Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 8 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 2920 dollars. How much did she invest at each rate? Amount invested at 6 percent interest is $ Jolene invests her savings in two bank accounts , one paying 6 percent and the other paying 8 percent simple interest per year . She puts twice as much in the lower - yielding account because it is less risky . Her annual interest is 2920 dollars . How much did she invest at each rate ? Amount invested at 6 percent interest is $​

Answer:

24

Step-by-step explanation:

[tex]8 * \frac{x}{8}=3 * 8[/tex]

x = 24

Answer:

24

Step-by-step explanation:

Let the number we are looking for = [tex]x[/tex].

∴ According to the question:

[tex]x[/tex] ÷ 8 = 3

• Multiply both sides by 8:
[tex]x[/tex] = 8 x 3

[tex]x[/tex] = 24

Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time will be calculated by using the relative speed concept.

Relative speed = Speed of father - Speed of Tommy

Relative speed = 1.65 - 1.35

Relative speed = 0.3 meter per second

Relative speed = Distance / Time

0.3 = 720 / Time

Time = 720 / 0.3

Time = 2400 seconds = 2400/ 60 = 40 minutes

We know that both departed at 3 pm they will meet at 3:40 pm.

Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

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Answer:

They will meet at 3:04 p.m

Step-by-step explanation:

Since they are walking toward each other, that means we should add their speed together:

speed = 1.35 m/s + 1.65 m/s

          = 3 m/s

Now that we have found the speed, we can calculate the time:

time = 720 meters / 3 m/s

      = 240 seconds

      = 4 minutes ( 240 seconds is 4 minutes)

Answer:

3.2 km

Step-by-step explanation:

4cm÷5km=0.8 per cm to km

4km×0.8 km=3.2 km represents

Answer:

3.2 km

Step-by-step explanation:

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

[tex]x=\frac{(4)(4)}{5} =\frac{16}{5} =3.2[/tex]

Hope this helps

Answer:

i think this is the answers

Step-by-step explanation:

-13.78xy

The category in the pie chart that was chosen by 1/8 of those that were surveyed is documentary.

From the pie chart, it can be seen that comedy and drama have the highest fraction as they have 1/4 each.

Therefore, the percentage of those who choose comedy or drama will be:

= (1/4 + 1/4) × 100

= 2/4 × 100

= 50%

Lastly, if 24% chose news, the others that choose others will be:

= 1/3 × 24

= 8%

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Answer:

AB = 11 units

Step-by-step explanation:

a given ratio also tells us how many equally sized units there are in the whole (in this case the line).

the ratio 4:7 tells us therefore, that from the whole line 7 ratii units (of 7+4 = 11 ratio units) are on the side of CB.

4 ratio units (of the 11 ratio units) are on the side of AC.

AC is the distance between A and C.

that is

0.6 - -3.4 = 0.6 + 3.4 = 4 line units

aha ! the distance is 4 units on the number line, and the ratio tells us that AC is 4 ratio units.

so, line unit and ratio units are 1:1 the same.

that means that CB with 7 ratio units is then also 7 line units long.

so, the whole line AB is then 4 + 7 = 11 line units long.

Answer:

11 units

Step-by-step explanation:

correct on plato

Answer:

If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

Answer:

C  - 22

Step-by-step explanation:

Put in '3 ' for 'x' in both of the equations....then multiply the results together

f(3)  = 3 (3)^2 - 5 = 22

g(3) =  -1

22 * -1  = -22

To solve for f(3)g(3):

* We know fg(x) means we need to multiply f with g replacing all x's with the x-value given

-22 is the answer

Hope it helps!

Answer:

The length of the shortest side of the pentagon would be:

40.2

For the given systems we have:

1) Swap the right sides of both equations in system A.

2) No, the systems are not equivalent systems.

The two systems are:

A:

-10x - 4y = 0

-2x + 7y = 8

B:

-10x - 4y = 8

-2x + 7y = 0

Notice that the only different thing between the systems is that the right sides are inverted. So, if we invert the right side of A, we will get system B.

2) Are the systems equivalent?

No, the systems are not equivalent because to go from system A to system B we only modified the right side of system A, the systems would be equivalent only if modifying both sides of A gave system B, but this is not the case.

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The arguments are valid therefore F  F →T

A truth table is a mathematical table which shows the truth values for a given set of arguments and tells if the argument is valid or invalid.

Analysis:

Argument 1( P)= if a person is on this reality show(true) T

Argument 2(Q) = the person is self absorbed true(T)

Laura is not self absorbed = False(≈Q)

Laura wont be on the reality show = False(≈P)

So she can only be on the reality show if she is self absorbed else she cannot.

so F F → T

Which means that the argument is valid.

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Answer: 1.9 inches

Step-by-step explanation:

- the equation to find the volume of a cylinder is V = π r^2 h

- so we can just change this equation around to H = V / π r^2

- so H = 384/ π 8^2 = 1.91 or 1.9

hope this helps :)

Final answer:

The value of the expression is 31.

Step-by-step explanation:

Substitution is a process of putting the values of variable in the expression.

Given: p=17 and q=3

To find: value of 2p-q

We will substitute the values and simplify.

