Solve the following word problem using matrices:

Part of $30,000 is invested at 6% yearly interest, another part at 7%, and the remainder at 8% yearly interest. The total yearly interest income from the three investments adds up to $2200. The sum of the amounts invested at 6% and 7% equals the amount of money invested at 8%. How much is invested at each rate?

(Enter your answer in the form $x,xxx--with the amount invested at 6% first, then 7%, then 8%.)

Answer:

The answer is 10 Pounds.

Step-by-step explanation:

You get 10 pounds because you divide your weight by 6 and 60 divided by 6 is 10.

Answer:

3.636363636

Step-by-step explanation:

Because that is 16.5 percent of 60, you can find this by dividing 60 by your percentage your trying to find of it, 16.5 in this case.

Using the confidence interval concept, an interval between 10 and 14.8 is likely to contain the true mean number of books read in the previous year by the population.

It means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

The bounds of the confidence interval are given by the estimate plus/minus the margin of error.

For this problem, we have that:

Hence the bounds are given by:

An interval between 10 and 14.8 is likely to contain the true mean number of books read in the previous year by the population.

More can be learned about confidence intervals at https://brainly.com/question/25890103

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Answer:

attached below is the prove

Step-by-step explanation:

In order to prove the expression for coefficient b[tex]_{2}[/tex] we have to find b[tex]_{0}[/tex] and b[tex]_{1}[/tex]

F(x) = [tex]b_{0} + b_{1} ( x - x_{0} ) + b_{2} ( x - x_{0} ) (x - x_{1} )[/tex]

i) Determine b[tex]_{0}[/tex]

at x = x[tex]_{0}[/tex]  

b[tex]_{0}[/tex] = f(x[tex]_{0}[/tex] )

ii) Determine b[tex]_{1}[/tex]

at x = [tex]x_{1}[/tex]

f ([tex]x_{1}[/tex]) = f ([tex]x_{0}[/tex] ) + b[tex]_{1}[/tex] [tex](x_{1} - x_{0} )[/tex] + 0

[tex]b_{1} = \frac{f(x_{1} )-f(x_{0} )}{(x_{1}-x_{0} ) }[/tex]

prove of the expression for the coefficient B2 in the quadratic interpolation

attached below is the detailed prove

Answer:

50%

Step-by-step explanation:

Given that:

P(late) = P(L) = 50% = 0.5

P(Eat) = P(E) =?

P(LnE) = 40% = 0.4

P(LuE) = 60% = 0.6

P(LuE) = P(L) + P(E) - P(LnE)

0.6 = 0.5 + x - 0.4

0.6 = 0.1 + x

0.6 - 0.1 = x

0.5 = x

P(E) = 0.5

0.5 * 100% = 50%

Answer:

3/35

Step-by-step explanation:

Chris got 28 out of 35 correct in his test

So

he get wrong=3

fraction= 3/35

So 3/35 is the answer

Answer: c

Step-by-step explanation:

I took the quiz

Answer:

The answer is D.

Step-by-step explanation:

Remember, think of what they would be like on a number line. The negative number closest to zero is greater than the negative numbers farther from zero. Any number that is to the left of a certain number is less than, if that makes any sense.

Answer:

y= 8th grade class,

y + 24 =160

subtract 24 from both sides

y=136

there are 136 students in the eight grade class

Step-by-step explanation:

Answer:

136 students

Step-by-step explanation:

7th grade= 160 students

8th grade= g students

g= 160-24

g= 136 students

- I hope this helps have a great day!

Answer:

C

Step-by-step explanation:

A number's absolute value is its distance from zero. -4 is 4 units from zero so its absolute value is 4

Hope this helps!

Answer:

4

Step-by-step explanation:

absolute value is is the non negative value of that number (example 3=3, -4=4

Answer:

13.3

Step-by-step explanation:

Answer:

B. -3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Plato

Answer:

the organize is a explanation to the earth

Step-by-step explanation:

yan lang alam ko

Answer:

ye thats true..

Step-by-step explanation:

Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

Close number to 641 is 640

Close number to 59 is 60

Estimate for 641/59 ⇒ 640/60

Line segment AD is 4cm. Because A is the center, any lines coming off the centerpoint are congruent. So if line AC is 4cm, then line AD has to be 4cm as well.

Comparing the two circles, the length of segment AD is 4 cm. On the first circle, the diameter is BAE is 8cm.

We should know that a circle is a figure in which all distances are equal from the center and the line from the center to the circumference is called radius.

The diameter is the line that passes through the center of the circle dividing the circle into two equal parts.

The given information are that the circles are the same

Diameter of the circles = 8cm

Radius = D/2= 8/2

Radius = 4 cm in each circle

Since the two circles shave the same diameter of 8cm and segments are different because the second has 3 segments while the first has 2 segments

The length of the segment AD = 4 because its from center to circumference that is radius

The first circle BAE is a diameter because it divides the circle into two equal halves

Therefore the length of segment AD is 4cm because it is a radius.

the diameter is BAE is 8cm.

