Which graph shows the solution to this system of linear inequalities?
y<-1/3x+2
y<_2x-3

Answer:

96 eggs

Step-by-step explanation:

A dozen is equal to 12 eggs, so 15 dozen is equal to 180 eggs

(Because 15*12 = 180)

We already know how many eggs are required for the 1st cake: 12 eggs.

Then it says "each successive cake needs twice as many eggs as the previos cake".

(Successive means the cake directly after the previous cake)

Here's how we find the number of eggs needed for the 2nd cake:

The 1st cake needed 12 eggs, and because the 2nd cake is directly after the 1st cake, we are going to need two times the amount of 12 eggs.

This equation represents the above scenario:

12*2 = 24

So we need 24 eggs for the 2nd cake.

Now we repeat this process for the 3rd cake, finding twice the amount of eggs from the 2nd cake to find the amount of eggs needed for the 3rd cake:

24*2 = 48

And we repeat it once more for the 4th cake, using the eggs from the 3rd cake:

48*2 = 96

So here's the list of how many eggs are required for each of the cakes:

1st cake: 12

2nd cake: 24

3rd cake: 48

4th cake: 96

If you add all the eggs from each of the cakes, you will get 180, which is the number of eggs needed for all four cakes. So our answer is correct.

Hope this helps (●'◡'●)

Answer:

6.67%

Step-by-step explanation:

By question I borrow $1000 for 3 years and I owe $200 interest . We can use the formula of Simple Interest as ,

[tex]\implies SI =\dfrac{ P*R*T}{100}[/tex]

[tex]\implies \$200 =\dfrac{3*\$1000*R }{100}\\\\\implies R = \dfrac{ \$ 200 * 100}{3*\$ 1000} \\\\\implies\underline{\underline{ R = 6.67 \%}} [/tex]

Answer:

(3) [tex]x = 7.5[/tex] and [tex]y = 51[/tex]

(4) [tex]x = 6[/tex]

Step-by-step explanation:

Question 3

Required

Solve for x and y

We have:

[tex]16x - 18 + 10x +3 = 180[/tex] --- angle on a straight line

Collect like terms

[tex]16x + 10x = 180 + 18 - 3[/tex]

[tex]26x = 195[/tex]

Solve for x

[tex]x = 195/26[/tex]

[tex]x = 7.5[/tex]

Also:

[tex]16x - 18 = 2y[/tex] ---- opposite angles

So, we have:

[tex]16 * 7.5 - 18 = 2y[/tex]

[tex]120 - 18 = 2y[/tex]

[tex]102 = 2y[/tex]

Divide by 2

[tex]51 = y[/tex]

[tex]y = 51[/tex]

Question 4:

Required

Solve for x

We have:

[tex]11x - 2 + 5x - 4 = 90[/tex] ---- angle at right-angled

Collect like terms

[tex]11x + 5x = 90 +2 + 4[/tex]

[tex]16x = 96[/tex]

Divide by 16

[tex]x = 6[/tex]

Answer

500,000 + 500,000 = 1,000,000

Step-by-step explanation:

The cost of the cereal if the grocery store buys 250 boxes is $475

Functions are written in terms of variables. If the cost function that represents the cereal is given as C(n), the equivalent expression if the grocery store buys 250 boxes is 1.9n

Substitute n = 250 into the function to have:

C(250) = 1.9(250)

C(250) = $475

Hence the cost of the cereal if the grocery store buys 250 boxes is $475

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Answer:

B

Step-by-step explanation:

The definition of a function is that any input will only have one output. Here, the input is the number of years, and the output is the value of the car. We know this because the question is asking why the value of the car is a function of the number of years. Therefore, based on the number of years, the value of the car is given.

Going back to the definition of a function, we can apply this year to say that any number of years will only have one car value. Another way to say this is that each time is associated with exactly one car value.

Answer:

D)

[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]

Step-by-step explanation:

(See the picture)

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

The general explicit formula for a geometric sequence is expressed as:

Given the following recursive functions:

[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]

Get the next two terms:

[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]

For the third term:

[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]

The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

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Answer:

9 + i

Step-by-step explanation:

You just simplify by combining the real and imaginary parts of each expression.

Hope this helps you!!

Answer:

x=70

Step-by-step explanation:

First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.

Next, because x is the mode and has to be the median as well, and our number line so far is

(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.

Finally, to calculate the mean, we have

mean = sum / count

The mean must be x, as it is equal to the mode, so we have

x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)

multiply both sides by 5 to remove the denominator

5 * x = 10+70+80+120+x

5 * x = 280 + x

subtract x from both sides to isolate the x and the coefficient

4 * x = 280

divide both sides by 4 to get x

x= 70

We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.

Answer:

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

[tex]e^{0.4[/tex] < e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]

where m = [tex]| f^{N+1 }(x) |[/tex]

so we have

| Error |  ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]

| Error |  ≤ ( 0.125 ) 0.0256

| Error |  ≤ 0.0032

Therefore, upper bound for the error, | Error |  ≤ 0.0032

Answer:

Hence, the roots of the polynomial equation are:

-2, 1, 4

Step-by-step explanation:

We are asked to find the roots of the polynomial equation:

We can also equate this equation to y to obtain a system of equation as:

and

Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.

