data, frequently in a highly idealised form.

Yes it makes sense to use the statistician model to predict calories calories in food items because the test of the overall model I.e F test is significant at any level of significance because the p value (2.2 e^-16)  is approximately zero which indicates that the model Is significant.

And also the individual test of each variable are all significant at any significance level (alpha) with p values ( 2e^-16, 2e^-16, 1.36e^-6).

Thirdly we can say of the strength of the relationship between calories and the independent variable through the R value = √R square = √0.929 = 0.9638 which indicates a strong relationship between them.

Therefore, the statistician model makes sense to predict the calories in food items.

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The equation of line in slope-intercept form is,

a.) y = -6x - 47

b.) y = x/6 - 8/3

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

We know, slope-intercept form is

y = mx + b

The given equation is in point slope form,

a.) y + 5 = -6 (x + 7)

b.)  y + 2 = 1/6 (x-4)

Now, let's write each equation in slope-intercept form,

a.) y + 5 = -6 (x + 7)

y + 5 = -6x - 42

y = -6x - 42 - 5

y = -6x - 47            [which is slope-intercept form]

b.) y + 2 = 1/6 (x-4)

y + 2 = 1/6 * x - 1/6 * 4

y + 2 = x/6 - 2/3

y = x/6 - 2/3 - 2

y = x/6 - [2/3 + 2]

y = x/6 - [(2 + 6) / 3 ]

y = x/6 - 8/3            [which is slope-intercept form]

Hence, the equation of line in slope-intercept form is y = -6x - 47 and y = x/6 - 8/3  

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Answer:

y =5x

Step-by-step explanation:

y = 5x

Because the slope is 5 and the y-intercept is 0.

Answer:

The combined value is $704

If you want the average pay as well it is about $235

Step-by-step explanation:

The problem asks for the combined value of the three paychecks. So all you have to do is add them to get 704.

I found the average value by adding them to 704 then dividing it by 3. The 3 came from the amount of values we have which is 3 paychecks. So we divide the total cost by 3 to get 235.

On solving the provided question, we got by the help of Slope formula - [tex]= 5x - y + 5 = 0[/tex]

A line's slope can be calculated as the ratio of how much y rises when x rises by a specific amount. A line's slope, or how much y increases as x increases, is indicated by the word "slope." Along the straight line, the slope is constant (equal) everywhere.

From the figure we got that,

X1 = 0, Y1 = 5

X2 = -1, Y2 = 0

(0,5) and (-1,0)

By the of slope formula

[tex]\frac{y - y1}{x - x1} = (\frac{y2 - y2}{x2 - x1} )(\frac{x - x1}{y - y1} )[/tex]

[tex]{y - 5} = (\frac{0-5}{-1-0} )({x - 0 )\\\\\\[/tex]

[tex]= > 5x - y + 5 = 0[/tex]

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The temperature on Sunday was 20° C

To find the sum of vectors u and v, we can add their components separately:

(u + v)x = (7cos 310° + 2cos 115°)

(u + v)y = (7sin 310° + 2sin 115°)

Using a calculator to evaluate these expressions, we get:

(u + v)x = -2.16

(u + v)y = 8.48

The magnitude of the sum vector u + v can be found using the Pythagorean theorem:

|u + v| = √((u + v)x^2 + (u + v)y^2)

= √(-2.16^2 + 8.48^2)

= √(72.3584)

= 8.51

The direction of the sum vector u + v can be found using the inverse tangent function:

θ = tan^(-1)((u + v)y / (u + v)x)

= tan^(-1)(8.48 / -2.16)

= tan^(-1)(-3.928571428571429)

= 143.13°

Rounding the magnitude to the nearest tenth and the direction to the nearest degree, we get:

u + v = 8.5 (cos 143°, sin 143°)

Therefore, the sum of vectors u and v is equal to 8.5 (cos 143°, sin 143°).

On dividing 1658 by 25 , the quotient is equal to 66.32.

As given in the question,

Dividend is equal to 1,658

Divisor is equal to 25

Unit place value of 1658 is equal to 8.

25 is not a factor of 1658

Smallest number to 1658 divisible by 25 is 1650

Divide 1658 by 25 we get remainder

Dividend = ( Divisor × quotient) + remainder

1658 = 1650 + 8

        = ( 25 × 66 ) + 8

Remainder is equal to 8

Quotient is equal to 66

In decimal form

1658 ÷ 25

= 66.32 is quotient.

Therefore, the quotient of dividing 1658 by 25 is equal to 66.32.

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Answer:

check this one

Step-by-step explanation:

this is the answer

Answer:

To write √73 in exponential form, we can use the fact that the square root of a number is the same as that number to the power of 1/2. Thus, we can write √73 as 73^(1/2).

Here's how we can show this using algebraic steps:

First, we can write the square root as a fractional exponent:

√73 = 73^(1/2)

Next, we can rewrite the fractional exponent using the rule that says that a^(m/n) = (a^m)^(1/n):

√73 = (73^1)^(1/2)

Finally, we can simplify the expression by evaluating the power of 1:

√73 = (73)^(1/2) = 73^(1/2)

Therefore, √73 can be written in exponential form as 73^(1/2).

1

substitute 9 as x because 9 is in the brackets

then follow bidmas

brackets first so -10 + 9 = -1

now indices so square -1 which is 1.

therefore you answer is 1

Answer: 12/7

Step-by-step explanation:  The answer is 12/7 because here is what we know: A group of friends collected toys to donate to children in need. After sorting the toys into boxes, that's what we know,  we also know that they found they had 6/7 of a box of stuffed animals, and we also know that they found 5/7 of a box of board games and

1/7 of a box of doll. What they want to know is  In total, how many boxes of toys did the friends collect?  so you take 6/7 from the box stuffed animals they found + 5/7 from the box of board games they found which equals 11/7 then you add the 11/7 with the 1/7 the box of dolls they found.  In total the friends collect 12/7 boxes. Hope this helps!

