Work Shown:
i = P*r*t
157.50 = 2250*r*7 ... plug in given values
157.50 = 2250*7*r
157.50 = 15750r
15750r = 157.50
r = 157.50/15750 ... divide both sides by 15750
r = 0.01
The interest rate is 1%
To go from 0.01 to 1%, you move the decimal point 2 spots to the right.
Alternatively, you would multiply by 100.
Answer:7%
Step-by-step explanation:
A section in a stained glass window is gaped like a trapezoid. The top base is 1 centimeter and the bottom base is 1.5 centimeters long. If the area of the section of glass is 3.5 square centimeters, how tall is the section?
Answer:
2.8 cm
Step-by-step explanation:
½(1+1.5)h = 3.5
h = 7/2.5 = 2.8 cm
Where is (-4) located on the number line?
what’s the difference between an ark and a radius on a circle?
Answer:
Step-by-step explanation:
The arc of a circle is a portion of the circumference of a circle and the radius is a straight line from the center of a circle to the circumference of a circle.
Maureen has two hollow containers. One is a 5 cm cube and the other is a cylinder of radius 2 cm. She completely fills the cube with water and then pours it into the cylinder.
What is the depth of the water in the cylinder? Give your answer in cm correct to 3 significant figures.
You can assume that the cylinder is tall enough to hold all the water from the cube.
Answer:
it's 9.947
Step-by-step explanation:
for this we need an equation which contain height in it so we used volume in both so we get height
π2^2h=5*5*5
π4h=125
h=9.947
To find the depth of water in the cylinder, calculate the volume of the cube and then use that volume to find the height of the cylinder.
Explanation:To find the depth of water in the cylinder, we need to calculate the volume of the cube and then use that volume to find the height of the cylinder.
The volume of a cube is given by V = s^3, where s is the length of a side.
The volume of the cube is (5 cm)^3 = 125 cm^3.
Now, we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height.
Using the volume of the cube as the volume of the water in the cylinder, we get 125 cm^3 = π(2 cm)^2h. Solving for h, we find h = 9.278 cm.
Therefore, the depth of the water in the cylinder is approximately 9.278 cm.
You need to buy enough sand to fill a sandbox to the top. The sandbox is modeled by the right rectangular prism in the diagram. How much sand do you need to buy?
A) 69 cubic feet
B) 70 cubic feet
C) 79 cubic feet
D) 80 cubic feet
Answer:80
Step-by-step explanation:
Mutiply all
Answer:
d
Step-by-step explanation:
how many degreese are in 1/9
angle
Answer:
10 degrees
Step-by-step explanation:
1/9 of 90 = 1/9 x 90 = 90/9 = 10
The correct answer is (b) [tex]$40^\circ$[/tex].
To find out how many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle, we first need to understand that a full circle has [tex]$360^\circ$[/tex].
To find [tex]$\frac{1}{9}$[/tex] of a circle, we need to divide [tex]$360^\circ$[/tex] by 9.
So, [tex]$\frac{360^\circ}{9} = 40^\circ$[/tex].
Therefore, [tex]$\frac{1}{9}$[/tex] of a circle is [tex]$40^\circ$[/tex].
Complete Question:
How many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle?
a. [tex]$90^{\circ}$[/tex]
b. [tex]$40^{\circ}$[/tex]
c. [tex]$42^{\circ}$[/tex]
d. [tex]$65^{\circ}$[/tex]
Question 2:
Describe the relationship between the following expressions:
3(25 x 25) and (25 x 25)
The relationship between the expressions 3(25 x 25) and (25 x 25) is that the first expression is 3 times greater than the second one.
Describe the relationship between the following expressions:
3 (25 x 25): This expression means 3 multiplied by the result of 25 multiplied by 25, which is 1875.
(25 x 25): This expression represents the result of multiplying 25 by 25, which is 625.
