Based on the calculation below, the amount of cash that the Smith and Jones manufacturing company kept in the bank was $500,000.
How do we calculate amount kept in the bank?Let x represents the amount of cash that Smith and Jones manufacturing company has.
Therefore, we have:
Interest amount from bank = Cash * A third * Bank interest rate = x * (1/3) * 0.5% = x0.0017
Interest amount from long-term investments = Cash * Two-third * Long-term investments interest rate = x * (2/3) * 3.5% = x0.023
Total interest earned = Interest amount from bank + Interest amount from long-term investments = $37,500 ...................... (1)
Substituting all the relevant values into equation (1) and solve for x, we have:
x0.0017 + x0.023 = $37,500
x0.025 = $37,500
x = $37,500 / 0.025
x = $1,500,000
Amount kept in the bank = Cash * A third = $1,500,000 * (1 / 3) = $500,000
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Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
The required coordinates are
Q'(-8, -9)
R'(-8, -1)
S'(-1, -10)
What is coordinate?
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.
You want the coordinates of Q', R', and S' after rotating figure QRS 90° CCW. You are given Q(-9, 8), R(-1, 8) and S(-10, 1).
Rotation CCW 90°
The transformation that maps coordinates to their image after rotation 90° CCW is
(x, y) ⇒ (-y, x)
The image points are
Q(-9, 8) ⇒ Q'(-8, -9)
R(-1, 8) ⇒ R'(-8, -1)
S(-10, 1) ⇒ S'(-1, -10)
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A recent survey showed that 73% of elementary school students have a pet, what is the ratio of students who have a pet to the students who don't have a pet
Answer:idek
Step-by-step explanation:
What is the value of f(-1) when f(x) = 2x + 2?
Enter your answer in the box.
f(−1) = □
(can someone explain it instead of just giving answer, the teachers suck at teaching anymore at least where i go)
The value of f(-1) when f(x) = 2x + 2 will be 0.
How to illustrate the expression?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this situation, we want to know the value of f(-1) when f(x) = 2x + 2. This will be Illustrated as:
f(-1) = 2x + 2
= 2(-1) + 2.
= -2 + 2
= 0
The value is 0.
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In March, Isaiah and Freddie had the same amount of money in their savings accounts. In April, Isaiah deposited $210 into his account. Freddie increased the money in his account by 15%. When they compared their balances, they found that they were still equal.
x + 210 = 1.15x where x is the amount in their accounts in March....subtract x from both sides 210 = .15x divide both sides by .15 x = $ 1400 Hope you get an A+ :))
. A swim coach has at most $800 to buy equipment for the swim team. Each
pull buoy costs $5.50 and each kickboard costs $10. Let X represent the
number of pull buoys and y represent the number of kickboards.
a. Write an inequality for the scenario..
5.50x+10y_< 800 I already wrote the inequality now graph the inequality
The inequality for number of pull buoys and the number of kickboards is; 5.50x + 10y ≤ 800.
How do you define a inequality?A statement of an order relationship between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
For the given question.
Let 'x' represent the number of pull buoys.
Let 'y' represent the number of kickboards.
The cost of each pull buoy = $5.50.
The cost of each kickboard costs = $10.
The total swim budget = $800.
The inequality for the scenario is -
5.50x + 10y ≤ 800.
Plot the graph;
Put x = 0; y = 80 ; (0, 80)
Put y = 0, x = 145.5 (145.5, 0)
Plot the obtained points on the graph.
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Determine the solutions of the equation:
|1/3x + 9| - 3 = 21
Step-by-step explanation:
21+3=24
1/3x+9=24
24-9=13
1/3x=13
13×1=13
3x=13
13/3=4.33
x=4.33
A trough at the end of a gutter spout is meant to direct water away from the house. The
homeowner makes the trough from a rectangular piece of of aluminum that is 20 in. long and 12
in. wide. He makes a fold along the long sides a distance of x inches from the edge. If he wants the
trough to hold 360 in³ of water, how far from the edge should he make the fold?
