A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?

The area of the given circle is 95 cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we know that the diameter of the circle is 11 cm.

Radius = Diameter/2

11/2

5.5 cm

Area of circle: πr²

3.14(5.5)²

3.14*30.25

94.985

Rounding off: 95 cm²

Therefore, the area of the given circle is 95 cm².

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The value of the exponent illustrated as 27^1/3 is 3.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this situation, it should be noted that 27^1/3 simply means the cube root of 27. This will give a value of 3.

Check: 3 × 3 × 3 = 27.

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Answer:

20:50 or 2:5

Step-by-step explanation:

30 dogs

20 cats

50 total animals

Part to whole relationship:

20:50

The temperature on Sunday was 20° C

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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Answer:

20%

Step-by-step explanation:

2 x 10 = 20

20%

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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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

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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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

Answer: (-1, 3)

Step-by-step explanation:

Midpoint formula: ((x1 + x2) / 2, (y1+y2) / 2)

((-5+7)/2, (4+2) / 2))

((-2/2), (6/2))

(-1, 3)

Answer:

5f + 4s

Step-by-step explanation:

Third option

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

Answer:

Step-by-step explanation:

5

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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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:

  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.

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:

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.

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

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:

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: 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!

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:

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 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:

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

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

Therefore the solution of this question is ratio length =  every 1 inch of toy car represents 1.5 feet of actual car

In mathematics, a ratio shows how two numbers are multiplied together. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.

Here,

A toy Jeep measures 12 1/2 inches.

Before calculating the ratio, let's first convert each size into the same unit of measure and decimal points:

=>12 ½ = 25/2  

=> 12.5 inches;

=> 18 ¾ = 75/4

=> 18.75 feet .

The actual length of a jeep is 18.75 feet.

The ratio can now be determined by converting feet to inches.

1 inch of a toy car equals 1.5 feet of an actual car because

=> 1 foot = 12 inches

=>  12.5 inches : 225 inches

 => 225 / 12.5

=> 18 inches

Therefore, every 1 inch of toy car represents 1.5 feet of actual car.

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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).