The interest rate on loan is 5.25%.
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Given, Principal amount=$125,000, time=10years, Interest=$65,625.
Let r be the rate of interest, on applying simplest interest formula
I=P.r.t
Where P=principal amount, r=rate, t=time.
I=125,000 x r x10
65,625=125,000 x r x10
r=[tex]\frac{65,625}{125,000(10)}[/tex]
r=0.0525
r=5.25%
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Type the missing number to complete the proportion. 18 deliveries in 3 hours = deliveries in 1 hour
Answer:
6 deliveries in 1 hour
Step-by-step explanation:
18 / 3 = 6
What is the equation in slope-intercept form of the line that passes through the point (-1,3) and is parallel to the line represented by y=2x−7?
Answer:
y = 2x + 5
Step-by-step explanation:
The slope of 2 parallel line are always the same. This means that we can easily tell that the slope of the equation that we are trying to solve has a slope of 2. To find the "b" in the slope-intercept form, plug in the coordinates given and that's how you get the answer above.
Select the correct answer from each drop-down menu. A transversal t intersects two parallel lines a and b, forms two groups of angles. On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8. In the figure, , and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5. (given) m∠1 + m∠3 = 180° (Linear Pair Theorem) m∠5 + m∠6 = 180° (Linear Pair Theorem) m∠1 + m∠3 = ∠5 + ∠6 ( ) m∠3 = m∠6 ( ) m∠1 = m∠5 (Subtraction Property of Equality)
The angles formed between the parallel lines a and b and their common transversal are; on line a; 1,2,3,4. On line b; 5,6,7,8,
A two column table can be used to prove m∠1 = m∠5 with the correct options underlined as follows;
Statements [tex]{}[/tex] Reasons
1. a ║ b [tex]{}[/tex] 1. Given
2. m∠1 + m∠3 = 180° [tex]{}[/tex] 2. (Linear pair Theorem)
3. m∠5 + m∠6 = 180° [tex]{}[/tex] 3. (Linear pair Theorem)
4. m∠1 + m∠3 = m∠5 + m∠6 [tex]{}[/tex]4. (Substitution property of equality)
5. m∠3 = m∠6 [tex]{}[/tex] 5. (Alternate interior angles)
6. m∠1 = m∠5 [tex]{}[/tex] 6. (Subtraction Property of Equality)
What are parallel lines?Parallel lines are lines on the same plane that do not intersect or have a common point as they extend indefinitely in both directions.
The theorems and properties used to prove that the angles m∠1 = m∠5 are as follows
Linear pair theorem;
The linear pair theorem states that two angles that together form a linear pair are supplementary angles (Add up to 180°)
Substitution property of equality;
The substitution property of equality states that if two variables have the same value, then one variable can replace the other variable in equations and expressions without changing their value.
Subtraction property of equality
The subtraction property of equality states that when the same quantity is subtracted from two equal expressions, the values of the new expressions will also remain equivalent
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Look at the picture and answer the four questions
Answer:1=translation, 2= translation, 3=rotation, 4= reflection
Step-by-step explanation:
Find the rate of change between the following points:
(1,5)
(-5, 1)
The rate of change between (1,5) and (-5,1) is 0.
What is the rate of change?
The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).
Let (x,y)=(1,5), (m,n)=(-5,1)
Rate of change=(n-y)/(m-x)=(-5-(5))/(1-1)=0.
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On my last birthday, a friend said
to me:
"In 15 years' time, your age will be
the square of your age 15 years
ago!"
Can you work out how old I am?
let thee present age be x.
(x-15)^2=x+15
=>x^2–31*x+210=0
=>(x-21)(x-10)=0
x=10 or x=21
present age can not be 10 as it would result at absurd negative age( -5) 15 years ago.
so present age is 21.
AEFC is a Rectangle
Find:
1) ZX=
2) ZY =
3) ZZ =
Explain:
Explain:
Explain:
Step-by-step explanation:
X = 51. Parallel line angle rules, alternate angle is equal.
Straight angle is 180
Right angle is 90
Y = 180 - 51 - 90 = 39
Z = Y = 39. Parallel line angle rules, alternate angle is equal.
As part of his semester project, a byu-idaho introductory statistics student calculates a 95% confidence interval for the true percentage of byu-idaho students who are from latin america. What does the phrase 95% confidence mean?.
"95% confidence interval" means that there is a 95% chance that the true fraction falls within the computed confidence interval.