Answer:20 in * (12 in - 2X in) * (X in) = 360 in3
This can be simplified by dividing both sides by 20 in:
20 in * (12 in - 2X in) * (X in) = (360 in3/ 20 in)
After dividing both sides by 20 in:
(12 in - 2X in) * X in = 18 in2
Distribute X in. across (12 in -2X in):
12X in2 - 2X2 in2 = 18 in2
1.Subtract 18 in2 from both sides:
12X in2 - 2X2 in2 - 18 in2 = 0
2. Rearrange the equation:
-2X2 in2 + 12X in2 - 18 in2 = 0
This for matches the form for a quadratic equation (Ax2 + Bx +C = 0)
You can then plug these values into the quadratic formula to solve for X
so your answer is X=3
Omar gave out a survey to some students in his school about their favorite color. 650 of those surveyed said their favorite color was blue. If 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
The total number of students surveyed by Omar in his school is 1000.
Here, we are given that Omar conducted a survey of some students in his school about their favorite color.
650 of those surveyed said their favorite color was blue.
Further, 65 percent of the students surveyed said their favorite color was blue.
Let the total number of students surveyed be x
Then, according to the given information,
65% of x is 650
Thus, we can form the following equation-
65/ 100 × x = 650
0.65x = 650
x = 650/ 0.65
x = 65000/ 65
x = 1000
Thus, the total number of students surveyed by Omar in his school is 1000.
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A school has 14 rooms with 28 desks in each room. How many desks are in the school?
Answer:
392
Step-by-step explanation:
There are 14 desks with 28 rooms, or
14 x 28
392
I'm trying to rank up so if you could mark this brainliest, it would really help
Name the property illustrated.
(7 + 8) + 9 = 7 + (8 + 9)
Answer:
24=24 ( associative property )
Points X(6,4) and Y(-4,-6) are the endpoints of XY. What are the coordinates of point Z on XY such that XZ is 4/5 the length of XY
Answer:
(-2, -4)
Step-by-step explanation:
Z_x = (Y_x - X_x) * (4/5) = (-4 - 6) * (4/5) = -8
Z_y = (Y_y - X_y) * (4/5) = (-6 - 4) * (4/5) = -8
-8 + 6 = -2
-8 + 4 = -4
Mr.Johnson orders gravel to cover his driveway. Below is a top view of the driveway. The gravel will be spread 3 inches deep.Write the depth of the gravel in ft
If Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet
The gravel will be spread 3 inches deep
Here we have to convert the depth in inches to the depth in feet
To convert the inches to feet, we have to divide the inches by 12.
Then,
3 inches = 3/12 feet
= 0.25 feet
Hence, if Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet
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If x = 15 units and h = 12 units, then what is the area of the rhombus pictured above?
A.
225 square units
B.
45 square units
C.
180 square units
D.
60 square units
The rhombus has an area value of 180 square units
How to calculate the area of the rhombus?From the question, the given parameters arr
Shape = Rhombus'
Base = x
Height = h
Also, from the question, we have
x = 15
h = 12
The above parameters mean that
Base = 15
Height = 12
The area of the rhombus is then calculated using the following area formula
Area = Base * Height
Substitute the known values in the above equation
This gives
Area = 15 x 12
Evaluate
So, we have the following equation
Area = 180
Hence, the area is 180 square units
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The area of the rhombus is 180 square units, which is the correct answer would be an option(C).
What is the area of the rhombus?The area of the rhombus is calculated as the product of its height and base.
The formula of the area of the rhombus is following
Area of the rhombus = Height × Base
The given rhombus has :
Height (h) = 12 units
Base (x) = 15 units
Area of the rhombus = Height × Base
Area of the rhombus = h × x
Substitute the values of x = 15 and h = 12 in the above equation
Area of the rhombus = 15 × 12
Area of the rhombus = 180 square units
Hence, the area of the rhombus is 180 square units
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Ples hlep me i need hlep w my hw cuz i cant figure it out and my friend is not here bc they gone and not hear anyways help me ples tysm
The distance traveled by the tip of the minute hand in 45 minutes is approximately 256.77 mm, while the distance traveled by the tip of the hour hand in 1 hour is approximately 267 mm.
