Answer:
Benjamin invested $4,500 at 8%.
Step-by-step explanation:
We know that Benjamin has invested $6,000 in two different accounts.
Let account 1 earn 8% interest per year be defined as [tex]x[/tex] and account 2 earn 7.5% interest per year as [tex]y[/tex].
The sum of both accounts must be $6,000:
[tex]x+y=6,000[/tex]
We also know that at the end of the year Benjamin earned $472.50, which is the sum of the interest he earned of the amount he invested in account 1 and in account 2, with their different interest rates (in this case, it is useful for us to transform the expression of the interest rate by dividing it by 100, so that it can be simplified):
[tex](0.08x)+(0.075y)=472.5[/tex]
We need to express the [tex]y[/tex] in terms of [tex]x[/tex].
From our first expression, we know that:
[tex]y=6,000-x[/tex]
So we substitute this value in our second equation and solve it:
[tex](0.08x)+(0.075(6,000-x))=472.5[/tex]
[tex](0.08x)+((0.075*6,000)-0.075x)=472.5[/tex]
[tex](0.08x)+((0.075*6,000)-0.075x)=472.5[/tex]
[tex]0.08x+450-0.075x=472.5[/tex]
[tex]0.08x-0.075x=472.5-450[/tex]
[tex]0.005x=22.5[/tex]
[tex]x=\frac{22.5}{0.005}[/tex]
[tex]x=4,500[/tex]
This way, we know that the amount that Benjamin invested in the account that earns 8% interest per year is $4,500.
Mr.matt plans to invest 7,500 in a savings account that earns 2.75% simple anual interest.if he makes no deposits or withdrawal ls how much money will his account be worth after 10 years
Six nickel is what Percent of a dollar
PLZZ HELP!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?
formula for volume of a sphere is V=4/3 x pi x R63
if diameter = 16 than radius = 16/2 = 8
so the equation would be 4/3 x pi x 8^3
Answer:
Option [tex]V=\frac{4}{3}\pi (8^{3})\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=16/2=8\ cm[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (8^{3})\ cm^{3}[/tex]
Add 2 then add 4! I dont get it at all plz help!
Paula is given a litre of water during her fitness assessment at the gym she drinks 375 milliliters of water how much is left
The standard error of the estimate, sest, is essentially the
in a grocery store steak cost $3.85 per pound if you buy a three pound steak and pay for it with a $20 bill how much change will you get
The change to be recieved is equal to $8.45
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The price per steak is given as $3.85 per pound.
Thus 3 pound of steak will cost 3×3.85=$11.55
Therefore the change to be recieved is =20-11.55
=$8.45
Hence, The change to be recieved is equal to $8.45
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The table below shows the surface area y in square inches, of a shrinking puddle in x hours
Time (x) (hours) 2 5 8 11
Surface area (y) 25 15 9 2
(Square inches)
Part a- what is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface are puddle. [choose the value of the correlation coefficient from -1,-0.99,-0.5,-0.02]
Part b - what is the value of the slope of the graph of surface area versus time between 5 and 8 hours and what does the slope represent?
Part c- does the data in the table represent correlation or causation?
Answer:
Step-by-step explanation:
Given is a table showing the surface area y in square inches, of a shrinking puddle in x hours
x y
2 25
5 15
8 9
11 2
r -0.993835256
Hence correlation coefficient is option B) -0.99
Part b:
Time Sur area
x y
2 25
5 15
8 9
11 2
r -0.993835256
slope -0.395083406
Intercept 11.53731343
slope =-0.395
Between 5 and 8, slope = [tex]\frac{change in y}{change in x} \\=\frac{9-15}{8-5} \\=-2[/tex]
Slope represents the change of y with respect to 1 unit change in x.
Part c:
Yes correlation strong and negative.
find the x intercepts of the parabola with vertex (5,-12) and y intercept (0,63)
Final answer:
To find the x-intercepts of the parabola with vertex (5,-12) and y intercept (0,63), substitute the vertex values into the equation of the parabola and find the value of the constant. Then, substitute the value of the constant back into the equation and solve for x to find the x-intercepts. The x-intercepts of the parabola are x = 3 and x = 7.
