7 students in a class,3/4 th pound of a cake .divide cake each student?

The sequence is arithmetic, since the forward difference between consecutive terms is -9.

7 - 16 = -9

-2 - 7 = -9

etc.

This means the sequence has the formula

[tex]a_n=16-9(n-1)=25-9n[/tex]

The sum of the first 30 terms is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\sum_{n=1}^{30}1-9\sum_{n=1}^{30}n[/tex]

Recall the formulas,

[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]

Then the sum we want is

[tex]\displaystyle\sum_{n=1}^{30}a_n=25\cdot30-\frac{9\cdot30\cdot31}2=\boxed{-3435}[/tex]

Answer:

If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.

Step-by-step explanation:

We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.

Answer: D. 8.25

Step-by-step explanation: A data set can be divided into 4 equal parts, called Quartile. A quartile divides the data into three points:

Interquartile Range (IQR) is a measure of variability based on data divided into quartiles or the measure of where the bulk of the values are.

To calculate interquartile range:

IQR = Q3 - Q1

The table shows Q1 = 27.825 and Q3 = 36.075, then

IQR = 36.075 - 27.825

IQR = 8.25

The value of interquartile range is 8.25.

Answer:

70

Step-by-step explanation:

If the team continues with same pace, they expected wins as per previous ratio:

Expected wins 70 out of 78 games

Answer:

3 pennies, 9 nickels, and 6 dimes

Step-by-step explanation:

We have three conditions:

(1)         p +        n +        d = 18

(2) 0.01p + 0.05n + 0.10d = 1.08

(3)                                   d = 2p

Multiply (2) by 100 and rearrange (3) to get a standard array.

(4)      p +   n +     d =   18

(5)      p + 5n + 10d = 108

(6)  -2p          +     d =    0

Subtract (4) from (5). This gives

(4)      p +   n +   d =  18

(7)            4n + 9d = 90

(6)  -2p          +   d =   0

Multiply (4) by 2 and add to (6). This gives

(4) p +   n +    d =  18

(7)        4n + 9d = 90

(8)        2n + 3d = 36

Double (8) and subtract from (7). This gives

(4)      p +   n +   d = 18

(7)            4n + 9d = 90

(9)                    3d = 18

Divide (9) by 3. This gives

(10) d = 6

Substitute (10) into (7). This gives

4n + 9(6) = 90

4n +   54 = 90

4n           = 36

(11) n       =    9

Substitute (10) and (11) into (4). This gives

p + 9 + 6 = 18

p +      15 = 18

p              =  3

Sasha has 3 pennies, 9 nickels, and 6 dimes.

Answer:

March through August

Step-by-step explanation:

Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:

[tex]S=56.9-40.7cos (\frac{\pi}{6}t)[/tex]

and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:

[tex]77=56.9-40.7cos (\frac{\pi}{6}t)[/tex]

if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:

[tex]56.9-40.7cos (\frac{\pi}{6}t)=77[/tex]

and now we solve for t

[tex]-40.7cos (\frac{\pi}{6}t)=77-56.9[/tex]

[tex]-40.7cos (\frac{\pi}{6}t)=20.1[/tex]

[tex]cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}[/tex]

[tex]cos (\frac{\pi}{6}t)=-0.4938[/tex]

[tex]\frac{\pi}{6}t=cos^{-1}(-0.4938)[/tex]

[tex]\frac{\pi}{6}t=2.087[/tex]

[tex]t=\frac{2.087(6)}{\pi}[/tex]

[tex]t=3.98 months[/tex]

but there is a second answer to this problem. Notice that the function cos can be 2.87 at [tex]2\pi-2.087=4.1962 rad[/tex] as well, so we repeat the process:

[tex]\frac{\pi}{6}t=4.1962[/tex]

[tex]t=\frac{4.1962(6)}{\pi}[/tex]

[tex]t=8.014 months[/tex]

So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:

(1,3.98)  (3.98,8.014) and (8,014, 13)

and find a test value for each of the intervals and test it.

(1,3.98) t=2

[tex]S=56.9-40.7cos (\frac{\pi}{6}(2))[/tex]

S=36.55

this is less than 77 so this is not our answer.

(3.98,8.014) t=5

[tex]S=56.9-40.7cos (\frac{\pi}{6}(5))[/tex]

S=92.15

this is more than 77 so this is our answer.

(8.014,13) t=10

[tex]S=56.9-40.7cos (\frac{\pi}{6}(10))[/tex]

S=36.55

this is less than 77 so this is not our answer.

so, since our answer is the interval (3.98,8.014)

this means that between the months of march and august we will be sellin more than 7700 units.

Complete Question

The complete question is shown on the first uploaded image

Answer:

The cost to buy 100 shares in ODX group Inc and 300 shares   peer Comms Lts is  

         [tex]C = \$ 775[/tex]

Step-by-step explanation:

   From the chat we that the cost of 100  ODX shares is  [tex]\$175[/tex]

    The cost of 100 peer Comms Lts  is  [tex]\$ 200[/tex]

Hence the cost 300 peer Comms Lts  is  [tex]k = 3 * 200 = \$ 600[/tex]

Now  the cost of  100 shares in ODX group Inc and 300 shares of  peer Comms Lts  is mathematically evaluated as

           [tex]C = 175 + 600[/tex]

           [tex]C = \$ 775[/tex]

The cost to buy 100 shares in ODX group Inc and 300 shares in peer comm LTD is $775.

