$17,818 is invested, part at 11% and the rest at 6%. If the interest earned from the amount invested at 11% exceeds the interest earned from the amount invested at 6% by $490.33, how much is invested at each rate? (Round to two decimal places if necessary.)

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

Answer:

16

Step-by-step explanation:

It’s a ratio.

x/12=21/28

21x=12*28

21x=336

x=336/21

x=16

Answer:

The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]

The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]

So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Step-by-step explanation:

First we need to find out what they all 3 equal, with multiplication.

5×5=25

10×5=50

20×5=100

In each of these problems, the answer is multiplying itself by 2 in order to get to the next answer. So this is how they are related

No piece of information is supplied to choose from ; However, the requirements for the test statistic of the hypothesis in question is given below.

Answer:

Kindly check explanation

Step-by-step explanation:

The hypothesis in the question above which is to be tested is a one sample proportion test ;

The test statistic formula for a one sample proportion test is given as :

Test statistic = (Phat - P) / √[P(1 - P) / n] ;

Where;

Phat = sample proportion

P = population proportion

n = sample size

Sample proportion = x / n ;

Therefore, once the parameters (Sample proportion, population proportion and sample size are given) then obtaining the test statistic is possible.

Answer:

(x+5, y-5) is the correct answer

Step-by-step explanation:

first, take -2 and 3 on x value; when you jump from -2 to 3, your answer is positive 5

second, take 4 and -1 on y value; when you jump from 4 to -1, your answer is negative 5

hence your answer for this question is a- (x+5, y-5)

Answer:

ABC = 148, 3*148 = 444

Step-by-step explanation:

We know that 111 = 3*  37, so all numbers of the form BBB has the factor 37.

So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.

Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.

So ABC is 148.

9514 1404 393

Answer:

  0.17 and 0.18

Step-by-step explanation:

Usually, a question like this asks for two integer values that bound the root. Here, those would be 0 and 1.

  √(3/100) = (√3)/10 ≈ 0.17320508...

You can truncate this at any point to find a number lower than √.03, then add 1 to that value's least-significant digit to find a number higher than √.03.

For example, if we use 4 digits, the two numbers bounding the root could be ...

  0.1732 and 0.1733

Answer:

probability of picking white is 6/10

and probability of picking orange is 4/10

Step-by-step explanation:

so probability of picking 2 white and 3 orange will be 9/25 + 64/100 = 8/125

Answer:

1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]

Step-by-step explanation:

1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]

[tex]5\cdot x - x = 5\cdot a + a[/tex]

[tex]4\cdot x = 6\cdot a[/tex]

[tex]x = \frac{3}{2}\cdot a[/tex]

b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]

[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]

[tex]x = 5-3\cdot a[/tex]

c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]

[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]

[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]

[tex]-x = a[/tex]

[tex]x = -a[/tex]

d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]

[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]

[tex]2\cdot x = 5\cdot a[/tex]

[tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]

[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]

[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]

[tex]3\cdot x +6 +5\cdot x = 0[/tex]

[tex]8\cdot x = - 6[/tex]

[tex]x = -\frac{3}{4}[/tex]

b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]

[tex]7\cdot x = 5\cdot (x-2)[/tex]

[tex]7\cdot x = 5\cdot x -10[/tex]

[tex]2\cdot x = -10[/tex]

[tex]x = -5[/tex]

c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]

[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]

[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]

[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]

[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]

[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]

[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]

[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]

[tex]-9\cdot x = -27[/tex]

[tex]x = 3[/tex]

Answer:

A Maybe

Step-by-step explanation:

Cogntive identification

Unable to answer mathematically or analytically

The Plan of the solid shape is shown by : (A)

A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.

A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.

solid shapes can take up space in the universe because they are more tangible and realistic.

In conclusion, the Plan of the solid shape is shown by : (A)

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Answer:

77:44

Step-by-step explanation:

Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.

Answer:

yes number 7 is included in this interval .

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

Answer:

the real answer is: 4493.75472

BUT for ESTIMATION STRATEGY it is: 4500

Step-by-step explanation:

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

Greetings from Brasil...

In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.

The translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

→ Vertical

F(X) + k ⇒ k units up

F(X) - k ⇒ k units down

In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.

F(X) = X³

4 units horizontal to the left: F(X + 4)

3 units vertical to the bottom: F(X + 4) - 3

So,

F(X) = X³

The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted

Every modification may be a part of a function's transformation.

Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).