A) The hour needle completes a complete rotation of 12 hr, in 45 min = 0.75 hours, it will be 0.75 ÷ 12 of a complete rotation.
Given that the hour arrow's tip touches the rim of a clock, the radius of the clock is equal to the distance of the pointer.
The circumference of a circle is:
C=2 × π × radius
The span crossed by the hand in 12 hours is:
2 × 36=76π mm
The space traversed in 45 min is:
0.75 ÷ 12 × 72π=4.5π mm
in 45min, the min hand will make 45 ÷ 60=3 ÷ 4. If the min hand is 150% of the hour hand, then its length is 150 ÷ 100 × 36 = 54 mm.
As a result, the point of the minute will go around the complete circumference of a circle with a radius of 54 mm, implying that for a full circle, we will have:
2 × π × 54mm = 108π mm.
As a result, the minute hand's tip will have moved 45 minutes in 45 minutes, 108 × 3 ÷ 4 × π = 81π mm.
B) The clock's hour hand measures 30 mm.
As a result, the radius of the minute hand is,
1.5 × 30 = 45mm
And the minute hand moves after one hour 2π × ( r )²:
2 × 3.14 × 45 × 45 = 90π mm
And the minute hand moves,
π ÷ 6 × 30 = 5π mm
As a result, the minute hand moves,
90π - 5π = 85π mm
= 267 mm
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plsssssssssssssss helpppppppppppppppppppppp
Solve the equation 6p = 2(5 - 2p).
Answer:
p=1
Step-by-step explanation:
6p=2(5-2p)
6p=10-4p
Add 4p on both sides
10p=10
Divide 10 on both sides
p=1
Hello!
Let's solve:
[tex]6p=2(5-2p)\\\\\text{Multiply 2 into the function in the parentheses}6p=10-4p\\\\\text{Add '4p to both sides}\\6p+4p=10-4p+4p\\10p=10\\\\\text{Divide both sides by 10}\\\frac{10p}{10} =\frac{10}{10} \\p=1[/tex]
Hope that helps!
A farmer planted 978 seeds each day for 30 days. How many seeds did the farmer plant in total? 29,140 seeds 29,240 seeds 29,340 seeds 29,440 seeds
Answer:
29,340
Step-by-step explanation:
978 x 30 =29,340
do you think you can help me with this problem this is what the question is about a glass bottle filled with oil that weighs 590 grams. After Sophia uses 200 milliliters of oil, the bottle of oil weighs 400grams. so do u think u can help me?
The function formula of the mass of the bottle to the function of the volume of the oil is M = 590 - 0.95V
How to write function formula?The glass bottle filled with oil weighs 590 grams.
After Sophia uses 200 millilitres of oil, the bottle of oil weighs 400grams.
Therefore, the weight M of the bottle of oil in grams is a function of V, the volume, in millimetres of oil Sophia has used.
Therefore, the formula of the function can be represented as follows
density = mass / volume
200 mm reduces the weight of the bottle by 590 - 400 = 190 grams.
V mm will reduce it to ?
cross multiply
190 × V / 200 = 19 / 20 V = 0.95V
where
V = volume of the oil reduced from the bottle
Therefore, the function formula will be as follows:
M = 590 - 0.95V
Where,
M = weight of the oil.
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250 word minimum essay on the steps of solving for both the x and y intercept.
Answer:
Step-by-step explanation:
In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y and an x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system. To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. For example In algebra, 2-dimensional coordinate graphs have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a range of values cross these axes are called intercepts. The y-intercept is the place where the line crosses the y-axis and the x-intercept where the line crosses the x-axis. For simple problems, it is easy to find the x-intercept by looking at a graph. You can find the exact point of the intercept by solving algebraically using the equation of the line.
