What is the simple interest for a principal of $650 invested at a rate of 9% for 5 years?

Answer:

120.

Step-by-step explanation:

If you're asking for LCM the answer is 120.

Answer:

Step-by-step explanation:

3, 5 and 8 are Relatively prime numbers (LCD(3, 5, 8) = 1).

Therefore LCM(3, 5, 8) = 3 · 5 · 8 = 120

If there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase

If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase

1) If the variables x and y have a strong positive correlation, what generally happens to y as x increases?

Let us first understand about strong positive correlation

Given that "x" and "y" has strong positive correlation

Correlation coefficients are used to measure the strength of the relationship between two variables.

Positive correlation:

Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction.  A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

When one variable moves higher or lower, the other variable moves in the same direction with the same magnitude.

Therefore if there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase

2) What if x and y have a strong negative correlation?

Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.

Negative correlation is a relationship between two variables whereby they move in opposite directions.

If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase

Answer:

Explanation:

To find a relationship modeled by the given function it is recommendable to factor it.

The function is:

The first step to factor it is to extract common factor 4x:

The second step is to factor the quadratic trinomial.

That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:

Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

Thus, the volume of the prism is the product of the three factors:

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]

  = [tex]\sqrt{7^2+(-6)^2}[/tex]

  = [tex]\sqrt{49+36}[/tex]

  = [tex]\sqrt{85}[/tex] ← exact distance

Answer:

he other guy is wrong there is no 85

Step-by-step explanation:

Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is. Slope can be found using the ratio [tex]\frac{rise}{run}[/tex] between any two points that are on that line.

To get from one point on the graph to another point, we would rise 2 units which means go up to units and run -1 unit or go across 1 unit to the left.

The variable that is used to represent slope is m. So for this line we would say that m = -2

The base b represents the y-intercept of the line. The of the base as how far we are going up or down on the y-axis. Since we go up 5 units on the y-axis, we have a base of 5 so b = 5.

Remember, slope = rise/run.

We can use the points (-1, 7) and (3, -1) to solve.

_______

Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]

= -1-7/3-(-1)

= -8/4

= -2

_______

The y-intercept is given in the line but let's solve just to check.

y = mx + b

7 = -2(-1) + b

7 = 2 + b

7 - 2 = 2 + b - 2

5 = b

Now, we can see that y-intercept is 5.

_______

After solving for both the slope and y-intercept we can put this into slope-intercept form.

y = mx + b

y = -2x + 5

_______

m = -2

b = 5

_______

Best Regards,

Wolfyy :)

Answer:

C

Step-by-step explanation:

Given the two functions, we need to find

(g ° f)(4)

This means, we need to put the function f(x) INTO the function g(x) and then evaluate that new function at x = 4.

We put the whole expression of f(x) into "x" of g(x). Shown below:

[tex]f(x)=x^2-3\\g(x)=\frac{x+2}{x}\\(gof)(x)=\frac{x^2-3+2}{x^2-3}\\(gof)(x)=\frac{x^2-1}{x^2-3}[/tex]

Now we plug in 4 into x and evaluate:

[tex](gof)(x)=\frac{x^2-1}{x^2-3}\\(gof)(4)=\frac{4^2-1}{4^2-3}\\(gof)(4)=\frac{15}{13}[/tex]

Thus,

correct answer is C

Answer:

[tex]\large\boxed{0.00003400=3.4\cdot10^{-4}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot 10^k[/tex]

where

[tex]1\leq a<10,\ k\in\mathbb{Z}[/tex]

[tex]0.0003400=0\underbrace{.0003}_{4\to}4=3.4\cdot10^{-4}\\\\0.00034=3.4:10000=3.4:10^4=3.4\cdot\dfrac{1}{10^4}=3.4\cdot10^{-4}\\\\\text{used}\ a^{-n}=\dfrac{1}{a^n}[/tex]

Let the number of rectangles = R

Perimeter is 2(L) + 2(W)

The length remains the same when you add more triangles ( 6).

The width changes by multiplying the width by the number of rectangles.

Since the width of the rectangles are 1, multiply the number of rectangles R by 1 to get R.

Now replace W in the perimeter frmula with R:

Now the perimetr would be: P = 2L + 2R

Answer:

8,16,24,32,48

Step-by-step explanation:

When dividing a number by 7, only 7 different remainders are possible.

