Each year, your bank account would accumulate $30 in interest.
A bank account is a financial account provided by a bank or financial institution that allows individuals or businesses to deposit money, make withdrawals, and perform various financial transactions. Bank accounts offer a secure and convenient way to manage and store your money.
To calculate the amount of money that would accumulate in your bank account each year from a $600 tax refund invested at 5% simple interest, we can use the formula:
Interest = Principal * Rate
where:
Principal = $600 (initial investment)
Rate = 5% (0.05 in decimal form)
Interest = $600 * 0.05
Interest = $30
Therefore, each year, your bank account would accumulate $30 in interest.
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Write the equation of the parabola that has its vertex at (−2, 7) and passes through (−1, 3). Answer asap! will give brainliest! no fake answers!
Answer:
y = -4(x +2)² +7
Step-by-step explanation:
You want the equation of the parabola with vertex (-2, 7) that passes through point (-1, 3).
Vertex formThe vertex form of the equation of a parabola is ...
y = a(x -h)² +k . . . . . . . . vertex (h, k)
We can use (x, y) = (-1, 3) and (h, k) = (-2, 7) to find the value of 'a'.
3 = a(-1 -(-2))² +7 = a +7
-4 = a . . . . . . . . subtract 7
Then the vertex form equation for the parabola is ...
y = -4(x +2)² +7
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Suppose that an individual has a body fat percentage of 18.8% and weighs 184 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
If an individual's body fat percentage is 18.8%, this means that 18.8% of their weight is composed of fat. We can use this information to find the weight of the fat in pounds as follows:
Weight of fat = body fat percentage * weight
Weight of fat = 18.8% * 184 pounds
Weight of fat = 0.188 * 184 pounds
Weight of fat = 34.592 pounds
Rounding this to the nearest tenth, we get:
The weight of the fat is about 34.6 pounds.
Complete the table: Theta 0 90 Cosine (theta) ? 0 a. 1 c. 2 b. -1 d. 0
The values of sin0 and sin 90 are 0 and 1 respectively
Table and values of a function
Given the following values of theta
Theta = 0 and 90 degrees
If theta = 0 dgrees
Sin (0) = 0
If theta = 90 degrees
Sin(90) = 1
Hence the values of sin0 and sin 90 are 0 and 1 respectively
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The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll?
A.
1
12
B.
7
12
C.
2
3
D.
3
4
7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll
The probability of rolling an even number on the first roll is 3/6 = 1/2, since there are three even numbers (2, 4, 6) out of six possible outcomes.
The probability of rolling a 1 on the second roll is 1/6, since there is only one outcome that will result in a 1.
To find the probability that at least one of these events occurs, we can add their probabilities and subtract the probability that both events occur:
P(even or 1) = P(even) + P(1) - P(even and 1)
Since the events are independent, the probability that both occur is simply the product of their probabilities:
P(even and 1) = P(even) × P(1) = (1/2) × (1/6) = 1/12
Substituting into the formula above, we get:
P(even or 1) = 1/2 + 1/6 - 1/12 = 7/12
Therefore, 7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll
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his inversely proportional to p p is directly
proportional to t Given that h = 9 and t = 64
when p = 4 find a formula for h in terms of t
Write any fraction in the form a/b
The formula that of h is h = 9k/16t
What is joint variation?Joint variation describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant.
h is inversely proportional to p and directly proportional to t , therefore
h = k t/p
when h = 9 and t = 64 and p is 4
9 = k 64/4
64k = 36
k = 36/64
k = 9/16
h = 9k/16t
therefore the formula of h interns of k and t is
h = 9k/16t
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a bank teller has 50 $20 and $5 bills in her cash drawer the value is $535 how many $20 bills are there
Answer:
19 $20 bills
Step-by-step explanation:
Let's assume the number of $20 bills in the cash drawer is "x."
The value of the $20 bills can be calculated by multiplying the number of bills by the denomination:
Value of $20 bills = 20 * x
Similarly, the value of the $5 bills can be calculated by multiplying the number of bills by the denomination:
Value of $5 bills = 5 * (50 - x) (since there are a total of 50 bills)
According to the given information, the total value of all the bills is $535:
Value of $20 bills + Value of $5 bills = $535
Substituting the expressions for the values:
20 * x + 5 * (50 - x) = 535
Simplifying the equation:
20x + 250 - 5x = 535
Combining like terms:
15x + 250 = 535
Subtracting 250 from both sides:
15x = 285
Dividing both sides by 15:
x = 19
Therefore, there are 19 $20 bills in the cash drawer.
can someone please help me with this ?
You need to match them in straight horizontal lines
Step-by-step explanation:
You need to replace the coordinates in the equations.
For example let's take (-6,-9) first. - 6 is the x coordinate and - 9 is the y coordinate. Let's replace it in the different equations and see which one is accurate.