The relationship between these expressions is that the first expression is 3 times greater than the second expression.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Using the three indicated points on the given line and the concept of similar triangles, show and explain why the slope of the line is the same between any two of these three points. Calculate the slope of the line.
Answer:
Slope = 3/2 or 1.5
Step-by-step explanation:
(0,1) (2,4) (6,10)
Slopes:
(4-1)/(2-0) = 3/2
(10-4)/(6-2) = 6/4 = 3/2
(10-1)/(6-0) = 9/6 = 3/2
Any two points on the line will give the same slope because a straight line has a constant slope
A recipe calls for 2/5 of a pound of chicken for each person. If there are 8 people to be fed how many pounds of chicken are required?
Answer:
3 1/5
Step-by-step explanation:
The 2 pounds of chicken are required to feed 8 people.
To find out how many pounds of chicken are required to feed 8 people, we can multiply the amount of chicken required per person by the number of people:
2/5 pound of chicken per person * 8 people = 2 pounds of chicken
Therefore, 2 pounds of chicken are required to feed 8 people.
Another way to solve this problem is to use ratios. We know that we need to feed 8 people and that we have 2/5 of a pound of chicken per person. We can set up a ratio to find out how many pounds of chicken we need:
8 people / 2/5 pound of chicken per person = x pounds of chicken
To solve for x, we can multiply both sides of the equation by 2/5 pound of chicken per person:
8 people * 2/5 pound of chicken per person = x pounds of chicken
x = 2 pounds of chicken
Therefore, 2 pounds of chicken are required to feed 8 people.
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The value of a car is $30,000. It loses 6.5% of its value each year. What will the value of the car be after 5 years?
The value of a car that costs $30,000 and depreciates at 6.5% annually will be $22,530 after 5 years, calculated using exponential decay.
The value of a car is $30,000 and it loses 6.5% of its value each year. To calculate the value of the car after 5 years, we can apply the concept of exponential decay. The value after one year would be the initial value minus 6.5% of the initial value. Mathematically, we can express this as:
V1 = V0 (1 - 0.065),
where V1 is the value after one year and V0 is the initial value. To find the value after 5 years, we would apply this formula iteratively or use the formula for exponential decay:
Vn = V0 x (1 - 0.065)ⁿ,
where Vn is the value after n years. Therefore:
V5 = $30,000 x (1 - 0.065)⁵,
V5 = $30,000 x (0.935)⁵,
V5 = $30,000 x 0.7510,
V5 = $22,530.
After 5 years, the value of the car will be $22,530.
What are the domain and range of the function f(x) = 3x + 5?
A. domain: (negative infinity, infinity); range: (0, infinity)
B. domain: (negative infinity, infinity); range: (5, infinity)
C. domain:(0, infinity); range: (negative infinity, infinity)
D. domain: (5, infinity); range: (negative infinity, infinity)
The equation for line bis y = -2x + 3. Line c is the result of dilating line b by a factor
of 2 with center (0, -2). What is the equation for line c?
Answer:
[tex]y = - 2x + 8[/tex]
Step-by-step explanation:
The given equation is
[tex]y = - 2x + 3[/tex]
This is the equation of line b.
We want to find the equation of line c, after b is dilated by scale factor of 2 with center (0,-2).
Note that line c and b still have the same because they are parallel.
Also the y-intercept of b is 3.
The distance of the y-intercept of line b from the center of dilation is 5.
After a dilation by scale factor of 2, the y-intercept of c will be 2(5) =10 units from the center.
The y-intercept of c will therefore be:
10+-2=8
The equation c is
[tex]y = - 2x + 8[/tex]
The probability of getting a heads and an even number if you fill a die and flip a coin at the same time.
Mrs.stevens has award winning rose bushes that grow at a rate of 3/4 foot per week. Her American home rose bush currently measures 5 feet tall, while her camp David Rose bush is 4 1/2 feet tall in two weeks how tall will mrs.stevens American home rose bush measure?
