The required simplified value of the given expression is given as 62.96.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression
= 3.04 × 21.5 - 9.12 / 3.8
= 65.36 - 2.4
= 62.96
Thus, the required simplified value of the given expression is given as 62.96.
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Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the function of Maureen's car is 26,525 (0.92)
a = 26,525 and b = 0.92
What is an exponential function?Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting value
b = the base function
x = the exponents
Considering the problem,
the starting = $26,525
the base = depreciation
the exponents = x
A year ago hence x = 1
$24,403 = $26,525(b)¹
b = 24,403 / 26,525
b = 0.92
hence we can say that a = 26,525 and b = 0.92
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Answer and explain please
The coordinates of the triangle before and after dilation is
preimage image
R (6, 9) R' (2, 3)
S (3, -9) S' (1, -3)
T (-6, -3) T' (-2, -1)
The rule that best describes the transformation is
(x, y) → (1/3 x, 1/3 y)How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
R (6, 9) → (1/3 * 6, 1/3 * 9) → R' (2, 3)
S (3, -9) → (1/3 * 3, 1/3 * -9) → S' (1, -3)
T (-6, -3) → (1/3 * -6, 1/3 * -3) → T' (-2, -1)
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I need help with written steps please
Answer:
a. To find the cost to surround the forest with a fence, we first need to determine the perimeter of the forest. The problem tells us that the perimeter is 45 yd. To convert this to feet, we can use the conversion factor of 3 feet per 1 yard. So, the perimeter in feet is:
45 yd x (3 ft/1 yd) = 135 ft
Next, we need to multiply the perimeter by the cost per foot to install fencing. We're told this cost is $6 per foot, so we can calculate the cost as:
135 ft x $6/ft = $810
b. To determine which region costs more to prepare, we need to calculate the cost per square yard for both the grassland and the forest. We're told that the cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is $25.
To find the total cost for the grassland, we'll multiply the area of grassland with the cost per square yard:
2400 yd x $15/yd = $36,000
To find the total cost for the forest, we'll multiply the area of forest with the cost per square yard:
60 yd x $25/yd = $1,500
We can see that the grassland cost $36,000 to prepare while the forest cost $1,500 which means Grassland costs more to prepare.
At an amusement park, only 17 people are allowed on a ride at the
same time. There are 157 people waiting in line. How many groups
of riders will there be?
Show your work.
Answer:
To find out how many groups of riders there will be, we need to divide the total number of people waiting in line (157) by the maximum number of people allowed on the ride at one time (17).
157 people / 17 people/group = 9.235 groups (approx)
But since the groups must be in whole numbers, we have to round up the value 9.235 groups to the next whole number, which is 10 groups.
So, the number of groups of riders will be 10.
Answer: 9 groups of riders.
Step-by-step explanation:
To find out how many groups of riders there will be, you need to divide the total number of people waiting in line by the maximum number of people allowed on the ride at one time.
157 (total people in line) ÷ 17 (people allowed per ride) = 9.235 (groups of riders)
Because you can't have a fraction of a group, you need to round down to get the whole number of groups.
So the answer is 9 groups of riders.
George can build a laptop twice as fast as her working together it takes them three hours which equation would you use to determine how long it would take Kurt working alone
Since George can build a laptop twice as fast as Kurt and working together takes them 3 hours, an equation which you would use to determine how long it will take Kurt working alone is: D. 1/t + 1/2t = 1/3.
How to determine the amount of time it would take Kurt working alone?In order to determine the amount of time it would take Kurt working alone, we would have to assign variables to the amount of time taken by George to build a laptop and the amount of time taken by Kurt to build a laptop, and then translate the word problem into an algebraic equation (expression) as follows;
Let the variable g represents the amount of time taken by George to build a laptop.Let the variable t represents the amount of time taken by Kurt to build a laptop.Let the variable w represents the combined work rate.Since George can build a laptop twice as fast as Kurt, an equation which models this situation is given by;
g = 2t .....equation 1.
Next, we would write an algebraic equation (expression) that models the combined work rate;
1/c = 1/t + 1/g .....equation 2.
Substituting equation 1 into equation 2, we have the following:
1/3 = 1/t + 1/2t
1/t + 1/2t = 1/3.
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Find the volume of the combined solid from the figure.
Answer:
1734
Step-by-step explanation:
We can simply solve the volume of the 2 different cubes. The bigger cube's volume is 15*12*8 = 1440. The volume of the small cube is 6*7*(15-4-4)=294.