Explanation:
To find the x-intercepts of the parabola with vertex (5,-12) and y-intercept (0,63), we need to find the values of x when y is equal to zero. Since the vertex of the parabola is (5,-12), the equation of the parabola can be written as[tex]y = a(x-5)^2 - 12.[/tex] To find the value of a, we can use the y-intercept (0,63) by substituting the values of x and y into the equation.
[tex]63 = a(0-5)^2 - 12[/tex]
63 = 25a - 12
25a = 75
a = 3
Now that we have the value of a, we can substitute it back into the equation and solve for the x-intercepts:
[tex]0 = 3(x-5)^2 - 12[/tex]
[tex]3(x-5)^2 = 12[/tex]
[tex](x-5)^2 = 4[/tex]
x-5 = ±2
x = 5 ± 2
Therefore, the x-intercepts of the parabola are x = 3 and x = 7.
express the confidence interval 0.38 p 0.54 in the form of p^ ± e
Using the law of sines in ABC, if c =135, b =10 degrees, c =45 find measure of A
Suppose f⃗ (x,y,z)=⟨x,y,4z⟩f→(x,y,z)=⟨x,y,4z⟩. let w be the solid bounded by the paraboloid z=x2+y 2 z=x2+y2 and the plane z=9.z=9. let ss be the closed boundary of ww oriented outward. (a) use the divergence theorem to find the flux of f⃗ f→ through s.
To find the flux of a vector field through a closed boundary using the divergence theorem, calculate the divergence of the vector field and evaluate the triple integral of the divergence over the solid bounded by the boundary. In this case, the flux is 3 times the volume of the solid.
Explanation:The student is asking how to use the divergence theorem to find the flux of a vector field through a closed boundary. In this case, the vector field is defined as f(x, y, z) = ⟨x, y, 4z⟩ and the closed boundary is a solid bounded by the paraboloid z = x^2 + y^2 and the plane z = 9.
To use the divergence theorem, we need to calculate the divergence of the vector field, which is the sum of the partial derivatives of f with respect to each variable. In this case, the divergence is 3.
Then, we can use the divergence theorem to find the flux through the closed boundary by evaluating the triple integral of the divergence over the solid bounded by the paraboloid and the plane. In this case, the flux is 3 times the volume of the solid.
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The flux of [tex]\(\vec{F}\)[/tex] through S is 24π.
To apply the divergence theorem, we first compute the divergence of [tex]\(\vec{F}\)[/tex]:
[tex]\nabla \cdot \vec{F} = \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (4z) = 1 + 1 + 4 = 6.[/tex]
The divergence theorem states that the flux of a vector field through a closed surface is equal to the triple integral of its divergence over the region enclosed by the surface.
Thus, we have:
[tex]\iint_S \vec{F} \cdot d\vec{A} = \iiint_W (\nabla \cdot \vec{F}) \, dV = \iiint_W 6 \, dV[/tex]
The region W is bounded below by the paraboloid [tex]\(z = x^2 + y^2\)[/tex], and above by the plane z = 4.
Converting to cylindrical coordinates, we have:
[tex]\iiint_W 6 \, dV = \int_0^{2\pi} \int_0^2 \int_{r^2}^4 6 \cdot r \, dz \, dr \, d\theta = 24\pi.[/tex]
Chris can be paid in one of two ways. Plan A is a salary of $350 per month, plus a commission of 7% of a sales. pLan B is a salary of $436 per month, plus a commission of 5% of sales. For what amount of sales is Chris better off selecting plan A
F(x) = 9 sin(x) + cot(x), −π ≤ x ≤ π find the interval of increase.
Final answer:
To find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. The interval of increase for the function is (0, π/2) and (π, 3π/2).
Explanation:
In order to find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. Let's first find the derivative of F(x). The derivative of sin(x) is cos(x) and the derivative of cot(x) is -csc^2(x).
So, the derivative of F(x) is 9*cos(x) - csc^2(x). Now, to find where the derivative is positive, we need to find the intervals where 9*cos(x) - csc^2(x) > 0. We can solve this inequality by analyzing the sign changes of the derivative function.