Given in question the graph here is missing.

We have to calculate the total cost of 100 shares in ODX group Inc and 300 shares in peer comms limited in year 5.

From the graph it is clear that, the x axis shows the no. of year and y axis shows the cost of 100 shares for each type.

From graph, the cost of 100 shares of ODX group in year 5 is $175.

And the cost of 100 shares of peer comm Ltd in year 5 is $ 200.

So the total cost of 300 shares of  peer comm Ltd in 5 year is $([tex]200\times3[/tex]) or $600.

Now final cost of 100 shares in ODX group Inc and 300 share in peer comm Ltd is [tex]($600+$175)[/tex] dollars.

Hence the cost to buy 100 shares in ODX group Inc and 300 shares in peer comm LTD is $775.

For more details on graph follow the link:

https://brainly.com/question/14375099

Answer: He was given $75 for his birthday

Step-by-step explanation:

The y - intercept represents the rate of which the money is being deposited in the account.

"An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero."

"The solution of linear equations in two variables, ax+by = c, is a particular point in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b, then the sum of these two values will be equal to c.

Basically, for linear equation in two variables, there are infinitely many solutions."

The given equation is y = 50x + 75

The y intercept represents the amount of money to be deposited in account. The rate of change of money in the account with represent to the months.

Hence, y represents money deposited in the account.

To know more about linear equation in two variable here

https://brainly.com/question/11897796

#SPJ2

Answer:

28

Step-by-step explanation:

We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]

We know that,

[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]

Here, n = 3

So,

[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]

So,

[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]

So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).

Answer:

71°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle

m<x + m<y = m<z

4n - 18 + n + 9 = 151 - 5n

5n - 9 = 151 - 5n add like terms

10n = 160

n = 16

Since m<z = 151 - 5n we replace n with 16 and 151 - 5×16 = 71

Answer:

A. 71

Step-by-step explanation:

x + y = z

4n - 18 + n + 9 = 151 - 5n

5n - 9 = 151 - 5n

10n = 160

n = 16

Z = 151 - 5(16) = 71

Answer:

g(3) = -5

Step-by-step explanation:

g(3) is basically the value of g(x) when x = 3. Therefore, g(3) = -3 - 2 = -5.

Answer:

[tex] \boxed{\sf g(3) = -5} [/tex]

Given:

g(x) = -x - 2

To Find:

g(3) i.e. g(x) where x = 3

Step-by-step explanation:

[tex]\sf Evaluate \ -x - 2 \ where \ x = 3:[/tex]

[tex] \sf \implies - x - 2 = - 3 - 2[/tex]

[tex] \sf - 3 - 2 = - (3 + 2) : [/tex]

[tex] \sf \implies - (3 + 2)[/tex]

[tex] \sf 3 + 2 = 5 : [/tex]

[tex] \sf \implies - 5[/tex]

Answer:

B

Step-by-step explanation:

-5z +1 = -2z +10

-3z = 9

z=9/-3

Z= -3

Answer:

the answer is exactly one solution

Step-by-step explanation:

this is the answer because i just took this question on khan academy and the one solution is z = -5 for the equation

Answer:

Sin of x does not change

Step-by-step explanation:

Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.

From trigonometry,

Sin(x)=opposite/hypotenose

Where x=4/5

Sin(4/5)= opposite/hypotenose

But we were given the scale factor of 2 which means the dilation is to two times big.

Then we have

Sin(x)=(2×opposite)/(2×hypotenose)

Then,if we divide by 2 the numerator and denominator we still have

Sin(x)=opposite/hypotenose

Which means the two in numerator and denominator is cancelled out.

Then we still have the same sin of x. as sin(4/5)

Hence,Sin of x does not change

Answer:

Step-by-step explanation:

sin of angle x = [tex]\frac{4}{5}[/tex]

If the triangle is dilated 2 times - it becomes two time larger.

4 times 2 = 8   and 5 times 2 = 10

So the ratio would be [tex]\frac{8}{10}[/tex],  which when reduced (divide numerator and denominator by 2)  becomes [tex]\frac{4}{5}[/tex].

This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.

So the answer is 4/5.

Answer:

  5/2

Step-by-step explanation:

Let u = sin(t). Then this is the integral ...