Confidence Intervals: Confidence intervals are the range of estimates for unknown parameters.
Confidence intervals are more than just a range of estimated values. It also tells you how stable the estimates are. A stable estimate is an estimate that has approximately the same value if the study is repeated. An unstable estimate is one that would vary from one sample to another.
The confidence interval determines the range that one can be certain that contains the true mean of the population.
This means that, The 95% confidence means, there is a 95% chance that the true proportion will be in the calculated confidence interval or 95 percent confidence interval, you have a 5 percent chance of being wrong.
Hence, the true statement that represents "95% confidence interval" is chance of true fraction of sucess.
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Find the value of
64 2
25
Give your answer as fraction in its simplest form.
Answer: 64/225 is already in simplest form
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator GCD (greatest common denominator) of 64 and 225
Divide both the numerator and denominator by the GCD
64÷1/225÷1
fraction: 64/225
Therefore, 64/225 simplified to lowest terms is 64/225.
A store sells 12 cans of soup for $7. 50 how much would it cost to purchase 6 cans of soup?.
Answer: $3.75
Step-by-step explanation:
Answer:
The cost of 6 cans of soup is 3.75
Step-by-step explanation:
12 = 7.50
1 can = x
12x = 7.50
We need to find the cost of 1 can. So we divide 7.50 by 12.
x = 0.625
Then multiply by 6.
0.625 x 6 = 3.75
As a result the cost of 6 cans of sup is $3.75
A person invests 5000 dollars in a bank. The bank pays 6.25% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 6500 dollars?
Based on the calculation below, the number of years the person must leave the money in the bank until it reaches 6500 dollars is 4.3 years.
How long must money be left in a bank to reach a particular amount?This can be calculated using the formula for calculating the future value (FV) as follows:
FV = PV(1 + r)^n ......................... (1)
Where:
FV = future value or the amount in the bank after certain years = 6500
PV = present value or the amount invested = 5000
r = quarterly interest rate = 6.25% / 4 = 0.0625 / 4 = 0.015625
n = number of quarters
Substituting relevant values into equation (1) and solve for n, we have:
6500 = 5000(1 + 0.015625)^n
6500 / 5000 = 1.015625^n
1.3 = 1.015625^n
Log linearize both sides, we have:
log1.3 = n * log1.015625
0.1139 = n0.0067
n = 0.1139 / 0.0067
n = 17 quarters
Number of years the money must be in the bank = n / number of quarters in a year = 17 / 4 = 4.25 years
To the nearest tenth of a year, we have:
Number of years the money must be in the bank = 4.3 years
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Answer:
Its actually 4.2
Step-by-step explanation:
saw it on delta
i need help, which one is it???
Answer
the one on the bottom left
Step-by-step explanation:
Simplify the expression.
Answer:
A
Step-by-step explanation:
-1/5 j + 3/4 - 5/2 j - 7/8 =
= (-2-25)/10 j + (6-7)/8 =
= -27/10 j - 1/8
The sum of an integer and 4 times the next consecutive even integer is 58. Find the
value of the greater integer.
By solving a linear equation, we will see that the value of the greater integer is 12.
How to find the greater integer?Let's define x as the smaller integer, then the greater integer is:
x + 2
(is +2 because is the next consecutive even integer)
We know the sum of an integer and 4 times the next consecutive even integer is 58.
So we can write the linear equation:
x + 4*(x + 2) = 58
x + 4x + 8 = 58
5x = 58 - 8
5x = 50
x = 50/5
x = 10
Then the greater integer is x + 2 = 10 + 2 = 12
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Solve each of these equations. Explain or show your reasoning. Reduce all fractions in the lowest terms. Do not convert fractions into decimals.
You'll need to show ALL of your work to receive points.
1. 3b + 9 -5b + 3 = -14 + 6b - 8
2. 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x
Answer:
b=17/4
x=-3/5
Step-by-step explanation:
This is what i put for the hw and i got 100% on it. If you want you can just write a bunch of random equations that look like they relate to the question and then just write and circle the answer, which is exactly what i did
Answer:
b = 17/4 x = -3/5Step-by-step explanation:
1) 3b + 9 - 5b + 3 = -14 + 6b - 8, for b?
→ 3b + 9 - 5b + 3 = -14 + 6b - 8
→ -2b + 12 = 6b - 22
→ -2b - 6b = -22 - 12
→ -8b = -34
→ b = -34/-8
→ [ b = 17/4 ]
Hence, the value of b is 17/4.