By analyzing the sign changes of 9*cos(x) - csc^2(x), we find that the derivative is positive when x is in the intervals (0, π/2) and (π, 3π/2). Therefore, the interval of increase for the function F(x) = 9*sin(x) + cot(x) is (0, π/2) and (π, 3π/2).
The revenue in dollars of a company that produces jeans can be modlelded by 2x^2+17x-175 the cost In dollars of producing the jeans can be modeled by 2x^2-3x-125 the number of jeans that have been sold is represented by x the profit is the difference between revenue and cost 20x-50 if 75 pairs of jeans are sold what's the company's profit
replace x with 75
20x-50 becomes
20(75)-50
20*75 = 1500-50 = 1450
the profit was $1450
Answer:
B
Step-by-step explanation:
A trinomial that contains the variable k the coefficient of the second degree term is 1, the coefficient of the first degree term is -7 and the constant term is -15 how would you write this?
If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.
Adam is going to cook a turkey for 14 people and wants to allow ¾ lb of turkey for each person.
1lb = 450 g
How much would a turkey cost for 14 people?
Can the side lengths of 12, 15, and 13 form a triangle?
Yes
No
Mount Rushmore is a sculpture that was carved using a model with a scale of 1 in :1 ft. If the model of George Washington’s face was 5 ft, how tall was the face on the actual sculpture? a. 5 ft c. 60 ft b. 40 ft d. 72 ft
The face on the actual sculpture of George Washington’s is 60 feet .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
Mount Rushmore is a sculpture that was carved using a model with a scale factor of 1 in = 1 ft.
As we know
1 feet = 12 inches
i.e
Scale factor is 12 for sculpture .
Now,
The model of George Washington’s face was 5 ft
As Scale factor is 12
So, the face on the actual sculpture
5 * 12 = 60 feet
Hence, the face on the actual sculpture of George Washington’s is 60 feet .
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There are 375 books sold at Sid's Bookstore. The table below summarizes these books by genre. This info is presented in circle graph. Find the central angle measure for Self Help slice in graph. Mystery 99, romance 81, self help 90, cooking 57, biography 48.
The central angle measure for the 'Self Help' slice in the circle graph is 86.4 degrees.
To find the central angle of the 'Self Help' slice in a circle graph (pie chart), we first need to calculate the total number of books sold, which is provided as 375.
We then take the number of 'Self Help' books which is 90, and determine what fraction of the total this represents. The fraction for 'Self Help' books is 90/375. A full circle has an angle of 360 degrees, so we multiply the fraction by 360 to find the central angle for that section of the pie chart.
= (90/375) * 360 = 0.24 * 360 = 86.4 degrees
Thus, the central angle measure for the 'Self Help' slice in the graph is 86.4 degrees.
Solve for x. Show your work.
- x < -12
126 employees is 3% of what number of employees
A wheel makes 5 13/16 revolutions per minute. If it rotates for 76 minutes, how many revolutions does it make?
multiply 5 13/16 by 76
5 13/16 * 76 = 441 3/4 revolutions
If 5(3x-7)=20, then what is 6x-8
5(3x-7) = 20
15x-35 = 20
15x = 55
x = 3.666666
so 6(3.666666) -8 = 13.99999 round to 14
Chin Woo bought a home for $160,000. He put down 20%. The mortgage is a 8 1/2% for 25 years. His yearly payments are?
factor out the polynomial: 12x^2+26x+12
Which statement is true about whether Z and B are independent events?
Z and B are independent events because P(Z∣B) = P(Z).
Z and B are independent events because P(Z∣B) = P(B).
Z and B are not independent events because P(Z∣B) ≠ P(Z).
Z and B are not independent events because P(Z∣B) ≠ P(B).
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
Z and B are independent events
When Z and B are independent events then
P(Z and B) = P(Z) * P(B)
P(Z∣B)= [tex]\frac{P(Z and B)}{P(B)}[/tex]
P(Z∣B)= [tex]\frac{P(Z)*P(B)}{P(B)}[/tex]
We cancel out P(B) on both sides
P(Z|B) = P(Z)
if BD is the midsegment and BD is parallel to to AE, then value of AE is
28.
56.
112.
None of the choices are correct.
A seven
digit number has a 0 in the ones place,as 6 in the tens thousands place,an 8 in the millions place,and fives in each of the remaining places .what is the number