Hope this helped out!
The answers help im confused
Answer:
P' (3, 1)
Q' (5, 1)
R' (5, 4)
S' (3, 4)
T' (3, 3)
U' (1, 3)
V' (1, 2)
W' (3, 2)
Step-by-step explanation:
What does it mean when a point is translated horizontally to the right by 6 units? That means its x coordinate is increased by 6 units, the y-coordinate is unchanged
(If it was translated 6 units to the left, it's x coordinate would decrease by 6 units)
So if we had a point say (1, 1) then its new x-coordinate will be (1+6, 1) or (7,1) The y-coordinate stays unchanged if the translation is horizontal
When a point is translated vertically by 6 units, its x-coordinate is unchanged but the new y coordinate is increased by 6 units (-6 units if the translation is vertically down)
So with a point (1, 1), an up translation will result in a new point (1, 7)
If both translations are applied both x and y coordinates will change to
(7, 7)
To figure out the new coordinates denoted by P'Q'R'S'T' of each of the points PQRST of the given figure:
Add 6 to the x-coordinate of each point and at the same time add 6 to the y-coordinate of that point
If you look at the graph, the original points and translated points for 6 units to right and 6 units up are
P(-3, -5) which translates to P'(-3 + 6, -5 + 6) or P'(3, 1)
The other new points are calculated the same way by adding 6 to both x and y coordinates
Q(-1, -5) ==> Q'(5, 1)
R(-1, -2) ==> R'(5, 4)
S(-3, -2) ==> S'(3, 4)
T(-3, -3) ==> T'(3, 3)
U(-5, -3) ==> U'(1, 3)
V( -5, -4) ==> V'(1, 2)
W(-3, -4) ==> W'(3, 2)
The attached graph shows the translated figure with the translated points. Essentially the original figure has been shifted 6 units to the right and 6 units up
Emma has 3/4 credits. It requires 1/4 of a credit to play a video game for one minute. How long can Emma play the video game with her credits? Use standard algorithm to show your work.
Emma can play video games for 3 minutes using the available credits
Credit available with Emma = 3/4 credits
Credits required to play a video game for one minute = 1/4
Credits: In an electronic gaming setting, a value earned through the exchange of cash or currency equivalents is referred to as "gameplay credits." It can also be obtained through gaming as a prize. You can exchange gameplay credits for money or money equivalents.
Time Emma can play video games with the credits:
Credit available with Emma/Credits required to play video game for one minute
= (3/4)/(1/4)
= 3/4*4
= 3
So, she can play for 3 minutes
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Determine the range of the following graph:
After inspecting the picture of the given graph, the range of the function is represented by the following set:
Inequality notation: - 5 ≤ y ≤ 0
Interval notation: y ∈ [- 5, 0]
What is the range of a given function?
Functions are characterized by the following three features:
Domain - Set of the input variables, represented by the horizontal axis.Range - Set of the output variables, represented by the vertical axis.Relation - How the input and output variables are related to each other.In this question we find the case of a function with one input variable and one output variable. That is:
x → f(x)
After inspecting the picture shown in the image we notice that the range of the graph is formed by the following set:
Inequality notation: - 5 ≤ y ≤ 0
Interval notation: y ∈ [- 5, 0]
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A paper company is designing a new, pyramid-shaped paperweight. Its development team has decided
that to make the width of the paperweight 4 inches less than the length and the height of the
paperweight 3 inches less than the length. The paperweight must have a volume of 12 cubic inches.
What are the dimensions of the paperweight?
The width is
inches, the length is
inches, and the height is
inches
Answer:
4x+3=12
Step-by-step explanation:
i came up to some degree, but not sure. i will post my notes after.
Note that sides AD and BE are perpendicular on the same side AC. So the angles CAD and CBE, both are equal to 90 degrees.
Beig the corresponding angles, ADC and BEC are also equal.
And the angle ACD is the common angle in both the triangles.
Therefore by the AAA criteria, the triangles CAD and CBE are similar.