So the total volume should be 1734
Answer:
1944 cm³
Step-by-step explanation:
Two rectangular parallelepipeds:
Upper: 12 x 7 x 6 = 504 cm³
Lower: 12 x 15 x 8 = 1440 cm³
Total: 504 + 1440 = 1944 cm³
Put the numbers in each category to which they belong.
PLEASE ASSIST ME
The perimeter of a triangular garden is 72 feet Find the length of the three sides if the middle length side is 2 feet greater than twice the length of the smallest side, and the longest side is 2 feet less than 3 times the length of the smallest side
3. Line DG is the perpendicular bisector of chord El.
EF = 7, EI = 9.5, and DG = 1.8.
What is the diameter of the circle? Show your work.
The diameter of the circle would be given as = 10
What is a diameter?Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.
The diameter of the circle can be found through finding first the radius of the circle.
The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.
Using the Pythagorean formula c² = a² + b²
The lines that represents ;
a= DG
b= EI/2 = 4.8
C= DI = ?
C² = DI
a² = 1.8²
b² = (9.5/2)² = 4.8²
c² = 2.24 + 23.04 = 25.28
C =√25.28
C = 5
Therefore the diameter of the circle = 5×2 = 10
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At the campus coffee cart, a medium coffee costs $3.55. MaryAnne brings $4.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave? (Round your answer to one decimal place.)
Answer:
0.4
Step-by-step explanation:
4.00-3.55 = 0.45 = 0.4
The tip she gives is given by approximately 12.7% of the price.
The cost of a medium coffee is given by = $ 3.55
Mary Anne brings $ 4 with her and buy a coffee.
So, the remaining dollars with her is given by = 4 - 3.55 = $ 0.45
According question she gives this remaining amount as tip.
Therefore she gives a tip of $ 0.45 on the price of $ 3.55
The percentage of her tip = (0.45/3.55) * 100% = 12.7 % [Rounding off to one decimal place]
Hence the tip she gives is given by approximately 12.7% of the price.
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A recipe requires 3½ cups of nonfat milk. A person already has ¾ cup. How much more is needed?
A. 2¾
B. 2¼
C. 3¼
D. 1¾
Show work please
Answer:
A. 2¾
Step-by-step explanation:
The person needs the difference. This is a subtraction problem.
3 1/2 - 3/4 =
3/4 is just a fraction, but you can think of 3/4 as a mixed numeral by writing 3/4 as 0 3/4. The whole part is 0 and the fractional part is 3/4.
= 3 1/2 - 0 3/4
Now we are subtracting two mixed numerals. You need to subtract the whole part, 0, from the whole part, 3, and the fractional part, 3/4, from the fractional part, 1/2.
For the fractional parts, we need a common denominator of 4.
= 3 2/4 - 0 3/4
Now we have both fractions with a common denominator of 4, but since we cannot subtract 3/4 from 2/4, we borrow 1 from 3 as 4/4.
3 goes down 1 to 2, and the 1 which is borrowed as 4/4 is added to the 2/4 to give you 2 6/4. 2 6/4 has the same value as 3 2/4. Now we have:
= 2 6/4 - 0 3/4
We subtract 0 from 2, and we subtract 3/4 from 6/4.
= 2 3/4
Answer: 2 3/4
Keisha reads a label on a measuring cup that shows 16 fluid ounces is the same as 2 cups. Using this information, how many fluid ounces are in 6 cups?
Salut/Hello!
Answer: 48 fluid ounces are in 6 cups
Step-by-step explanation:
We know there are 16 fluid ounces in 2 identical cups which results one cup is equal to 16 ÷ 2 = 8
After that we can find out how many fluid ounces are in 6 cups. 6 × 8 = 48
I hope it'll be useful! :]
A tree is 7 feet 1 inch tall. How tall is it in inches?
Answer:
85 inches
Step-by-step explanation:
7*12+1=84+1=85
The ten -digit number 3872649A0B is divisible by 36 . The letters A and B each represent single digit even numbers. Find the sum A+B.
The sum of A + B, considering that the ten-digit number is divisible by 36, is given as follows:
A + B = 6.
How to obtain the sum of A and B?The sum of A and B is obtained considering the rule for a divisibility by 36.
To be divisible by 36, the numbers must be divisible by both 4 and 9, for which the rules are given as follows:
Divisible by 4: the last two digits of the number are divisible by 4.Divisible by 9: the sum of the digits of the number is a multiple of 9.The ten-digit number is given as follows:
3872649A0B
The sum of the digits is given as follows:
3 + 8 + 7 + 2 + 6 + 4 + 9 + A + 0 + B = 39 + A + B.
Hence the condition for a divisibility by 36 is given as follows:
39 + A + B = 45
A + B = 6.
Which is the result for the sum in the context of this problem.
