You have $5000 to invest in two different accounts. In order to save the money you need for college, you need to average 6.9% interest. If the two accounts pay 5.5% and 8% interest, how much should you invest in each account?

A) $2400 in 5.5%, $2600 in 8%

B) $2500 in 5.5%, $2500 in 8%

C)$2200 in 5.5%, $2800 in 8%

D) $2800 in 5.5%, $2200 in 8%

Answer:

V =91.125 in ^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the side length

V= 4.5 ^ 3

V =91.125 in ^3

Given : Length of side of a cube = 4.5 inches.

We know that,

Volume of cube = (side)³ cu. units

= (4.5)³ inches³

= 91.125 inches³

Hence,

Volume of a cube = 91.125 inches³

Answer:

-20

Step-by-step explanation:

-Follow PEMDAS.

-2 negatives equal a positive.

-6 + 54/(-9) - 5 - 3

-6 + (-6) - 5 - 3

-12 - 5 - 3

-20

-20

Use PEMDAS

-6- -54/(-9) -5+-3

-6+54/(-9) -5+-3

-6+-6-5-3

-12-5-3

-17-3

-20

Answer:

The error was on the diameter. The tire diameter was supposed to be;

4.6+15+4.6=24.2

The student only includes one sidewall width

Step-by-step explanation:

The question is on circumerence of a tire

Here we apply the formulae for circumference of a circle

C=2 [tex]\pi[/tex]×r or [tex]\pi[/tex] × d where r is the radius of the tire and d is the diameter

Finding d= diameter of rim + sidewall to the right +sidewall to the left

d= 15+4.6+4.6=24.2 inches

r=d/2= 12.1

C=2 ×[tex]\pi[/tex]×r

C=2×3.14×12.1 =75.99 Inches

Answer:

 94.18                            

Step-by-step explanation:

Given in the question a semi circle and a right angle triangle

Step 1

Find the diameter of the semi circle

To find the diameter we will use pythagorus theorem

here,

hypotenuse will be diameter of semicircle

height = 9

base = 4

Plug values in the formula above

diameter = √(9²+4²)

diameter = √97

Step 2

Find radius

Step 3

Area

π(√97/2)²

= 76.18

Step 4

Total surface area = area of circle + area of right angle triangle

                               = 76.18 + 1/2(9)(4)

                               = 94.18

Answer:

2

Step-by-step explanation:

512^(1/9)

Write 512 as power of 2:

(2^9)^(1/9)

Multiply the exponents:

2^(9 × 1/9)

2^1

2

Answer:

2

Step-by-step explanation:

Answer: -0.52

Step-by-step explanation:

From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.

i.e. the value of correlation coefficient must be negative.

Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.

From all the given options -0.52  is the value which is contained in interval  0.40 to 0.59 .

Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52

Answer:

Step-by-step explanation:

Givens

Formula

V = (a * b)/2  * h

Solution

V = (10 * 11)/2   * 10

V = 110/2  * 10

V = 55 * 10

V = 550

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

[tex]A_ {b} = \frac {b * h} {2}[/tex]

Where:

b: It is the base of the triangle

h: It's the height of the triangle

Substituting the values:

[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]

Then, the volume is:

[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]

ANswer:

550

Answer:

x = -2 and y = 2

Step-by-step explanation:

We have the following system of linear equations;

y=x+4

y=-2x-2

To solve the above system, we shall be equating the right hand sides of the two equations since we have y's on the left hand side of both equations;

x + 4 = -2x - 2

add 2x on both sides of the equation;

x + 4 + 2x = -2x - 2 + 2x

3x + 4 = -2

subtract 4 on both sides of the equation;

3x + 4 - 4 = -2 - 4

3x = -6

x = -2

We can use the first equation y=x+4 to determine the value of y;

y = -2 + 4

y = 2

The solution to the system of linear equations is thus;

x = -2 and y = 2

Answer:

A. y = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

For horizontal asymptote, if the degree of numerator is equal to the degree of the denomenator, then we take the ratio of cofficient of highest degree variable

f(x) = [tex]\frac{6}{8}[/tex]

      = [tex]\frac{3}{4}[/tex]

The correct option is A.

The horizontal asymptote of the function f(x)=(6x^3 - 5x - 3)/(8x^3 - 2x + 5) is A. y=3/4. This answer is reached by comparing the degrees and coefficients of the numerator and denominator.

The question posed pertains to determining the horizontal asymptote of the function f(x)=(6x^3 - 5x - 3)/(8x^3 - 2x + 5). The horizontal asymptote of a rational function (a ratio of two polynomials) can be found by comparing the degrees of the numerator and denominator.

In this function, both the numerator and denominator are of the third degree, implying the coefficients of the leading term define the line of the horizontal asymptote. Hence, the horizontal asymptote of this function is y = 6/8 = 3/4 in shorthand.

So, the correct answer to your question, the horizontal asymptote of the given function, is A. y = 3/4.