Y = 2/3 x - 5 = 2/3×(-6) - 5 = - 9
(we were supposed to get y as - 9 and therefore this one is correct)
Our first match —> (-6,-9) & y = 2/3x - 5
Next coordinate, (-9,-11.5)
Replace in second because we found the first one already.
Y = 1/2 x - 7 = 1/2×(-9) - 7 = - 11.5
(y is supposed to be -11.5 so this one is correct too)
(-9,-11.5) & y = 1/2x- 7
Next coord, ( 4,-1)
Y = 6/8×(4) - 4 = - 1
(woah this one is correct too haha, why are they in the exact order-)
(4,-1) & y = 6/8 x - 4
Last ones left are the last two obviously but we can cross check.
Y = 4/8×(-8) + 1 = -3
Correct.
(-8,-3) & y = 4/8 x + 1
In a village there are 60 families with 4 members each. Out of
these 28 families speak only Tamil and 20 families speak only
Urdu. How many family members speak both Tamil and
Urdu
Answer:
12
Step-by-step explanation:
28 plus 20 equals to 48 and then each divide 4
Determine each segment length in right triangle ABC
B
45°
I
D
14
7√3
7
45°
A
14
14√3
14√2
The length of AB and CB is 7√2.
Using Trigonometry
cos 45 = B/ H
cos 45 = AD / AB
1/√2 = 7 / H
H = 7√2
Then, CB = AB = 7√2
Now, using Pythagoras theorem in ΔABC
AC² = AB² + CB²
14² = (7√2)² + CB²
CB² = 196 - 98
CB = 7√2
Thus, the length of AB and CB is 7√2.
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A firm produces 6 shirts at a total cost of $187. The marginal cost of the last shirt is $12. What is the average total cost of producing 5 shirts by the firm?
The average total cost of producing 5 shirts by the firm is $35.
How to find the verage total cost of producing 5 shirts by the firmWe can use the following formula to calculate the average total cost (ATC) of producing 5 shirts:
ATC = Total Cost / Quantity
We know that the firm produces 6 shirts at a total cost of $187, so the total cost of producing 5 shirts can be estimated by subtracting the marginal cost of the last shirt from the total cost of producing 6 shirts:
Total Cost of producing 5 shirts = Total Cost of producing 6 shirts - Marginal Cost of the last shirt
= $187 - $12
= $175
Now we can use the formula to find the average total cost of producing 5 shirts:
ATC = Total Cost / Quantity
= $175 / 5
= $35
Therefore, the average total cost of producing 5 shirts by the firm is $35.
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Find the original price of a pair of shoes if the sale price is $10 after a 75% discount
Answer:
7.5
Step-by-step
to get this answer you need to multiply 10*75 than divide it by 100
10 0
----- --------
100 75
What type of transformation is shown below?
The transformation that maps the blue triangle into the orange one is a rotation.
What is the transformation shown?First, a translation only moves the figure (it does not change the orientation), and in the image we can see that the orientations are different, then we can discard the translation.
Similarly with the dilation which only changes the size, we can discard that one too.
Finally, if we do a reflection over a given line the orientation can be changed, but there must be a line of symmetry (the line used for the reflection) between the two figures, that we can't see here.
Then the remaining option is the correct one, this is a rotation.
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Subtract A) 101two-10 two=_two
1) The difference is 11two
2) The difference is 30 seven
What is a number base?A number base, usually referred to as a numeral system or radix, is a system of digits and rules used to represent numbers. In a positional numeral system, it specifies the number of distinct digits or symbols that can be used to represent values.
Let us first convert to base 10, carry out the operation and then return to the required base.
Hence;
101two = 5 ten
10 two = 2 ten
5 ten - 2 ten = 3 ten or 11two
b) 62seven = 44 ten
23 seven = 17 ten
44 ten - 23 ten = 21 ten or 30 seven
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11. What is the domain of the function shown?
Match the expression on the left with its simplified form on
the right. Answer options on the right may be used more
than once.
-(-9)
| -9|
-|9|
|9|
-|-9|
-9
9
The expressions on the left matched with the simplified form on the right:
-(-9) = 9
|-9| = 9
-|9| = -9
|9| = 9
-|-9| = -9
Mathematical rules to simplify the expressions:
a negative sign multiplied by a negative sign is equal to a positive sign
a positive sign multiplied by a negative sign is equal to a negative sign.
a positive sign multiplied by a positive sign is equal to a positive sign.
Also, this sign | | indicates that the number is positive.
Therefore,
-(-9) = 9
|-9| = 9
-|9| = -9
|9| = 9
-|-9| = -9
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What is the volume of a rectangular prism if the length is 21 feet width is nine and height is seven that's not nice what is the volume of a rectangular prism if the length is 21 feet width is nine and height is 7 feet
The volume of the prism is 1323 feet³ (cubic feet).