Learn more about a circle;

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Answer: the first one is d the second one is c

Step-by-step explanation: e2020

Answer: B

Step-by-step explanation:

20 divided by 5 =4 and 5x4=20

Answer:

The probability is   [tex]P(X <  3) =  0.7843 [/tex]

Step-by-step explanation:

From the question we are told that

   The low yield rate is  [tex]q = 0.98[/tex]

    The sample size n = 80

Hence the probability that the bottle is bad

       [tex]p = 1- q[/tex]

=>    [tex]p = 1 - 0.98[/tex]

=>     [tex]p =0.02[/tex]

Generally the distribution of yield follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

Generally the probability less than three bottles are bad is mathematically represented as

    [tex]P(X <  3) = P(X = 0 ) + P(X = 1 )+ P(X = 2)[/tex]

=>  [tex]P(X <  3) = ^{80}C_0 *  0.02^0 *  (1- 0.02)^{80-0} +^{80}C_1 *  0.02^1 *  (1- 0.02)^{80-1}+ ^{80}C_2 *  0.02^2 *  (1- 0.02)^{80-2}[/tex]

=>  [tex]P(X <  3) = 1 *  1 * 0.1986 + 80 *  0.02 *  0.2027 + 3160 *  0.0004 * 0,2068[/tex]

=>  [tex]P(X <  3) =  0.7843 [/tex]

Answer:784 i think

Step-by-step explanation:

98 x 8 = 784. My teacher told me that when multiplying %'s you do the precent # x the #

Answer:

L=10cm , W=30cm

Step-by-step explanation:

First use the given that W=10+2*L

Use P=2W+2L=80, substitute W in the perimeter formula

2(10+2L)+2L=80 and solve for L,

20+4L+2L=80 isolate variable L and combine like terms,

6L=80-20,

L=10, so W=10+2*10=10+20=30

Answer:

$1400

double is $2800

Step-by-step explanation:

$35,000 x .04 = $1400

if sales double, the commis soon will double so $1400 x 2 = $2800

Answer:

[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]

Step-by-step explanation:

So if we first graph the given equation, we'll see the graph I've attached below.

Remember that piecewise functions are functions that change based on the circumstances. I know that sounds super confusing, but it's actually really simple!

In this case, for example, we see the line increasing from -∞ to [tex]0[/tex], and then suddenly going downwards and decreasing. That's a good spot for us to notice because that indicates a change. We notice that the function looks different when [tex]x<0[/tex] or [tex]x>0[/tex]. If you break the function into those two parts, you see that they are just linear equations, but they're only visible when x is either greater than or less than 0.

Now that we notice this pattern, we can find the equation of the lines for both lines.

The points (-3,-8) and (-1,-2) are points on the first line, the one that increases (on the left). We can use those points to find the slope of the first line. Remember the slope equation:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Plug in your points:

[tex]m=\frac{-2-(-8)}{-1-(-3)}[/tex]

[tex]m=\frac{6}{2}[/tex]

[tex]m=3[/tex]

So, the slope of the first line is 3. The y-intercept, looking at the graph, is 1. The equation of the first line is [tex]y=3x+1[/tex]. We'll need this later.

Let's do the same thing for the second line. Just looking at the graph, we can see that this is the same exact line, just with a negative slope. So, the equation for the second line is [tex]y=-3x+1[/tex].

So now we can set up a piecewise function.

[tex]f(x)\left \{ {{3x+1} \atop {-3x+1}} \right.[/tex]

The two functions in the bracket are the two different functions used in this graph. Now we need to figure out where each function is effective. Well, they share a y-intercept. Remember that a true function cannot have two points with the same x value. So the first function is effective to the left of x=0, while the second is effective to the right of x=0. In other words, when [tex]x\leq 0[/tex], [tex]f(x)=3x+1[/tex]. But, when [tex]x>0[/tex], [tex]f(x)=-3x+1[/tex]. Now our piecewise function looks like this:

[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]

And that is our piecewise function for the original function.

I know this is confusing, so please let me know if you have any questions! I hope this helps!

Answer- each width = 10, each length = 21

Explanation: from the question we know that L=2w + 1 and we also know that a rectangle has the perimeter of 62 when we plug it in the equation we will get 62= 2(2w+1+w) we will multiply the 2 now and we will get 62=4w+2+2w we will combine like terms and we will minus two from both sides ending up with 60=6w we will divide six from both sides and we will get w=10 then we will use l=2w+1 to find the length and it will be 21

Answer:

-$114/11 months

Step-by-step explanation:

The price is decreasing which means the number is going down which makes the rate negative