The remainders when dividing by 7 can not exceed 6, so the numbers in which we are interested can be represented as 7k+k or just 8k, where k=1, 2, ... , 6.

Answer:

8, 16, 24, 32, 40, 48

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]9(2x+1)-4(x-6)=6(2x+1)+5(x-6)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(9)(2x)+(9)(1)+(-4)(x)+(-4)(-6)=(6)(2x)+(6)(1)+(5)(x)+(5)(-6)\\\\18x+9-4x+24=12x+6+5x-30\\\\\text{combine like terms}\\\\(18x-4x)+(9+24)=(12x+5x)+(6-30)\\\\14x+33=17x-24\qquad\text{subtract 33 from both sides}\\\\14x+33-33=17x-24-33\\\\14x=17x-57\qquad\text{subtract}\ 17x\ \text{from both sides}\\\\14x-17x=17x-17x-57\\\\-3x=-57\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-57}{-3}\\\\x=19[/tex]

The completed table shows that the product of wavelength and frequency (k) is approximately constant for X-rays, radio waves, green light, and UV rays. Here are the final values for a, b, c, and d: [tex]a = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ b = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ c = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.[/tex]

To determine if wavelength varies inversely with frequency, we can use the formula [tex]\(k = \text{wavelength} \times \text{frequency}\).[/tex]. Rearranging this formula to solve for k, we get [tex]\(k = \frac{1}{\text{frequency}} \times \text{wavelength}\)[/tex].

Now, we can calculate the values of k for each type of radiation:

[tex]\[a = \frac{1}{3 \times 10^{18}} \times (1 \times 10^{-10}) = \frac{1}{3} \times 10^{-28} \, \text{m/s}.\]\[b = \frac{1}{3 \times 10^9} \times (1 \times 10^{-1}) = \frac{1}{3} \times 10^{-10} \, \text{m/s}.\]\[c = \frac{1}{5 \times 10^{11}} \times (600 \times 10^{-6}) = \frac{1}{3} \times 10^{-8} \, \text{m/s}.\]\[d = \frac{1}{7.5 \times 10^{14}} \times (4 \times 10^{-7}) = \frac{4}{30} \times 10^{-21} \, \text{m/s}.\][/tex]

Now we express the values in terms of [tex]\(10^8\)[/tex]:

[tex]\[a = \frac{1}{3} \times 10^{-20} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{-2} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{0} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{4}{30} \times 10^{-13} \, \text{m/s} = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]

So, the completed table is as follows:

[tex]\[a = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]

Answer:

y= 1/2x-1

Step-by-step explanation:

The equation of a line is y= mx+c

m represents the slope of the line

c represents the y-intercept

So we plug in our information into the equation.

The slope is 1/2 so y= 1/2x + c

The line crosses at (0,-1) which makes -1 the y-intercept as the line crosses at this point on the y-axis.

Therefore, y= 1/2x-1

To write an equation for a line with a slope of 1/2 that crosses the y-axis at the point (0,-1), we can use the slope-intercept form of a linear equation, y = mx + b. Substitute the given values into the equation to get y = (1/2)x - 1.

To write an equation for a line with a slope of 1/2 that crosses the y-axis at the point (0,-1), we can use the slope-intercept form of a linear equation, which is y = mx + b.

Here, 'm' represents the slope and 'b' represents the y-intercept.

Since the slope is 1/2 and the y-intercept is at (0,-1), we can substitute these values into the equation to get y = (1/2)x + (-1) or y = (1/2)x - 1.

This equation represents a line with a slope of 1/2 and crosses the y-axis at the point (0,-1).

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I believe 50% of 284 =142

Answer:

284/50*100 = 586 or simply double 284

Step-by-step explanation:

Answer: 24/55

Step-by-step explanation:

multiply both numerators and denominators

6/11 × 4/5 = 24/55

Answer:

7960

Step-by-step explanation:

4000+99*40

4000+3960

7960

Answer:

A

Step-by-step explanation:

I just did it

Based on the above description, the areas of triangle ABC and DEF  is compared to The area of △ABC is equal to the area of △DEF.

Looking at the image show:

The area of  △ABC

= 4 x 3 x 1/2

=6

The  area of  △DEF

= 6 x 2 x 1/2

= 6

Therefore, from the above, the areas of triangle ABC and DEF  is compared to The area of △ABC is equal to the area of △DEF.