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Answer:

40 + 20 + 10 + 5 is a geometric series

Step-by-step explanation:

* Lets revise the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Series:

∵ U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

∴ Un = ar^n-1, where a is the first term , r is the constant ratio

  between each two consecutive terms , and n is the position of

  the term in the series

* Now lets check the answers to find the correct one

# 40 + 50 + 60 + 70

∵ 50/40 = 5/4

∵ 60/50 = 6/5

∵ 5/4 ≠ 6/5

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 42 + 44 + 46

∵ 42/40 = 21/20

∵ 44/42 = 22/21

∵ 21/20 ≠ 22/21

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 80 + 40 + 120

∵ 80/40 = 2

∵ 40/80 = 1/2

∵ 2 ≠ 1/2

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 20 + 10 + 5

∵ 20/40 = 1/2

∵ 10/20 = 1/2

∵ 5/10 = 1/2

- There is a common ratio between each two consecutive terms

∴ 40 + 20 + 10 + 5 is a geometric series

Answer:

D 40 + 20 + 10 + 5

Answer:

d

Step-by-step explanation:

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]

+5 is the additive inverse of (-5)

it is so as. -5 +5 =0

Hope it helps...

Regards,

Leukonov.

The additive inverse of a number is what you need to add to the given number to equal 0. This would be the opposite of the given number.

The opposite of -5 would be positive 5.

-5 + 5 = 0

The answer is 5

Answer:

Step-by-step explanation:

45 Mins

Hello There!

First, let me just explain briefly what is an independent variable and a dependent variable.

An independent variable is the variable that changes during an experiment to see if it has an effect on another variable.

A dependent variable is what is being measured in the experiment. It’s also known as outcome or effect.

In this case, the dependent variable is the number of liters of water your drink because that’s what your measuring.

The independent variable is the number of times you drink all the water in your bottle because that changes during the experiment.

Answer: More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.

Step-by-step explanation:

12:00 p.m. to 6:00 p.m: 135 bees

6:00 p.m to 9:00 p.m: 28 bees

b and c is the answer .

Number 7 - Second answer

Number 8 - Third answer

Answer:

-x,y?

Step-by-step explanation:

if it's being reflected across the y-axis then that should go in to the negative side of the graph and the same if its being reflected across the x-axis, in which case it would be x,-y

Answer:

P'(-x,y)

Step-by-step explanation:

The question is asking you to reflect over the y-axis. You pick a random point in the first quadrant and reflect that point over the y-axis. The point will land in the second quadrant and the x-value will have been negated (changed sign).

Ex.

(5,4) would become (-5,4)

P(x,y) reflected over the y-axis P'(-x,y)

Answer:

look at the calculator.

ANSWER

EXPLANATION

We want to graph the inequality:

[tex]3y - 5x \: < \: - 6[/tex]

To this inequality, we must first of all graph the corresponding linear equation:

[tex]3y - 5x = - 6[/tex]

When x=0, we have

[tex]3y - 5(0) = - 6[/tex]

[tex]3y = - 6[/tex]

y=-2

We plot the point (0,-2)

When y=0,

[tex]3(0) - 5x = - 6[/tex]

[tex]x = \frac{6}{5} [/tex]

[tex]( \frac{6}{5} ,0)[/tex]

We plot the points and draw a dashed straight line through them.

We test for (0,0).

[tex]3(0)- 5(0)\: < \: - 6[/tex]

[tex]0 < \: - 6[/tex]

This is false hence we shade the lower half plane. See attachment.

y < -1/2 x + 2

I will try the first-two points. You can then finish.

Let x = 2 and y = 3.

3 < (-1/2)(2) + 2

3 < -1 + 2

3 < 1

False statement. Choice A is not the answer.

Let x = 2 and y = 1

1 < (-1/2)(2) + 2

1 < -1 + 2

1 < 1

False statement. Choice B is not the answer.

Do the same thing with the remaining points. One of the points will make the given inequality a true statement.

The point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

The inequality is given as:

y < 1/2x + 2

Next, we test the options

A. (2, 3)

3 < 1/2 * 2 + 2

3 < 3 ---- false

B. (2, 1)

1 < 1/2 * 2 + 2

1 < 3 ---- true

Hence, the point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

Read more about inequality at:

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It is important to do the same thing to both sides of an equation because in the end, both sides will be equivalent, or equal, therefor making the problem true. If you didn't do the same thing on both sides of an equation, one side would be incorrect and not equal to the other side. Hope this helps! Please mark brainliest. Thank you v much! :)

It's necessary to do the same thing to both sides of an equation to maintain balance and allow valid operations. This basic principle is crucial for solving and simplifying equations in mathematics.

In mathematics, it is necessary to do the same thing to both sides of an equation to perform valid operations. An equation represents a balance; what is done to one side must also be done to the other to maintain this balance. For instance, if you add, subtract, multiply, or divide a value from/to one side of an equation, you have to do the same to the other side. This principle is essential for solving and simplifying equations. For example, in the equation 5x + 3 = 18, to solve for x, you would subtract 3 from both sides, establishing the new equation 5x = 15, maintaining the balance.

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The volume of a cylinder is given by

[tex]V = A_bh[/tex]

Where [tex]A_b[/tex] is the base area and h is the height.

So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have

[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]

Since the height was doubled. We deduce that

[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]

So, if the height is doubled, the volume will double as well.