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In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest. Jennifer plans to repay the loan in January. Assume this loan is a simple interest loan calculated monthly. What will be the total amount she will owe to the bank on January 31st? If necessary, round to the nearest cent.
Answer: The total amount Jennifer will owe to the bank on January 31st is $3,458.75
Step-by-step explanation: In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest for 4 months. As this loan is a simple interest loan calculated monthly, we need to calculate the total amount she will owe to the bank on January 31st.
We use the formula for simple interest which is:
Interest = Principal x Interest rate x Time
Interest = $2,500 x 11.75/100 x 4/12 = $958.75 (rounding to the nearest cent)
Now we can add the interest to the principal amount to get the total amount that Jennifer will owe to the bank on January 31st.
Total amount = Principal + Interest
Total amount = $2,500 + $958.75 = $3,458.75 (rounding to the nearest cent)
So, the total amount Jennifer will owe to the bank on January 31st is $3,458.75
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Alec's parents give him x dollars per month for his allowance. However, since his birthday is
in February, he gets an extra 20% bonus that month.
Pick all the expressions that represent how much Alec's allowance is in February.
x + 0.2x
+
1.2x
*
D
X
⠀
Alec's parents give him x dollars per month for his allowance. However, since his birthday is in February, he gets an extra 20% bonus that month. The allowance in February can be represented by the expression x + 0.2x because Alec will get the regular allowance of x dollars plus an extra 20% bonus which is equal to 0.2x dollars.
x + 0.2x = Alec's allowance in February
The expression 1.2x is not correct because it represents Alec's allowance multiplied by 1.2 which is not the same as the allowance plus the bonus.
So the correct answer is x + 0.2x.
Write a slope-intercept equation for a line passing through the point (5, - 3) that is parallel to the line 5x + 7y =9. Then write a second equation for a line passing through the point (5, - 3) perpendicular to the line 5× + 7y = 9.
The equation of the line passing through the point (5, - 3) that is parallel to 5x + 7y = 9 will be 5x + 7y - 4 = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation of the line is given below.
5x + 7y = 9
The equation of the line that is parallel to the line is given as,
5x + 7y + d = 0
The line is passing through (5, -3). Then we have
5(5) + 7(-3) + d = 0
25 - 21 + d = 0
4 + d = 0
d = - 4
The equation of the line passing through the point (5, - 3) that is parallel to 5x + 7y = 9 will be 5x + 7y - 4 = 0.
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give me a sum using all bodmas operations that equals 6
The BODMAS acronym is for:
Brackets (parts of a calculation inside brackets always come first).Orders (numbers involving powers or square roots).Division.Multiplication.Addition.Subtraction.Addition and Subtraction
The final step is to calculate any addition or subtraction. Again, subtraction and addition rank equally, and you simply work from left to right.
Example:
⇒4 + 6 − 7 + 3 = ?
You start on the left and work your way across.
⇒4 + 6 = 10
⇒10 − 7 = 3
⇒3 + 3 = 6
The answer is 6.
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How many more seniors are on academic watch than freshman
The number of seniors that are on academic watch than freshman will be 868.
How to solve the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, since there are there are 2435 seniors and 1567 freshmen on academic watch. The number of seniors that are on academic watch than freshman will be:
= 2435 - 1567
= 868
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Complete question
In a school, there are 2435 seniors and 12567 freshmen on academic watch. How many more seniors are on academic watch than freshman
Place value of the 4 in 2, 487, 492
Please please look at the picture and answer the question thank you
Answer:
y = 3x -1
Step-by-step explanation:
You want the equation of the line through the points (0, -1) and (1, 2), among others.
Y-interceptThe y-value when x=0 is the y-intercept. The table shows you it is -1.
SlopeThe slope is the difference in y-values when x-values increase by 1. For the first two points in the table, the y-value shows an increase of ...
2 -(-1) = 3
This means the slope is 3.
Slope-intercept equationThe slope-intercept equation of a line is ...
y = mx +b . . . . . . . where m is the slope, and b is the y-intercept
For your line, we have determined m=3, b=-1, so the equation is ...
y = 3x -1
help me pleace!!!!!!!
Step-by-step explanation:
For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.
For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.
For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.
Because 2×3=6
A a triangular object is placed in front of a plane mirror. Use the law of reflection and principles of ray diagramming to construct the image that the subject will formed behind the mirror. After during the image, describe it in terms of 1) distance from the mirror 2) it's size compared to the image 3) orientation (inverted from right to left or inverted from left to right) and 4) type real or virtual
Please find attached the drawing, created with MS Word, of the image of the triangle following the reflection across the mirror surface.