Hence, the point of intersection of the two graphs are:

(-2,4), (1,-5) and (4,40)

Hence, the roots of the polynomial equation are:

-2, 1, 4

Answer:

the operating characteristics have been solved below

Step-by-step explanation:

we have an average of 10 minutes per customers

μ = mean service rate = 60/10 = 6 customers in one hr

the average number of customers that are waiting in line

mean arrival λ = 2.5

μ = 6

[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]

= 6.25/21

= 0.2976

we calculate the average number of customers that are in the system

[tex]L=Lq+\frac{2.5}{6}[/tex]

= 0.2976+0.4167

= 0.7143

we find the average time that a customer spends in waiting

[tex]Wq=\frac{0.2976}{2.5}[/tex]

= 0.1190 hours

when converted to minutes = 0.1190*60 = 7.1424 minutes

[tex]0.1190+\frac{1}{6}[/tex]

=0.2857

probability that arriving customers would wait for the service

= 2.5÷6 = 0.4167

Answer:

s = -4

Step-by-step explanation:

Your goal is to manipulate the equation so you can isolate s

9s + 20 = -16

Subtract 20 from both sides to get:

9s = -36

Divide both sides by 9 so s is alone

you end up with s = -4

Answer:

s  = -4

Step-by-step explanation:

9s+20=−16

Subtract 20 from each side

9s +20 -20 = -16 -20

9s = -36

Divide by 9

9s/9 = -36/9

s  = -4

Answer:

5 1/4

Step-by-step explanation:

* is multiplication

1 3/4 is 1.75

so

24/1.75 = 72/×

1.75 * 72 = 24 * x

126 = 24x

24x = 126

x = 5.25 or 5 1/4

Total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.

The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of .

According to the given question.

Number of cups or butter required for making 24 cookies = [tex]1\frac{3}{4} =\frac{7}{4}[/tex]

⇒ Number of cups of butter required to make 1 cookie = [tex]\frac{\frac{7}{4} }{24} =\frac{7}{(24)(4)}[/tex]

Therefore,

The number of cups of butter required to make 72 cookies

= [tex]72[/tex] × [tex]\frac{7}{(24)(4)}[/tex]

= [tex]\frac{21}{4}[/tex]

= [tex]5\frac{1}{4}[/tex]

Hence, total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.

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tan graph and its tax because tax=0

Answer:

8/9

Step-by-step explanation:

Find what fraction of their goal they have raised by adding the amounts from last year and this year together:

7/9 + 1/9

= 8/9

So, they have raised 8/9 of their goal

Answer:

Step-by-step explanation:

the ratio of 24 to 36 is the same as  x to 12

[tex]\frac{24}{36}[/tex] = [tex]\frac{x}{12}[/tex]

then

12*([tex]\frac{24}{36}[/tex])=x

[tex]\frac{24}{3}[/tex] = x

8 = x  

that's it :)

Answer: Interior angle: 150 degrees Exterior angle: 30 degrees

Step-by-step explanation:

We use the angle formula to find the value of an interior angle: 180*(12-2)/12 = 150 degrees. Since an exterior angle is the supplement of an interior angle, the measure of an exterior angle is 180 - 150 = 30 degrees

Answer:

μ = 170 customers per day

σ = 45 customers per day

n = 31

[tex]\mu_x = 170[/tex]

[tex]\sigma_x = 8[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.

This means that [tex]\mu = 170, \sigma = 45[/tex]

Suppose she takes a random sample of 31 days.

This means that [tex]n = 31[/tex]

For the sample:

By the Central Limit Theorem, the mean is [tex]\mu_x = 170[/tex] and the standard deviation is [tex]\sigma_x = \frac{45}{\sqrt{31}} = 8[/tex]

Answer:

f(6) = 3

f'(6) = 1/6

Step-by-step explanation:

Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))

We know that:

y = f(x) passes through the point (6, 3)

Then we already know that:

f(6) = 3.

Now we also know that the tangent at this point, also passes through (0, 2)

Remember that a line can be written as:

y = a*x + b

Where in this case, a = f'(6)

so we just want to find the slope of this line.

Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And we know that the tangent line passes through the points (0, 2) and (6, 3)

Then the slope is:

a = (3 - 2)/(6 - 0)  = 1/6

Then we have:

a =  f'(6)  =1/6

Answer:

A

Step-by-step explanation:

graph is 6 units to the right

if it had been (x+6)^2

it would have been 6 units to left

Answer:

C. 37.8 units

Step-by-step explanation:

ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units

DF = 17× tan (38°) = 17× 0.7813 = 13.3 units

CD = 10/13.3 × 21.6 = 16.2 units

so, the length of CE = 21.6+16.2 = 37.8 units

Answer:

Step-by-step explanation:

I don't think so. This equation has but one definite answer and the left and right sides don't produce the same result.

subtract 5m from both sides

6 = 4m - 5m

6 = - m                 Multiply both sides by - 1

-6 = m

An identity is something like 4x + 5x = 9x

It doesn't matter what x is. Any value of x will make the right side = to the left side. This becomes more important when you will study trigonometry.

Answer:

the value of the following 8711×99+8711 is

Step-by-step explanation:

871100

Answer:

871100

Step-by-step explanation:

use BODMAS

first multiply 8711×99

=862389

Then add 862389+8711

=871100

Answer:

Slope: 2/3

Y-intercept: 6

Answer:

SECOND ONE

Step-by-step explanation:

Answer:

it can not cleared clear but it can not cleared

Answer:

your selected answer is right