Putting the values of variables in the expression as

2p-q = 2x17-3 =34-3 = 31

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[tex]\large\text{Hey there!}[/tex]

[tex]\large\textbf{What does your current question look like?}[/tex]

[tex]\mathsf{2p - q}[/tex]

[tex]\large\textbf{How will we make the question easier to solve?}[/tex]

[tex]\mathsf{2p - q}[/tex]

[tex]\mathsf{= 2(17) - 3}[/tex]

[tex]\mathsf{= 34 - 3}[/tex]

[tex]\mathsf{= 31}[/tex]

[tex]\large\textbf{What is the \boxed{overall} answer?}[/tex]

[tex]\large\boxed{\mathsf{17}}\large\checkmark[/tex]

[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]

Step-by-step explanation:

in such a case the easiest approach might be using the point-slope form of a line equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

so, in our case that would be

y - 8 = 8(x - 4)

simplified this would be

y - 8 = 8x - 32

y = 8x - 24

FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).

Answer:

v240

Step-by-step explanation:

Answer: All real numbers

Step-by-step explanation:

I assume you meant [tex]y=5.3^x[/tex].

In this case, the domain is the set of real numbers, as is with most standard exponential functions.

Answer:

n = 4

Step-by-step explanation:

[tex]\frac{n}{6} =\frac{24}{36}[/tex]

cross multiply

24*6 = 144

n * 36 = 36n

144 = 36n

divide both sides by 36

n = 4

answer is D

n=4

simplify the fraction on the right to get 4/6

n/6 = 4/6

since denominators are same, you can cancel those

therefore, your answer will be n=4

Answer:

[tex]9^{28}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](9^7)^{4}[/tex] = [tex]9^{7(4)}[/tex] = [tex]9^{28}[/tex]

The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.

The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:

[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]

From the given equation:

P = 0.006A² - 0.02A + 120

where;

128 =  0.006A² - 0.02A + 120

= 0.006A² - 0.02A + 120 - 128

= 0.006A² - 0.02A - 8

where:

[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]

[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]

= 38.2195 or -34.8862

Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.

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Answer:

9.00,9.20,9.30

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

Find 5y-3 , given -3y - 8 = 7.

First, we will multiply -3y - 8 = 7 by [tex]-\frac{5}{3}[/tex] to get 5y first.

[tex]-\frac{5}{3} (-3y-8)=-\frac{5}{3} (7)\\5y+\frac{40}{3} =-\frac{35}{3} \\[/tex]

Now we will get the constant on the left side of the equation to 3.

[tex]5y+\frac{40}{3} -\frac{40}{3} =-\frac{35}{3} -\frac{40}{3} \\5y=-25\\5y-3=-25-3\\5y-3=-28[/tex]

Answer:

It's A 48,736

Step-by-step explanation:

Answer:

48,856.11

Step-by-step explanation:

Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.

[tex]A=(40000)e^{0.025*8}[/tex]

Multiply inside the exponent

[tex]A=(40000)*e^{0.2}[/tex]

raise e to the power of 0.2

[tex]A\approx40000*1.221[/tex]

Multiply

[tex]A=48,856.11[/tex]

Answer:

Step-by-step explanation:

C=(10,-1)

D=(-6,3)

[tex]mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1[/tex]

mid point=(2,1)

The midpoint of line segment CD is M = (2, 1).

We have,

To find the midpoint of the line segment CD, we can use the midpoint formula:

M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)

Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:

M = ((10 + (-6))/2, (-1 + 3)/2)

= (4/2, 2/2)

= (2, 1)

Therefore,

The midpoint of line segment CD is M = (2, 1).

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The range of x-values extrapolation occurs in between x < 0 and x > 6

We have given that,

On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).

The Range is the difference between the lowest and highest values.

Therefore we can conclude that the,

range of x-values extrapolation occurs in between x < 0 and x > 6.

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The value of the given complex number is -1

Given the polar form of a complex number expressed as:

[tex](cos\theta + isin\theta)^n\\[/tex]

This can also be expressed according to the de moivre's theorem as;

[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]

Given the expression below;

[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]

Hence the value of the given complex number is -1

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The equation of the quadratic function shown in the graph y - 8 = -2(x + 1)².

The vertex of this parabola is (-1, 8).  It opens downward, so the x² term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or.y - 8 = a(x + 1)².

Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)² or a = -2

The desired equation is y - 8 = -2(x + 1)^2

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The solution to the system of equations is: (1, -8).

The solution is the coordinate of the point where both lines of the equations meet.

Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:

3y = 6x - 30

y = 6x/3 - 30/3

y = 2x - 10 --> eqn. 1

Find the slope (m) and y-intercept (b) of the first graphed equation:

Slope (m) = change in y/change in x = rise/run = -4/2 = -2

The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.

The first equation would be: y = -2x - 6 ---> eqn. 2

Subtract eqn. 2 from eqn. 1 to eliminate x

y = 2x - 10 --> eqn. 1

y = -2x - 6 ---> eqn. 2

2y = 0 - 16

2y = -16

y = -16/2

y = -8

Substitute y = -8 into eqn. 1 to find x:

-8 = 2x - 10

-8 + 10 = 2x

2 = 2x

2/2 = x

1 = x

x = 1

The solution is therefore: (1, -8).

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Answer: (1.-3), (-1,-5)

Step-by-step explanation:

Substituting the x coordinates into the equation, we get that the result is equal to the y coordinate of the points.

Thus, the points lie on the line.

The given graph is a function.

The correct option is (B).

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

As we draw the vertical line then for one input x there is one output.

Hence, the given graph is function.

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