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A(-2,-4), B(-4,-2), C(-6,-4)

Translating by (2,3) adds 2 to the x and 3 to the y so gives

A'(0,-1), B'(-2,1), C'(-4, -1)

Reflecting in x=0 (the y axis) keeps the ys the same but negates the xs

A''(0,-1), B''(2,1), C''(4,-1)

I'll leave the drawing to you.

Answer:

ivan will

Step-by-step explanation:

16mph

16/3=5.333

60/3=20minutes

so instead of 5 miles in 20 minutes like pedro ivan did 5.333 repeating

Answer:

If the company produce and sell 'x' no. of thing-a-ma-bob , then

C(x) = $ (8809 + 2.05x)

R(x) = $ 4.92x

To make a profit the company must produce and sell at least 3070 thing-a-ma-bobs.

Step-by-step explanation:

If the company produces and sells "x" no. of thing-a-ma-bob, then,

the cost function is given by,

C(x) = $ (8809 + 2.05x) ------------------------(1)

The revenue function is given by,

R(x) = $ 4.92x -------------------------------------(2)

If C(x) = R(x), then,

4.92x = 8809 + 2.05x

⇒ 2.87x = 8809

⇒ x = [tex]\frac {8809}{2.87}[/tex]

⇒ x [tex]\simeq [/tex] 3069.34

So, to make a profit the company must produce and sell at least 3070 thing-a-ma-bobs.

Answer:

515

Step-by-step explanation:

If it's a multiple of five and not ten, that would be the units digit must be 5. Hundreds=units. 11-10=1. So the answer is 515

The number is a multiple of 5 but not 10, with the units and hundreds digits being the same and their sum being 11. Therefore, the number is 505.

This question can be solved by analyzing the given clues. The number is a multiple of 5 but not 10, so it cannot end in 0. The units and hundreds digits are the same, meaning they both have to be a single digit number. Additionally, the sum of the three digits is 11.

Since the units and hundreds digits are the same, and their sum is 11, they both must be equal to 5. Thus, the number is 505.

If Jerri decides to make four small cakes out of a large cake recipe, she should divide the quantity of the required ingredient (in this case, cinnamon) by 4. Hence, for each small cake, she should use 1/12 of a tablespoon of cinnamon.

The recipe Jerri is working with requires one-third of a tablespoon of cinnamon for a large cake. If she decides to use the same recipe to make four small cakes, she should divide the quantity of the cinnamon by 4, as the four smaller cakes together will make up the same quantity/volume as the one large cake.

The calculation can be done as follows: (1/3) tablespoon of cinnamon divided by 4 equals 1/12 tablespoon. Therefore, for each smaller cake, Jerri should use 1/12 of a tablespoon of cinnamon.

The correct answer is (A) 1/12 of a tablespoon.

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Answer:

see explanation

Step-by-step explanation:

Given

8x - 6 > 12 + 2x ( subtract 2x from both sides )

6x - 6 > 12 ( add 6 to both sides )

6x > 18 ( divide both sides by 6 )

x > 3

Any value of x greater than 3 will be in the solution set

Answer:

120 Grams.

Step-by-step explanation:

In the illustration, the dial is on 30 grams as the increments increase by 5 grams per tick mark. Taking this info, we can say that since the eggs have the same mass then 30 × 4 is equal to 120 grams.

The system of equations -3x + 3y = 9 and 2x - 7y = -14 belongs to the branch of math called Algebra. You can solve the system using methods like substitution or elimination. The solution for the system is x = -2, y = 1.6.

The given equations are part of the math branch known as Algebra, specifically a system of linear equations. The system consists of the following equations:

-3x + 3y = 9 and 2x - 7y = -14

To solve for x and y, you use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2 and the second equation by 3:

-6x + 6y = 18 and 6x - 21y = -42

Then, sum both equations (this will cancel the x variable, leading to a single equation with y):

-15y = -24

Finally, divide by -15 to solve for y, which gives y = 24/15 or 1.6. Substituting y into the first equation gives x = -2.

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Answer: y = 4.88 + 0.525x

The equation of the line of best fit for the data shown in the picture is y=0.894x+0.535

A straight line is a combination of endless points joined on both sides of the point.

We have a data in the table:

Let's suppose the equation for the line is:

y = mx + c

Where m is the slope of the line and c is the y-intercept.

