Which point is a solution to y<4x + 5?

Barry will post all of his parcels separately at £17.84

The information in the table have the amount to post certain weights of the parcel. This will be used to ascertain how much to send Barry's parcel

Barry's parcel will contains (starting from the least)

weight of parcel                    cost of posting as from the table

less than 1 kg (1kg to 5kg)      £2.04

0.245 kg (1kg to 5kg)             £2.04

2.7 kg (1kg to 5kg)                  £2.04

4.16 kg (1kg to 5kg)                £2.04

27.3 kg (More than 20kg)      £9.68

addition of the costs

= £2.04 * 4 + £9.68

= £17.84

hence the cost of sending the five parcels is £17.84

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Answer:

<1 = 33

Step-by-step explanation:

The sum of the angle of a triangle is 180

31+116+x = 180

x+147=180

x = 180-147

x = 33

Answer:

Angle BFC is complimentary to AFB. Its measure is 12.

Step-by-step explanation:

Complementary angles add up to 90 degrees. When these two angles combine, it adds up to 90. 90-78 = 12. This angle's measure is 12.

B: (6,12,18,44,54)

I just did this and this was correct.

Answer:option B

Step-by-step explanation:i got it right trust me

Answer:

1/8

Step-by-step explanation:

There are 24 coins total. 3 of them are quarters. So Jillian has a 3 in 24 chance of picking up a quarter. Simplifying 3/24 we get 1/8

The probability of randomly picking a quarter is P = 0.125

If we assume that all the coins have the same probability of being randomly picked, the probability of picking a particular type of coin is equal to the quotient between the number of coins of that type that we have, and the total number of coins.

In this case, we have 3 quarters, and a total of:

T = (6 + 7 + 8 + 3) = 24

Then the probability of randomly picking a quarter is:

P = 3/24 = 0.125

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Answer:

Principal = 20833.334

Step-by-step explanation:

simple interest = $5000.

Rate = 3%

Time = 8 years.

Principal = ?

Principal =

\( = \frac{100 \times simple \: interest}{r \times t} \\ = \frac{100 \times5000 }{3 \times 8} \\ = \frac{500000}{24 \\ } \\ = 20833.334\)

Principal = $20833.334.

Answer:

Step-by-step explanation:

The area of the square is given as 1134 m². Let's assume that the side length of the square is "s". Then, we can write the area of the square as s² = 1134. Solving for "s", we get s = √1134. The perimeter of the square is given by P = 4s. Substituting the value of "s", we get P = 4√1134. To simplify this expression, we can factor out the perfect square factor of 36 from 1134, which gives us 1134 = 36 x 31. Therefore, P = 4√(36 x 31) = 4 x 6√31 = 24√31. Hence, the perimeter of the square is 24√31 m.

Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

Hello

2/7 = 2x5/7x5 = 10/35

10/35 > 6/35

=> 2/7 > 6/35

Answer:

J.3h+2≥14

Step-by-step explanation:

Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.

Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.

Answer:

a

The 95% confidence interval is   \(0.5753<  p <0.62474\)  

b

 This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

c

 The margin of error is   \(E =    0.02474 \)  

d

 The confidence interval becomes wider

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1506

    The sample proportion is  \(\^ p = 0.60\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =    1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)    

=>   \(E =    0.02474 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \(0.60 - 0.02474 <  p <0.60 + 0.02474\)  

=>   \(0.5753<  p <0.62474\)  

This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider  

Answer:

the answer for no.19. is 129°

Step-by-step explanation:

firstly as you can see line DE is actually the diameter which is equal to 180°. the angle CD is equal to 51° so all we have to do is minus 51° from 180° which is equal to 129°.

You can also minus 108° from 180° the answer is 72° therefore the angle for line BFE is 72°. Add all the answer should be 360° which is the total degrees for a circle.

It will take 2.76 seconds an object to fall to the top.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that The height of a building is 1957 feet.

S = the distance

Given d = 16t²  is the function for the height as a function of time.  It will hit the ground when h=0 so:

16t² - 1957 =0

16t² - 1957 =0

16t² =1957

t²  =1957 /16

t=√(1957 /16) seconds

t≈ 2.76 seconds  (to nearest hundredth of a second)

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Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

Answer:

Approximately 3.4 years more or less

Step-by-step explanation:

If we represent this exponential growth as P=185(1.16)^n where n is the number of years passed and P is the population, then:

P=185(1.16)^n

305=185(1.16)^n

1.65=1.16^n

log₁.₁₆(1.65)=log₁.₁₆(1.16^n)

3.37=n

So the deer population will reach 305 in approximately 3.4  years.

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Here, we have,

to find the equation of the regression line for a given data:

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is

ŷ= 6.45x + 31.5.

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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complete question:

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

(a) x=3 hours

(b) x=4.5 hours

(c) x=13 hours

(d) x=1.5 hours

The unit rate of cups of lemonade per lemon is in the ratio of 6:1.