If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:

Vertical shift, often known as phase shift:

Y=f(x+c) with a left shift of c units (same output, but c units earlier)

Y=f(x-c) with a right shift of c units (same output, but c units late)

Vertical movement:

Y = f(x) + d units higher, up

Y = f(x) - d units lower, d

Stretching:

Stretching vertically by a factor of k: y = k f (x)

Stretching horizontally by a factor of k: y = f(x/k)

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) = x³

And , the transformed function has coordinates as A ( -4 , -3 )

So , when function is shifted 4 units to the left , we get

g' ( x ) = ( x + 4 )³

And , when the function is shifted vertically by 3 units down , we get

f ( x ) = ( x + 4 )³ - 3

Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3

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Answer:

The percentage is  k  =  2.3%

Step-by-step explanation:

From the question we are told that

  The  population mean is  [tex]\mu = 47[/tex]

    The  standard deviation is  [tex]\sigma = 14[/tex]

Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the  percent of the fourth grade students receive a prize is mathematically represented as

     [tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]

Generally

     [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

   [tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]

   [tex]P(X > 75) = P(Z > 2)[/tex]

From the standardized normal distribution table  

      [tex]P(Z > 2) =0.023[/tex]

=>   [tex]P(X > 75) = 0.023[/tex]

The  percentage of the fourth grade students receive a prize is  

  k =  0.023 * 100

   k  =  2.3%

Answer:

The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"

Step-by-step explanation:

Given:

[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex]   [tex]_{where} \ \ n \geq 1[/tex]

In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]

[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]

square the above value:

[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]

[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]

Answer:

5 big sleds and 1 small sled

Answer:

|b|= 4b+15

-b=4b+15

-b-4b= 15

-5b= 15

b= 15/-5

b= -3

the ans -3

If [tex]a<0[/tex] the [tex]|a|=-a[/tex]

So

[tex]|b|=4b+15\\-b=4b+15\\5b=-15\\b=-3[/tex]

Hello There!!

I'm not a 100% sure this right.

Step-by-step explanation:

f(x)=ax2+bx+c for which f(1)=0, f(-2)=6 and f(2)=-14

0 = a +b +c

6 =4a -2b +c

-14=4a+2b +c

subtract third equation from second to get

20 = -4b and so b=-5

first equation is now 5 = a+c

second is now -4=4a+c

subtract to get -9=3a and so a=-3

equation one now is 0=-3-5+c or c=8 Hope This Helps!!

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

Answer:

point A is the rays endpoint

Step-by-step explanation:

Answer:

The "endpoint" of a ray is the origin point of the ray, or the point at which the ray starts.

Step-by-step explanation:

A ray starts at a given point, the endpoint, and then goes in a certain direction forever ad infinitum.  The origin point of a ray is called "the endpoint".

Cheers.

Answer:

[tex]\huge\boxed{n = 108\ nickels}[/tex]

Step-by-step explanation:

Let the nickels with Katy be n

So, the condition is

n = 6 (Shaun nickels)

While Nickels of Shaun = 18 , So

n = 6 (18)

n = 108 nickels

Answer:

This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.

Step-by-step explanation:

The hypothesis testing technique is used to test an assumption regarding population parameter. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. A right tailed test is where the most of data is in the right side. This is one tailed test where the direction is specified.

Answer:

The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers

Step-by-step explanation:

IQR of trail mix data = 105 - 90 = 15

The range of cracker data = 100 - 70 = 30.

Therefore, the first option is NOT TRUE.

To check if option 2 is correct, calculate the lower limit to see if 70 is below the lower limit. If 70 is below the lower limit, then it is an outlier in the trail mix data.

Thus, Lower Limit = [tex]Q_1 - 1.5(IQR)[/tex]

Q1 = 90,

IQR = 105 - 90 = 15

Lower Limit = [tex]90 - 1.5(15)[/tex]

Lower Limit = [tex]90 - 22.5 = 67.5[/tex]

70 is not less than the lower limit, therefore, 70 is not an outlier for the trail mix data. The second option is NOT TRUE.

The upper quartile of the trail mix data = 105.

The maximum value of the cracker data = 100.

Therefore, the third option is NOT TRUE.

Range can be used to determine how much variable there is in a data represented on a box plot. The greater the range value, the greater the variation.

Range of trail mix data = 115 - 70 = 45

Range of cracker data = 100 - 70 = 30.

The range value for the number of calories in trail mix is greater than that for cracker, therefore, the number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers.

The fourth option is TRUE.

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

  C)  549 km²

Step-by-step explanation:

The area of the regular pentagon is given by ...

  A = (1/2)Pa

where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.

The lateral area is the product of the perimeter and the height:

  LA = Ph

Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...

  total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)

  = (45 km)(6 km +6.2 km) = 549 km^2

Answer:

x = 3, y = 4

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.