  [tex]\displaystyle\int_0^{\frac{\pi}{2}}{5u}\,du=\left.\dfrac{5u^2}{2}\right|_0^{\frac{\pi}{2}}=\dfrac{5}{2}(\sin(\frac{\pi}{2})^2-\sin(0)^2)=\dfrac{5}{2}(1-0)=\boxed{\dfrac{5}{2}}[/tex]

Answer:

0.09

Step-by-step explanation:

Let x = ages of mother

x  :  22   17    27    20    23     19      24    18    19    24

N = 10

Mean = ∑x/N = 218/10 = 21.8

Difference in mean = 21.8 - 20 = 1.8

If significance level = 5% or 0.05

∴ Rejection region = 1.8 X 0.05 = 0.09

Answer:

It is option A

Step-by-step explanation:

A is correct option

Answer:

It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.

Step-by-step explanation:

Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered  by adding salt to the water. A student discovered that adding half a cup of salt to  a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is  the freezing temperature of the gallon of salt water?

0° - 7° = -7°

Answer:

-3x - 7y = 36

Step-by-step explanation:

The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.

If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:

-3(-5) - 7(-3) = C, or

15  + 21 = C, or C = 36

Then the desired equation is -3x - 7y = 36.

Answer:

Any value that has x less than or equal to 19 is a solution

Step-by-step explanation:

x – 5 ≤ 14

Add 5 to each side

x – 5+5 ≤ 14+5

x  ≤ 19

Any value that has x less than or equal to 19 is a solution

Answer:

[tex]\boxed{x\leq 19}[/tex]

Step-by-step explanation:

[tex]x-5\leq 14[/tex]

[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]

[tex]x-5+5 \leq 14+5[/tex]

[tex]x\leq 19[/tex]

Answer:

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays

against Ha : p1≠ p2  (claim)  ( two sided)

The significance level is set at ∝= 0.05

The critical value for two tailed test at alpha=0.05 is ± 1.96

or Z∝= 0.05/2= ± 1.96

The test statistic is

Z = p1-p2/√pq(1/n1 +1/n2)

p1= proportions of households  decorating in city 1  = 45/60=0.75

p2= proportions of households  decorating in city 2 = 40/50= 0.8

p = the common proportion on the assumption that the two proportion are same.

p =   [tex]\frac{n_1p_1 +n_2p_2}{n_1+n_2}[/tex]

Calculating

p =60 (0.75) + 50 (0.8) / 110

p=  45+ 40/110= 85/110 = 0.772

so  q = 1-p= 1- 0.772= 0.227

Putting the values in the test statistic and calculating

z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)

z= -0.05/√ 0.175244 ( 110/300)

z= -0.05/0.25348

z= -0.197

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Answer:

Brainliest! Hope I helped!

Step-by-step explanation:

you know its greater than 1cm and less than 2cm,

1 and 7hundreths cm is = 1.07 cm

thats not right because you know it is greater than that for sure!

so the only answer left is 1.7 cm

You answer is 1.7 cm

another way...

read the ruler and see the answer

Answer:

1.7 cm.

Step-by-step explanation:

The midpoint of 1 - 2 is 5 so count the lines after 5 and you get .7 to add to one cm.

Hope this helps, have a good day :)

Answer:

Policeman A = 56 tickets

Step-by-step explanation:

Policemen A + B = 70

If Policeman B hands out x no of tickets...

Then Policeman A hands out 4x no of tickets

meaning...

x + 4x = 70

5x = 70

x = 70/5

x = 14

Therefore Policeman A hands out..

4x = 4 × 14 = 56 tickets

Complete Question

In a genetics experiment on​ peas, one sample of offspring contained 372 green peas and 35 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was​ expected?

Answer:

The  probability is  [tex]P(g) = 0.9140[/tex]

No it is not close to the probability expected

Step-by-step explanation:

From the question we are told that

    The sample size is  [tex]n = 372 + 35= 407[/tex]

      The  number of  green peas is  [tex]n_g = 372[/tex]

    The  number of  yellow  peas is  [tex]n_y = 35[/tex]

The  probability of getting an offspring pea that is green is mathematically represented as

         [tex]P(g) = \frac{n_g}{n}[/tex]

substituting values

         [tex]P(g) = \frac{372}{ 407}[/tex]

         [tex]P(g) = 0.9140[/tex]

The  expected probability is  [tex]\frac{3}{4} = 0.75[/tex]

But what we got is  [tex]P(g) = 0.9140[/tex]

So we can say that the value obtained is not equal to the expected value

Answer: 1, 2, 4, 8, 16, and 32.

Step-by-step explanation:

Factors are what we can multiply to get the number.

Factors of 32:

1 x 32=32

2 x 16=32

4 x 8=32

Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer:

The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Step-by-step explanation:

Call X is the number of hours that the author uses on monthly basis.

Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.

Total bill value if the author uses TalkLots service is $20 + $4X

The total fees between 2 providers equal as:

$80 + $1 X = $20 + $4X => 3X = $60 => X = 20

Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Answer:

Left angle = 60°

Top angle = 120°

Right angle = 60°

Step-by-step explanation:

Use what you know about angle relationships to set up equations you can solve for each variable.

The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.

You have two variables, so you need at least two equations (I made three but only used two).

The work is in my attachment, comment of you have questions.

Answer:

3 =x

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x*x

Divide each side by x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x from each side

3x-3x +3 = 4x-3x

3 =x