Answer:

  0.1220

Step-by-step explanation:

You want the probability that greater than 90 out of 149 software users will not call tech support, given that the probability a given user will not call is 56%. You want the value using the normal approximation to the binomial distribution.

For a sample size of n, and probability p of "success", the normal approximation to the binomial distribution can be used if ...

  min(pn, (1-p)n) > 5

Here, that is ...

  min(0.56·149, 0.44·149) > 5

  65.6 > 5 . . . . . . . . true, the normal approximation is appropriate

Then the parameters of the normal distribution are ...

  µ = pn = 0.56·149 = 83.44

  σ = √((1-p)µ) = √(0.44·83.44) ≈ 6.0592

The probability that X = N will occur can be considered to be ...

  P(N -0.5 < X < N +0.5)

Then the probability that X > N will be modeled using the normal distribution as ...

  P(X > N +0.5)

For this problem, we want ...

  P(X > 90.5) . . . . using the normal distribution with µ = 83.44, σ = 6.0592

The attached calculator shows that value to be ...

  P(>90) ≈ 0.1220 . . . . . . rounded to 4 decimal places

__

Additional comment

A probability calculator says the actual binomial distribution result for this problem is 0.1217.

Answer:

x=4/3, 8/3

Step-by-step explanation:

We will solve this in two steps, one where the right hand side is 2, one where it is -2. This is because the equation is satisfied either way when [tex]|6-3x|[/tex] is equal to either of those values.

Let's start with 2. We have [tex]6-3x=2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 4/3. This is the first value.

Now, we solve for when it equals -2. We have [tex]6-3x=-2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 8/3. This is the second value.

Feel free to contact me with any questions about my answer. I hope this helps!

The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.

The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.

Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.

Here,

Number of samples, N=2000

Probability of responding correctly,

=1092/2000

=0.546

Z-score at 90% confidence level,

=1.645

Margin of Error ME,

=z*√(p*(1-p)/N)

=1.645*√(0.546*(1-0.546)/2000)

=1.645*√(0.546*0.454)/2000

=1.645*√(0.248/2000)

=1.645*√0.000124

=1.645*0.011

=0.0180

With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.

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Graph (D) represented the inequality solution of 5+x<3(2x+4).

The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

So, we have the inequality:

5 + 8x < 3 (2x+4)

Now, we need to plot this on the graph:

(Refer to the graph attached below)

We can easily tell that this is identical to graph sin option (D).


Therefore, graph (D) represented the inequality solution of 5+x<3(2x+4).

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Answer:

20%

Step-by-step explanation:

2 x 10 = 20

20%

The density of  a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is  0.003 kg / m³.

Density of the matter means space taken by matter.

To find the density, density = mass of matter / volume of mass.

Given that mass of the pumpkin 2.0 kg and a volume of 0.0060 m³.

Now the density from the formula;

Density = mass of pumpkin / volume of pumpkin

Density = 2.0 / 0.0060

Multiply by 10000,

Density = 20000 / 60

Density = 2000 / 6

Density = 1000 / 3

Density = 0.003 kg / m³

Therefore, the density of  a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is  0.003 kg / m³

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Answer:

-5x+9y=-18

Dividing both sides by -18

-5x/-18+9y/-18=-18/-18

5x/18-y/2=1

x/(18/5)-y/2=1. eqn(i)

eqn (i) is comparing with x/a+y/b=1, we get

x - intercept (a) =18/5

y-intercept (b) = -2

The factory produces 72 bottles of juice per minute.

What is the rate?

A rate is a special ratio in which the two terms are in different units. If a 12-ounce can of corn costs $69, the rate is $69 for 12 ounces. This is not a proportion of two comparable units, such as shirts. This is a proportion of two dissimilar units: cents and ounces.

To find the factory's production rate in bottles per minute, we need to divide the number of bottles produced by the time it took to produce them. In this case, the factory produced 360 bottles in 5 minutes, so the production rate is:

360 bottles / 5 minutes = 72 bottles/minute

This means that the factory produces 72 bottles of juice per minute.

Hence, the factory produces 72 bottles of juice per minute.

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Answer:

x=2.5, 5/2

y=1.5, 3/2

Step-by-step explanation:

2x-2(-5x+14)=2

2x+10x-28=2

12x=30

x=2.5

y=-5(2.5)+14

y=-12.5+14

y=1.5

Answer:

5f + 4s

Step-by-step explanation:

Third option

Using proportions, James need 750ml for 24 pancakes

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

To find the amount of milk James need, we need to use proportions.

8 pancakes = 250ml milk

24 pancakes = x

cross multiply both side and make x the subject of formula

8 × x = 24 × 250

8x = 6000

Divide both sides by coefficient of x

8x / 8 = 6000 / 8

x = 750

He needs 750 ml of milk

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Answer:

Step-by-step explanation:

1 1/3 cups peanut butter

proof:

1 1/3 +1 1/3+1 1/3+1 1/3+1 1/3+1 1/3 = 8 cups

True, In a paired test, a factor is what you are testing to see the effect of because its effect is unknown.

The paired t-test is a technique for determining whether or not the mean difference between two measurement pairs is zero. When your data values are paired measurements, you can apply the test.

The dependent samples t-test, paired difference t-test, matched pairs t-test, and repeated-samples t-test are other names for the paired t-test. You might not be able to test for normality if your sample sizes are too small. You might have to rely on your comprehension of the information. You might also do a nonparametric test that doesn't make the assumption of normality.

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Answer:

No

Step-by-step explanation:

The graph should be a line with negative slope, but the given graph is of a line with positive slope