Answer:

x = 56.7°

Step-by-step explanation:

Sin (x) = Oppo. / Hypo.

Sin (x) = 66/79

Sin (x) = 0.8354

     x = 56.7°

Answer:

x ≈ 56.7

Step-by-step explanation:

In the right triangle with hypotenuse 79 use the sine ratio to find x

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ([tex]\frac{66}{79}[/tex] ) ≈ 56.7

Answer: Option a:

[tex](f * g) (x) = 2x[/tex]

Step-by-step explanation:

The expression [tex](f * g) (x)[/tex] refers to the multiplication of two functions f and g.

In this case we know that the functions are:

[tex]f (x) = x\\\\g (x) = 2[/tex]

Then you must multiply the two functions we get.

[tex](f * g) (x) = f (x) * g (x)\\\\(f * g) (x) = 2 * x\\\\(f * g) (x) = 2x[/tex]

The correct answer is option a.

Answer:

Required system of equation is

4s+3c=26 and 5s+2c=29.

Step-by-step explanation:

Let cost of 1 sundaes = s

Let cost of 1 cone = c

Then statement "Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26", gives equation:

4s+3c=26...(i)

And statement "Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes " gives equation:

5s+2c=29...(ii)

Hence required system of equation is

4s+3c=26 and 5s+2c=29.

Answer:

4s+3c=26

5s+2c=29.

Step-by-step explanation:

Answer:

the required quotient is 173.92

Step-by-step explanation:

If a÷b=c,

then,

a is the dividend

b is divisor

and c is quotient.

By the question,

a=2.26108

b=0.013

c=?

now,

a÷b=c

or, 2.26108÷0.013=c

or, 173.92=c

Answer:

[tex]1.738\cdot 10^{10}[/tex]

Step-by-step explanation:

We are asked to find the the quotient of the division problem, where [tex]2.26\cdot 10^8[/tex] is dividend and 0.013 is divisor.

Represent dividend and divisor as fraction:

[tex]\frac{2.26\cdot 10^8}{0.013}[/tex]

Convert 0.013 into scientific notation:

[tex]0.013=1.3\cdot 10^{-2}[/tex]

[tex]\frac{2.26\cdot 10^8}{1.3\cdot 10^{-2}}[/tex]

Using exponent property [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:

[tex]\frac{2.26}{1.3}\cdot 10^{8-(-2)[/tex]

[tex]\frac{2.26}{1.3}\cdot 10^{8+2}[/tex]

[tex]1.738\cdot 10^{10}[/tex]

Therefore, our required quotient would be [tex]1.738\cdot 10^{10}[/tex].

Answer:

c=$1.59-s

Step-by-step explanation:

Let

s ----> the sale price per pack

c ---> cost savings

we know that

The  equation that represent this situation is

c=$1.59-s

Answer:

25 gallons

Step-by-step explanation:

Given:

total no. of gallons= 50

Percentage of sulfuric acid= 50%

Number of gallons of sulfuric acid= total no. of gallons x Percentage of sulfuric acid

Putting values in above equation:

Number of gallons of sulfuric acid= 50 x 50/100

                                                        = 50 x 1/2

                                                        = 25 !

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, multiply the volume of the solution by the concentration.

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, you can use a simple calculation. The percent concentration represents the fraction of sulfuric acid in the solution, so you can calculate the amount of sulfuric acid by multiplying the volume of the solution by the concentration:

Volume of sulfuric acid = Volume of solution * Percent concentration

Volume of sulfuric acid = 50 gallons * 0.50 = 25 gallons

Therefore, there are 25 gallons of sulfuric acid in the 50-gallon solution.

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Answer:

The value of P( A and B ) is 0.08.

Step-by-step explanation:

When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,

That is, If X and Y are independent events,

Then, P(X∩Y) = P(X) × P(Y),

or P(X and Y) = P(X) × P(Y),

Here, P(A) = 0.40 and P(B) = 0.20,

Hence, P(A∩B) = P(A) × P(B)

= 0.40 × 0.20

= 0.08

The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.

To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:

Step 1: Understand the Concept of Independence

For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.

Step 2: Apply the Independent Event Formula

Since (A ) and (B ) are self-contained,

[tex]P(A) \times P(B) = P(A \cap B)[/tex]

Step 3: Substitute the Given Probabilities

Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]

Step 4: Perform the Multiplication

Calculate the product of 0.40 and 0.20:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]

Step 5: Interpret the Result

The probability that both events ( A ) and ( B ) occur is 0.08.

Therefore, the correct answer is (a) 0.08.

Complete Question:

A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?

A. 0.08

B. 0.60

C. 0

D. 0.80

The answer is:

The average speed for the total trip is 753.19 mph.

To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.

So, calculating we have:

- First distance and speed: 3334 miles at 760 mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]

Therefore, we have that the first distance was covered in 4.39 hours.

- Second distance and speed: 2244.7 miles at 740mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]

Therefore, we have that the second distance was covered in 3.03 hours.

Now, calculating the average speed, we have:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Substuting we have:

[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]

[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]

Hence, we have that the average speed for the total trip is 753.19 mph.

Have a nice day!