The value of m is given by:

[tex]\rm m = \frac{S_{xy}}{S_{xx}} }[/tex]    and

[tex]\rm S_{xy} = \sum_{i=1}^{n}x_iy_i-\frac{(\sum_{i=1}^{n}x_i)(\sum_{i=1}^{n}y_i)}{n}[/tex]

[tex]\rm S_{xx} = \sum_{i=1}^{n}x_i^2-\frac{(\sum_{i=1}^{n}x_i)^2}{n}[/tex]

From the table(data is not mentioned we have assumed the data) the values of  [tex]\rm \sum_{i=1}^{n}x_iy_i= 415[/tex], [tex]\rm {\sum_{i=1}^{n}x_i= 44[/tex], [tex]\rm {\sum_{i=1}^{n}y_i= 42[/tex],

[tex]\rm {\sum_{i=1}^{n}x_i^2= 438[/tex], and n = 5.

[tex]\rm S_{xy}= 415-\frac{44\times42}{5} \Rightarrow 45.4\\\\\rm S_{xx}= 438- \frac{44^2}{5} \Rightarrow 50.8[/tex]

[tex]\rm m = \frac{45.4}{50.8} } \Rightarrow 0.8937 \approx0.894[/tex]

For c we have to calculate the means of x and y for this:

[tex]\rm \bar{x} = \frac{\sum x}{n} \Rightarrow \frac{44}{5} \Rightarrow8.8[/tex]

[tex]\rm \bar{y} = \frac{\sum y}{n} \Rightarrow \frac{42}{5} \Rightarrow8.4[/tex]

Now, put the above values in the equation of a line to find the value of c

8.4 = (0.894)(8.8)+c

c = 0.5328 ≈ 0.535

Now the line is y = 0.894x+0.535

Thus, the line of best fit for the data shown in the picture is y=0.894x+0.535

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Answer:

8 liters of 15% solution and 72 liters of 65% solution

Step-by-step explanation:

If x is the liters of 15% solution, and y is the liters of 65% solution, then:

x + y = 80

0.15x + 0.65y = 0.60(80)

Solve the system of equations with substitution or elimination.  Using substitution:

0.15x + 0.65(80 − x) = 0.60(80)

0.15x + 52 − 0.65x = 48

4 = 0.5x

x = 8

y = 72

You need 8 liters of 15% solution and 72 liters of 65% solution.

8 liters of the 15% solution and 72 liters of the 65% solution are required.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

If x is the liters of 15% solution, and y is the liters of 65% solution, then:

x + y = 80

0.15x + 0.65y = 0.60(80)

Use substitution or elimination to solve the mathematical model. Using a substitute

0.15x + 0.65(80 − x) = 0.60(80)

0.15x + 52 − 0.65x = 48

4 = 0.5x

x = 8

y = 72

8 liters of the 15% solution and 72 liters of the 65% solution are required.

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Answer:

x = 26    m∠DAB =  80°      m∠ADC = 100°

Step-by-step explanation:

Given,

ABCD is a parallelogram in which AB ║ DC and AD║ BC.

m∠DAB = 4x-24  

m∠ADC = 2x+48

Solution,

Since ABCD is a parallelogram so sum of two consecutive angle is 180°.

[tex]m\angle DAB+m\angle ADC=180\°\\4x-24+2x+48=180\°\\6x+24=180\°\\6x=180-24\\6x=156\\x=\frac{156}{6}=26[/tex]

Now substituting the value of x we get the value of ∠DAB and ∠ADC .

[tex]m\angle DAB=4x-24=4\times26-24=104-24=80\°[/tex]

[tex]m\angle ADC=2x+48=2\times26+48=52+48=100\°[/tex]

Thus the value of x is 26 and m∠DAB is 80° and m∠ADC is 100°

Answer:

280

Step-by-step explanation:

Answer:280

Step-by-step explanation:

From 240 to 260 you add 20 each time so 260 plus 20 will give us the answer (280)

Answer:

$343

Step-by-step explanation:

To get 30% of 490 we divide 30% by 1

30% ÷ 1 = 147

Now, we subtract 490 by 147

490 - 147 = 343

Answer:

0.5x + 7.5 / (x + 6)

Step-by-step explanation:

Let x be the number of wooden beads

wooden bead = $0.50 each

glass bead = $1.25 each

since average cost of bead = (cost of wooden bead + cost of glass bead)/ total number of beads

equation is (0.5x + (6*1.25))/(x + 6)

The model equation is therefore 0.5x + 7.5 / (x + 6)