Answer:
The answer would be 6.5 feet.
Pre-Thinking:
Knowing that the rose bushes grow at a rate of 3/4 feet per week, we can turn that into 0.75, a decimal.
Because, we need to know the height of the rose bush in 2 weeks, multiply 0.75 by 2.
0.75 * 2 = 1.5
Working and Stuff:
Because we only need the length of the American Home Rose Bush, which is 5 feet tall, we can discard the other rose bush.
Lastly, add 1.5 to 5.
1.5 + 5 = 6.5 feet
Amazing MS-Paint drawing of a rose bush:
Paul needs to wrap yellow tape around the perimeter of a new patio in the shape of a semicircle. The diameter of the patio is 42 meters.
Use 3.14 for .
The minimum length of yellow tape Paul needs to wrap around the patio is meters.
Answer:
Step-by-step explanation:
We need to find the circumference
d= 42 m
r= 42/2 = 21 m
Circumference =2πr or πd
= 3.14*42
=131.88 m
length of yellow tape Paul needs to wrap around the patio = 131.88/2 + 42
= 65.94 + 42 = 107.94 m
The floor of a rectangular room is to be tiled with 1/3 foot square tiles along a 9 3/8 foot wall. How many tiles will be needed along the wall?
Answer: Therefore, approximately 225/8 tiles will be needed along the 9 3/8 foot wall.
Step-by-step explanation:
To determine how many tiles will be needed along the 9 3/8 foot wall, we need to find the number of tiles that can fit in that space.
First, let's convert the mixed number 9 3/8 to an improper fraction. To do this, we multiply the whole number (9) by the denominator (8) and add the numerator (3):
9 * 8 + 3 = 75/8
Now, we have the length of the wall as 75/8 feet.
To find the number of tiles needed, we divide the length of the wall by the length of each tile. The length of each tile is 1/3 foot.
Dividing 75/8 by 1/3, we multiply the first fraction by the reciprocal of the second fraction:
(75/8) / (1/3) = (75/8) * (3/1)
Simplifying the calculation, we get:
(75 * 3) / (8 * 1) = 225/8
Therefore, approximately 225/8 tiles will be needed along the 9 3/8 foot wall.
To tile a 9 3/8 foot wall with 1/3 foot square tiles, 282 tiles are needed.
Explanation:The question is asking how many 1/3 foot square tiles will be needed along a 9 3/8 foot wall in your rectangular room. To find the answer, we first need to convert the length of the wall, which is given in mixed number, into an improper fraction. So, 9 3/8 is equal to 75/8 feet. Since each tile covers 1/3 foot, the number of tiles needed along the wall will be total distance divided by the length covered by each tile.
Therefore, the number of tiles = (75/8) ÷ (1/3) = (75/8) * (3/1) = 281.25
However, because we can't use a fraction of a tile, this number needs to be rounded up. Hence, you'll need 282 tiles to cover the 9 3/8 foot wall.
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Company A is offering $6,000 for the first month's salary and will increase the amount each month by $5,000. Company B is offering $700 or the first month and will double the pay each month.
Use the given table to determine for which month Company B's payment will first exceed Company A's payment?
A) Month 4
B) Month 6
C) Month 7
D) Month 9
The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
Step-by-step explanation:
Step 1:
Company A offers $6,000 for the first month and increases the salary each month by $5,000.
Company B offers $700 for the first month but doubles the payments each month.
We need to determine which month company B's payment is greater than company A's payment.
Step 2:
According to the table, at month 6 company A pays $31,000 while company B pays $22,400.
However after this month, in the seventh-month company A pays $36,000 while company B pays $44,800, which is higher than company A's salary.