1) The object and the image are equidistant from the mirror
2) The object and the image following the reflection across a plane mirror are have the same side lengths and are therefore congruent
3) The image of the triangle is upright, and virtual and inverted from left to right
What are the laws of reflection?The laws of reflection are;
1) The angle made by the incident ray and the normal line (the angle of incidence) is equal to the angle made by reflected ray and the normal line
2) The incident ray, the reflected ray and the normal are coplanar
3) The incident ray is on the other side of the normal with regards to the refracted ray
1) The distance of the points on the object from the mirror are the same as the distance of the corresponding point from on the image from the mirror
2) A reflection of an object across a plane mirror is a rigid transformation such that the size of the object and the size of the image are the same.
Therefore, ΔABC ≅ ΔA'B'C'
3) The coordinates of the image formed following the reflection of a point (x, y) across the y-axis is; (-x, y)
The y-coordinate remains the same, and the x-coordinates changes from positive to negative, and the location of the object on the left of the y-axis, produces an image on the right of the y-axis. Therefore
Therefore, the image is upright and inverted from right to left
The image of the triangle cannot be played on the screen, therefore, the image is virtual
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Becky's dinner would have cost $30 but she had a 40% off coupon. How much did Bedky pay for dinner?
Answer:
If Becky had a 40% off coupon, that means she saved 40/100 = 0.4 of the original price.
To find how much she paid for dinner, we can multiply the original price by the percentage of the price that she paid:
30 * (1- 0.4) =30*0.6 = $18
Becky paid $18 for her dinner.
Is it possible to have a 3/8 in. Pipe with an inside diameter of 21/32 in.
Answer: No, it is not possible to have a 3/8-inch pipe with an inside diameter of 21/32 inches
Step-by-step explanation:
The inside diameter of a pipe is always smaller than the outside diameter. The outside diameter of a pipe is a measurement of the pipe's exterior, while the inside diameter is a measurement of the pipe's interior. Therefore, if the pipe is 3/8 inches in outside diameter, the inside diameter will be less than 3/8 inches.
In addition, 21/32 inches is greater than 3/8 inches, so it is not possible to have a 3/8 inches pipe with an inside diameter of 21/32 inches. This is because the inside diameter is always smaller than the outside diameter.
- C
Consider the quadratic function y = ax2. As |a| increases, the graph . As |a| decreases, the graph .
As the value of a decreases the graph will expand.
What is a quadratic function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Given that consider the quadratic function y = ax². When the function is plotted on the for the value of an increases the graph contracts and if the value a decreases the graph expands.
The graph is attached with the answer below. In the graph, the quadratic function is shown at the two values of a.
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Obtain an estimate for the following computation by rounding the numbers so that the resulting arithmetic can easily
be performed by hand or in your head. Then, use a calculator to perform the computation. How reasonable is your
estimate when compared to the actual answer?
348 +598
Round the two numbers to the nearest ten. An estimate of the sum is
an example
Get more help.
Clear all i need help for this math please
In actuality, modern electronic calculators with advanced features are specialised computers with a specific function.
Is calculator a computing device?The two numbers can be rounded to the closest ten to get an estimate for the calculation 348 + 598.
Rounding 348 to the nearest 10, we get 350.
600 is the result when 598 is rounded up to ten.
Consequently, 350 + 600 = 950 is what we estimate the sum of 348 and 598 to be.
The correct calculation is 348 + 598 = 946 when using a calculator.
In comparison to the actual answer of 946, our guess of 950 is 4 higher. This indicates that we slightly overestimated the result in our estimation. Since the figures are rounded to the closest 10, there isn't much of a change, and this is reasonable.
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The area of the figure below is 9ft.What is the height of the triangle if the base of the triangle is 4.5
[tex]area = \frac{1}{2} \times base \times height \\ 9 = \frac{1}{2} \times 4.5 \times h \\ 9 = 2.25h \\ \frac{9}{2.25} = \: \frac{2.25h}{9} \\ 4 = height[/tex]
A trader sold 1.6 lot EURUSD. How many units of Euros did he sell?
Answer:
let's see jssjsjnsjsjsjsjsjsjsjsjsjs
Check all that apply. – is the reference angle for:
3
MA. T
3
B.
] c.
☐ D.
15:
3
2;}
3
19:1
3
Answer:
A, C, D
Step-by-step explanation:
You want the angles in the list that have π/3 as the reference angle.
Reference angleThe reference angle is the smallest angle between the angle's terminal side and the x-axis. The cosine and sine of the reference angle have the same magnitude of the cosine and sine of the angle in question.
The attached table shows that 7π/3, 2π/3, and 19π/3 have the same reference angle: π/3.