Step-by-step explanation:1. Annotate the values.Length= 21 feet.
Width= 9 feet.
Height= 7 feet.
2. Find a formula.The formula to calculate the volume of rectangular prisms is the following:
[tex]\sf V_{RP} =l*w*h[/tex]; where "l" is the length; "w" is the width, and "h" is the height of the prism.
Check the attached image to see where these values are measured from.
3. Calculate.Substitute the variables in the formula by the values on step 1.
[tex]\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.[/tex]
The volume of the prism is 1323 feet³ (cubic feet).
-------------------------------------------------------------------------------------------------------
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Answer:
The volume of the rectangular prism is 1323 cubic feet.
Step-by-step explanation:
Step 1: Write down the formula for the volume of a rectangular prism:
[tex]\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}[/tex]
Step 2: Substitute the given values for the length, width, and height:
[tex]\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}[/tex]
Step 3: Multiply the numbers together:
[tex]\qquad\Large\rm\implies{V = 1323\: ft^3}[/tex]
Step 4: Write the final answer with the appropriate units:
The volume of the rectangular prism is 1323 cubic feet.
[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
Find an equation for the graph sketched below
Answer:
f(x) = 5^x -2
Step-by-step explanation:
You want the equation for the graph attached.
Exponential functionThe graph has a horizontal asymptote for negative values of x, and rises rapidly for positive values of x. This suggests an exponential function.
TranslationThe graph of the parent exponential function will pass through the point (0, 1), which is 1 unit above the horizontal asymptote. Here, the horizontal asymptote is y = -2, and the graph passes through (0, -1).
This tells us the graph is vertically translated down 2 units and not translated horizontally at all. (Horizontal translation is equivalent to a vertical scale factor. The lack of it tells us the vertical scaling is 1.)
BaseThe parent exponential function b^x rises b units above the horizontal asymptote when the value of x is 1. Here, the function rises to +3 from the asymptote of -2 at x=1, so the base of the exponential is 3-(-2) = 5.
EquationThe equation for the graph is ...
f(x) = 5^x -2
Confirmation is shown in the attachment.
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can anyone help please !! i need to find the volume !
355.2
i use my notebook and showed my work by doing 3.7x8x12 which is equal to 355.2
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo
Answer:
yes
Step-by-step explanation:
common sense
Answer:
843,75 feet away
Step-by-step explanation:
speed of sound is 1.125 feet per sec
to calculate the distance of the canyon use : distance =(speed of sound ×time)/2
(1,125feet/sec ×1,5sec)/2
=843,75 feet away
If
R
=
{
x
|
x
>
0
}
and
S
=
{
x
|
x
<
3
}
, what is the number of integers in
R
∩
S
?
A. Zero
B. Two
C. Three
D. Four
As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.
In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.
The intersection of two sets contains only the elements that are present in both sets. In this case,
R ∩ S = {x | x > 0 and x < 3}
The integers that are present in this set are 1 and 2.
Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
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Based on your answer to Part A, calculate the value of the most appropriate center value of the heights
I thought of a number. 7 times the number decreased by 13 equals 5 times the number increased by 5. What was my number?
Answer:
Convert the word problem into equation
Let the number be x
By the problem
7x-13=5x-5
Transport the 5x to lhs and -13 to rhs
7x-5x=13-5
2x=8
x=8/2
x=4
Therefore the number is 4
Step-by-step explanation:
Find the missing values and perimeter
The required length of the segments are found as :
AB = 3.16
AC = 5.1
BC = 5.66
Perimeter = 13.92
What is perimeter?A perimeter is described as a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
We make use of the distance formula:
Distance = √ ((x2 - x1)² + (y2 - y1)²
segment AB:
x1 = 1, y1 = 5
x2 = 4, y2 = 4
= √ ((4 - 1)² + (4 - 5)²
= √ (9 + 1)
= √ (10)
= 3.16
Segment AC:
x1 = 1, y1 = 5
x2 = 0, y2 = 0
= √ ((0 - 1)^2 + (0 - 5)^2)
= √ ((-1)^2 + (-5)^2)
= √ (1+ 25)
=√ (26)
= 5.1
Segment BC:
x1 = 4, y1 = 4
x2 = 0, y2 = 0
= √ ((0 - 4)² + (0 - 4)²
=√ ((-4)² + (-4)²
= √ (16 + 16)
= (32)
= 4 x √(2)
= 5.66
Perimeter = segment AB + segment AC + segment BC
Perimeter = 13.92
Perimeter = 13.92
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the complete question is attached in the image:
An expression is shown below:
2x3y + 8xy − 4x2y − 16y
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
The given expression, rewritten by factoring out the greatest common factor is 2y(x³ + 4x - 2x² - 8)
The given expression factored completely is (2xy - 4y)(x² + 4)
Factoring an expressionFrom the question, we are to rewrite the given expression by factoring out the greatest common factor and also by factoring completely
The given expression is
2x³y + 8xy - 4x²y - 16y
The greatest common factor is the expression that is common t each of terms in the given expression
The greatest common factor is 2y
Factoring out the greatest common factor
2x³y + 8xy - 4x²y - 16y
2y(x³ + 4x - 2x² - 8)
Factoring the expression completely
2x³y + 8xy - 4x²y - 16y
2xy(x² + 4) - 4y(x² + 4)
(2xy - 4y)(x² + 4)
The complete factoring of the expression is (2xy - 4y)(x² + 4)
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Determine the equation of FG?