So The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
4b-4=3b+4
solve for b
Answer:
4b-3b=4+4
b=8
Step-by-step explanation:
Hence, the value of b is 8
#hope it helps
Answer:
b=8
Step-by-step explanation:
4b-4=3b+4
You have to add 4 to both sides so that all the like terms are together
4b=3b+8
Then you subtract 3b from each side so that the like terms are all together
b=8
A paddock contains ducks and sheep. There are total of 42 heads and 96 feet in the paddock. How many ducks and how many sheep are in the paddock
What is an equivalent fraction of 2
Answer:
[tex]\frac{2}{1}[/tex]
Step-by-step explanation:
[tex]\frac{2}{1} = 2[/tex]
If a fractions denominator is a one that means the fraction is equal to the numerators whole number in this case we have 2/1 since the denominator is a 1 that means the whole fraction is equal to 2 because the numerator is 2.
Hope this helps.
Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack has 3 partially filled cases: 1 case is 12 full, 1 case is 14 full, and 1 case is 25 full. How many total
Answer:
51 loaves
Step-by-step explanation:
Given that one case contains 20 loaves.
-Sum the number of partially filled cases and divide to get complete cases:
[tex]T_{loaves}=12+14+25\\\\=51[/tex]
#He has a total of 51 loaves:
[tex]20 loaves = 1 case\\51 loaves=x\\\\x=\frac{51}{20}\\\\x=2 \ rem 11[/tex]
Hence, Zack has a total of 51 loaves (2 full cases, 1 partial of 11 loaves)
Question 6
Name the image of F(-3, 1) after being translated along the vector <5. - 1>.
Answer:
F' (2, 0 )
Step-by-step explanation:
A translation < 5, - 1 > means add 5 to the x- coordinate and subtract 1 from the y- coordinate, that is
F(- 3, 1 ) → F'(- 3 + 5, 1 - 1 ) → F'(2, 0 )
The image of the point F(-3, 1) after being translated along the vector <5, -1> is (2, 0). The process involves adding the vector components to the original point's coordinates.
Explanation:The initial point on the coordinate system is F(-3, 1). A translation moves a point by a specific vector. This vector is <5, -1>, meaning we move the point 5 units to the right and 1 unit down.
To perform the translation, we add the components of the vector to the coordinates of the original point. So, we add 5 to the x-coordinate (-3) and -1 to the y coordinate (1). This gives us the following results:
x-coordinate: -3 + 5 = 2y-coordinate: 1-1 = 0So, the image of F(-3, 1) after being translated along the vector <5, - 1> is the point (2, 0).
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Juan wants to start a lemonade stand to earn money.
He needs money to purchase the materials before he
can sell the lemonade and earn money. His mother
agrees to loan him $10. He makes a list of the items he
wants to buy.
Answer:
1. 13 2. 10
Step-by-step explanation:
5) What is the solution to the system of equations?
y=-2x+1 and y=-4/7x +1
A) (0,1)
B) (1,0)
C) (-2,1)
D) (-2, -4/7)
Answer:
-2x + 1 = -4/7x + 1
-14/7x + 1 = -4/7x + 1
-10/7x = 0
x = 0
y = -2(0) + 1
y = 1
(0,1)
answer is a
Adam wishes to advertise his business, so he gives packs of 16 red flyers to each restaurant
owner and sets of 4 blue flyers to each clothing store owner. At the end of the day, Adam
realizes that he gave out the same number of red and blue flyers. What is the minimum
number of flyers of each color
Answer:
16
Step-by-step explanation:
The Lcm of 16 and 4 is 16. I hope this helps
Answer:
The minimum number of flyers of each color is 16
Step-by-step explanation:
Since they are trying to find the minimum number of flyers of each color, they are looking for the least common multiple. That means that are trying to find the number that corresponds to 4 and 16 at the lowest value.
Step 1: Find the LCM
4 can be multiplied by 4 to get 16
4 * 4 = 16
Answer: The minimum number of flyers of each color is 16
The slope of a line is and the y-intercept is -1/5. What is the equation of the line written in slope-intercept form? Type the equation in the space provided. Be sure to use the slope-intercept form noted in the lesson. Do not type spaces in your answer. If necessary, use the / key to represent a fraction bar.