The unit rate is the ratio of two or more quantities or values that are compared to one another.

Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.

The number of lemons required to make 18 cups of lemonade = 3 lemons

Rate of lemonade per lemon = 18/3 = 6/1

Ratio = 6:1 or 1:6

Conversely, the rate of lemon per cup of lemonade = 1/6

Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.

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Answer:

$32.70 ÷ 5

Each case is $6.54.

Step-by-step explanation:

$3270 for 5 cases, meaning you would split $32.70 into 5.

$32.70 ÷ 5 phone cases = $6.54

This also means each case is $6.54. To prove this, multiply by 5.

If a manufacturer manufactures 5,000 dozen of sweaters, and sells 3,000 dozen of them only, then the total profit he/she earns from the these sweaters is [1000(3x - 5y)], assuming that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y".

As per the question statement, a manufacturer miscalculates the demand of the market and manufactures 5,000 sweaters, but sold only 3000 of them.

We are required to calculate the total profit earned by the manufacturer from the sale of the sweaters.

Since, no data about the manufacturing cost of the sweaters and their selling price is provided in the question statement, let us assume that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y". Solving with these variables will give us a generalized answer which we can use for any value.

Now, Since assumed that, manufacturing cost of one sweater is "x", then, manufacturing cost of 5000 sweaters will be \((5000*x)=5000x\).

Similarly assumed that, selling cost of one sweater is "y", and then, selling cost of 3000 sweater will be \([(3000*y)=3000y]\).

Now, we know that,

[Profit = (Total Selling Cosy) - (Total Manufacturing Cost)],

Therefore, in this case, total profit from the sale of 3000 sweaters

\(=(3000y-5000x)\\=1000(3y-5x)\).

Now, on using real integers or numbers in place of "x" and "y", if the value of Profit comes negative, it will mean, that for those values of "x" and "y", the manufacturer makes loss, not profit.

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Answer:

a) 400 meters

b) 67 meters

c) 124.790 meters

Step-by-step explanation:

Given data :

g1 = - 0.4 %

g2 = +2 %

change of grade of sag curve ( a ) = 0.6 %

Elevation of PVI ( h2 ) = 124.80 m

a) compute the length of the curve using the relation below

a = \(\frac{g2-g1}{L}\) .  hence ; L = ( g2 - g1 ) / a

L = ( 2 -(-0.4 ) / 0.6

  = 2.4 / 0.6 = 4  

 =  400 meters

b) compute the elevation of the lowest point of the curve

slope of the vertical curve = 0

0 = 2ax l + b

 = 2( \(\frac{g2-g1}{L}\) ) x  + g1

∴ x = \(\frac{-g1L}{(g2-g1)}\)  = ( 0.4 * 4 ) / ( 2 + 0.4 ) = 1.6 / 2.4 =  0.67 stations

therefore x ( elevation of the lowest point ) = 67 meters

C) compute the elevation at Sta. 12 + 125.60

Given that the rate of change of elevation is the same at all points

= \(\frac{h2 - h1 }{PVI -P0}\)  = 0.4 -------- ( 1 )

where h2 = 124.80

           h1 = ? ( elevation of p0 ) at 12 + 125.60

           PVI = 12 + 150.06

            p0 =  12 + 125.60

back to the above equation

- h1 = 0.4 ( PVI - P0 ) - h2

     = 0.4 ( 12.150 - 12.1256 ) - 124.80

-h1   = -124.790

hence h1 = 124.790 m

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer:

a) common difference = 5

b) common difference =  - 2

c) not an arithmetic sequence

last question:
nth term: aₙ = 3n - 1

a₅₀ = 149

a₄₀₀ = 899

Step-by-step explanation:

Common difference d = difference between successive terms
For a)
d = 9 -4 = 14 - 9 = 5

For b)
d = 8 - 10 = 6 - 8 = -2

For c) 5, 5, 2, 0
5  -5 = 0
which is not equal to
2 - 5 = 3
So this is not an arithmetic sequence
(unless of course the series numbers have been copied wrong)

For the last question

Sequence = 2, 5, 8, 11, 14, ...

d = 5 - 2 = 8 -5 =  3

The nth term of an arithmetic sequence is given by the formula:

aₙ = a₁ + d(n-1)

where a₁ = first term = 2

d = 3

So
aₙ = 2 + 3(n- 1)
aₙ = 2 + 3n - 3
aₙ  = 2 -3 + 3n

aₙ = -1 + 3n
aₙ = 3n - 1

Check:

a₂ = 3(2) - 1 = 5
a₃ = 3(3) - 1 = 8
a₄ = 3(4) - 1 = 11

a₅₀ = 3(50) - 1 = 150 - 1 = 149

a₃₀₀ = 3(300) - 1 = 900 - 1 = 899