The equation of line FG is given as follows:
y = -0.5x - 5.5.
How to obtain the equation of FG?The circle has a center of (1, -1), hence the equation is given as follows:
(x - 1)² + (y + 1)² = r².
Point (-1, -5) is on the circumference of the circle, hence the radius is obtained as follows:
(-1 - 1)² + (-5 + 1)² = r²
r² = 40.
Hence:
(x - 1)² + (y + 1)² = 40.
Applying implicit differentiation, the derivative is given as follows:
2(x - 1) + 2(y + 1)m = 0
2x - 2 +2m(y + 1) = 0
m = (x - 1)/(y + 1)
At x = -1 and y = -5, hence the slope is given as follows:
m = -2/4
m = -0.5.
Hence the equation is given as follows:
y + 5 = -0.5(x + 1).
y = -0.5x - 5.5.
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A baseball team plays in a stadium that holds 48000 spectators. With the ticket price at $12 the average attendance has been 20000. When the price dropped to $11, the average attendance rose to 24000. Assume that attendance is linearly related to ticket price.
What ticket price would maximize revenue $______
The ticket price that maximizes revenue is $8.50.
What ticket price maximizes revenue for the baseball team?Let x be the ticket price in dollars
Let y be the attendance.
We are given two points: (12, 20000) and (11, 24000).
Using the point-slope formula, we can find the equation of the line:
y - 20000 = (24000 - 20000)/(11 - 12) * (x - 12)
y = -4000x + 68000.
Revenue R is equal to the product of price and attendance: R = xy.
Substituting y = -4000x + 68000, we get:
R = x(-4000x + 68000)
R = -4000x^2 + 68000x.
Using [tex]x = -b/(2a)[/tex] where a and b are the coefficients from the form ax2 + bx + c]
= - 68000/(2*-4000)
= 8.5.
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What is the negation of the following statement?
At least one angle is obtuse.
A) At least one angle is not obtuse.
B) None of the angles are obtuse.
Answer:
A
Step-by-step explanation:
Negation statements have the word "not" in them or taken out of them. In this case, not is added to the statement.
Please use the same data set to answer ALL questions on this page.
Question 4 (2 points)
Sam works at a doggy daycare. For ten days, she counted the number of dogs at the
daycare each day.
Number of dogs
47 38 72 56 40 64 30 80 66 51
The box that depicts the number of dogs at the daycare each day is Box C which shows median of 60. The Option C.
What is the median number of dogs?The full data for number of dogs at the daycare each day is:
[tex]47,38,72, 56, 40, 64, 30, 80, 66, 51, 33, 74, 70, 69[/tex]
To get median, we will arrange the numbers in ascending order which is:
[tex]30, 33, 38, 40, 47, 51, 56, 64, 66, 69, 70, 72, 74, 80[/tex]
Since we have an even number of observations (14), the median will be the average of the two middle numbers.
The two middle numbers are 56 and 64. So the median is:
= (56 + 64) / 2
= 120 / 2
= 60.
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calculate the length of the hypotenuse
these are all problems designed to practice the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides, and A, B, C being the corresponding opposite angles.
I
and remember :
sin(90) = 1
a)
4/sin(30) = c/sin(90) = c
4/0.5 = c = 8 cm
b)
17/sin(53) = c/sin(90) = c
c = 21.28630619... cm
c)
6/sin(41) = c/sin(90) = c
c = 9.14551852... cm
You move right 8 units. You end at (5, -3). Where did you start?
If we move 8 units right and end up at the coordinate (5,-3) the starting point is (-3,-3)
In an x-y plane, the x-axis is the axis along the horizontal of the plane. Similarly, the y-axis is the axis along the vertical of the plane.
Thus, the change in the position affects the coordinates of the x and y axis accordingly.
Given:
Change in position: 8 unit rights
Thus, the movement is along the x-axis in the positive direction
Final position: (5,-3)
Starting point can be found by subtracting the movement of the particle from the endpoint.
Thus, Starting position: (5-8,-3) or (-3,-3)
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