The equation of the line in slope intercept form is y = mx - 1/5, where m is the slope of the line.
Explanation:The subject of this question is mathematics, specifically geometry, and it pertains to how to write the equation of a line in slope-intercept form given the slope and the y-intercept. However, it appears there was a typographical issue as the slope wasn't provided in the question. Let us assume that the slope of the line is m.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this situation, if the slope is m and the y-intercept is -1/5, the required equation of the line in slope-intercept form can be written as y = mx -1/5.
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Which is the solution to the inequality? y + 15 less-than 3
A.) y less-than negative 12
B.) y greater-than negative 12
C.) y less-than 18
D>) y greater-than 18
Answer:
Option A.) y less-than negative 12
Step-by-step explanation:
we have
[tex]y+15<3[/tex]
solve for y
subtract 15 both sides
[tex]y+15-15<3-15[/tex]
[tex]y<3-15\\y<-12[/tex]
therefore
y less-than negative 12
Answer:
A
Step-by-step explanation:
A candy store makes a 10-lb mixture of gummy worms, candy corn, and sourballs. The cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. The mixture calls for three times as many gummy worms as candy corn. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
Step-by-step explanation:
Let the number of pounds of each ingredient be as follows:
Gummy Worms = x pounds
Candy Corn = y pounds
Sourballs = z pounds
The store makes a mixtures of 10 pounds. This means the sum of x, y and z would be 10. Setting up the equation:
[tex]x + y +z = 10[/tex] (Equation 1)
The mixture calls for 3 times as many gummy worms as candy corn. This means amount of gummy worm will be 3 times the candy corn. Setting up the Equation:
[tex]x=3y[/tex] (Equation 2)
Cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. So cost of x, y and z pounds would be:
1x , 3y and 1.5z, respectively. The total cost of mixture is $15. So we can set up the Equation as:
[tex]x+3y+1.5z=15[/tex] (Equation 3)
Using the value of x from Equation 2, in Equations 1 and 3 give us following two equations:
[tex]4y+z=10[/tex] By substitution in Equation 1. (Equation 4)[tex]6y+1.5z=15[/tex] By substitution in Equation 3. (Equation 5)
Multiplying the Equation 4 by 1.5 and subtracting from Equation 5 gives us:
[tex]6y +1.5z-1.5(4y+z)=15-1.5(10)\\\\ 6y+1.5z-6y-1.5z=15-15\\\\ 0=0[/tex]
When two sides of equations turn into something that is always positive, we conclude that there are infinite number of solutions. In such cases, we fix a variable and give different values to it, to find corresponding values of other variables. Lets re-write the solution in terms of z.
From Equation 4, we have:
[tex]y=\frac{10-z}{4}[/tex]
From Equation 2, we have:
[tex]x=3(\frac{10-z}{4} )[/tex]
Therefore, the solution set will be:
[tex](3(\frac{10-z}{4} ), \frac{10-z}{4} , z)[/tex]
Now in order to find any combination of ingredient, we give any value to z. Let, z is equal to 2 grams.
So,
x would be = 6 grams
y would be = 2 grams
So, one of the possible amount of ingredients that store can use is:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
Newton goes on a 10-day road trip. He takes $435 with him.
sends all of his money and spends the same amount
day. How much money does he spend each day?
Answer:
$43.5
Step-by-step explanation:
435/10 = 43.5
$43.5/day
Between the time Iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature dropped by 14°.
Write an addition expression for the temperature relative to when Iko woke up.
Answer: -3 degrees
Step-by-step explanation:
Lets say that the original temperature was "x."
The temperature rose by 11 degrees so it is now at 11+x.
Then the temperature fell by 14 degrees so you subtract. 11+x-14
11-14= -3 so you subtract 3 degrees from the original temperature and there fore the relative temperature is -3
I hope this helps!!!