So their corresponding sides must be proportional,
[tex]\begin{gathered} \frac{AD}{BE}=\frac{AC}{BC} \\ \frac{4\sqrt[]{138}}{\sqrt[]{138}}=\frac{6\sqrt[]{3}+BC}{BC} \\ 4=\frac{6\sqrt[]{3}+BC}{BC} \\ 4BC=6\sqrt[]{3}+BC \\ 3BC=6\sqrt[]{3} \\ BC=2\sqrt[]{3} \end{gathered}[/tex]The price of Stock A at 9 A.M. was $12.17. Since then, the price has been increasing at the rate of $0.06 each hour. At noon the price of Stock B was $12.67. It begins to decrease at the rate of $0.08 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
If at noon the price of Stock B was $12.67. It begins to decrease at the rate of $0.08 each hour. If the two rates continue, the number of hours that the prices of the two stocks be the same is 3.57 hours.
Determining the stock number of hoursLet the hours when they equalize be h
Hence,
12.17 + .06h =12.67 - .08h
Combine like terms
.06h + .08h=12.67 - 12.17
.14h=.5
Divide both sides by .14h
h = .5/ .14
h = 3.57 hours
Therefore we can conclude at the number of hours is 3.57 hours .
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What is the correct form of the partial fraction decomposition for the expression
13x-7
(x+2)(4x-3)
?
Answer:
fraction decomposition for the expression
13x - 7/(x+2)(4x-3)
if angles k and j are supplementary and adjacent, which statement about the two angles is true ?
Let's evaluate the statements:
Supplementary angles: that means the sum of ∠K and ∠J is 180°.
Adjacent angles: that means that ∠K and ∠J common side and a common vertex.
So, let's observe the angles:
Given:
Linear pairs of angles are those two adjacent angles whose sum is 180°.
Answer: ∠K and ∠J are linear pairs.
Given the midpoint (M) and either endpoint of AB. find
the other endpoint.
A(-1, 2) and M(3,6)
a B is (7, 10)
b Bis (9, 12)
c B is (10, 10)
d B is (13, 10)
The other endpoint is (7,10).
Assuming that your midpoint M = (x, y) and endpoint A = (x1, y1) are both present: Coordinates of the double midpoints are 2x, 2y. To find the x-coordinate of the missing endpoint, subtract the known endpoint's x-coordinate from the first value: x₂ = 2x - x₁.
The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint.
An alternate solution would be to substitute (-1, 2) for (x1,y1) and (3,6) for (x2,y2) into the midpoint formula:
(x - 1)/2 = 3
x -1 = 6
x =7
(y + 2)/2 = 6
y + 2 = 12
y =10
Solving each equation for (x2,y2) yields the solution (7,10).
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jacob said that -3 is a rational number. aaron said that -3 is an irrational number. who is correct?explain
Any number in the form of p/q where q not equal to zero is called as rational Number. -3 is rational number and Jacob is correct.
What are Rational numbers and Irrational Numbers?Any number in the form of p/q where q not equal to zero is called as rational Number.
An Irrational Number is a real number that cannot be written as a simple fraction: 1.5 is rational, but π is irrational. The root values will also be irrational.
The number -3 is a rational number. We can write -3 in the form of p/q, i.e -3/1 where p is -3 and q is 1.
All rational numbers are obtained by dividing one integer by another.
Since it is possible to obtain -3 by dividing the integer
i.e -3 by 1, as in -3/1,
So -3 is a rational number.
Hence -3 is not a irrational number because -3 we can written as a simple fraction.
So Jacob is correct.
Hence -3 is rational and Jacob is correct.
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Write a rule of reflection
???????
The rule for the reflection is (x, y) ---> (x+6, y).
what is Reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.
Given:
The coordinates of L is ( -3, 6).
Now, after the reflection
The x- coordinates increases +6 units on right side.
and, y- coordinates remains the same.
Hence, the rule for the reflection is (x, y) ---> (x+6, y).
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