2) 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x, for x?
→ 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x
→ -2x + 13 = 25 + 30x - 12x
→ -2x - 18x = 25 - 13
→ -20x = 12
→ x = 12/-20
→ [ x = -3/5 ]
Hence, the value of x is -3/5.
Solve each of these equations. Explain or show your reasoning. Reduce all fractions in the lowest terms. Do not convert fractions into decimals.
You'll need to show ALL of your work to receive points.
1. 3b + 9 -5b + 3 = -14 + 6b - 8
2. 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x
I can help you!
Answer:
1) b = 17/4
2) x = -3/5
Step-by-step explanation (question one):
Step 1: Simplify both sides of the equation.
3b +9 + −5b + 3 = −14 +6b +−8
(3b +−5b) +(9 +3)=(6b) +(−14 + −8) (Combine Like Terms)
−2b +12 = 6b −22
Step 2: Subtract 6b from both sides.
−2b +12 −6b = 6b −22 −6b
−8b +12 = −22
Step 3: Subtract 12 from both sides.
−8b +12 −12 = −22 −12
−8b = −34
Step 4: Divide both sides by -8.
(-8b/-8) = (-34/-8)
Step 5: Get your Answer
b = 17/4
Step-by-step explanation (question two):
Step 1: Simplify both sides of the equation.
2x +5 + −4x +8 = (5)(5) +(5)(6x) + −12x (Distribute)
2x +5 + −4x +8 = 25 +30x + −12x
(2x+−4x) + (5+8) = (30x +−12x) +(25) (Combine Like Terms)
−2x +13 = 18x +25
Step 2: Subtract 18x from both sides.
−2x +13 −18x= 18x +25 −18x
−20x +13 = 25
Step 3: Subtract 13 from both sides.
−20x +13 −13 = 25 −13
−20x=12
Step 4: Divide both sides by -20.
(-20x/-20) = (12/-20)
Step 5: Get your Answer
x = -3/5
Hope this helped you, good luck with your homework!
find perimeter and area of composite figure
the perimeter of the composite figure is 20cm and its area is 37cm².
what is perimeter ?
Perimeter is the total length of the boundary of a two-dimensional shape or figure. In other words, it is the distance around the outside of a shape. To find the perimeter of a shape, you simply add up the lengths of all its sides.
In the given question,
To find the perimeter of the composite figure, we need to add up the lengths of all the sides.
Starting from the left side of the figure, we have a vertical line segment of length 6cm, followed by a horizontal line segment of length 5cm, then another vertical line segment of length 2cm, followed by a slanted line segment of length 3cm, then another horizontal line segment of length 2cm, and finally, a vertical line segment of length 2cm.
So the perimeter of the composite figure is:
Perimeter = 6cm + 5cm + 2cm + 3cm + 2cm + 2cm
Perimeter = 20cm
To find the area of the composite figure, we can break it down into simpler shapes and add up their areas.
The composite figure can be split into two rectangles, one with dimensions 6cm x 5cm and the other with dimensions 2cm x 2cm, and a right triangle with base 3cm and height 2cm.
The area of the first rectangle is:
Area = length x width
Area = 6cm x 5cm
Area = 30cm²
The area of the second rectangle is:
Area = length x width
Area = 2cm x 2cm
Area = 4cm²
The area of the right triangle is:
Area = (base x height) / 2
Area = (3cm x 2cm) / 2
Area = 3cm²
Therefore, the total area of the composite figure is:
Area = 30cm² + 4cm² + 3cm²
Area = 37cm²
So the perimeter of the composite figure is 20cm and its area is 37cm².
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PLEASEEEEE HELP MEEEE MATHHHHHHHHHHHHHH SUCKS FOR ME
What is the value of
∠E is 74° because it is alternate to the given angle of 74°.
∠E is and the 74° angle are alternate interior angles. Alternate interior angles are a pair of angles on the inner side of two parallel lines. But the angles should be on the opposite sides of the transversal. A transversal line is a straight line that intersects two or more parallel lines.
So here, ∠E and 74° lie on the inner sides of two parallel lines on the opposite sides of the transversal.
Therefore <E = 74°
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Write a recursive formula for am, the nth term of the sequence
16, 7, -2, -11, ....
aₙ = aₙ₋₁ - 9 is the recursive formula of Arithmetic progression.
Arithmetic progression is a sequence of number in order with same difference .
A fixed number is added to any term of a AP to get next term . That Fixed number is known as common difference.
In the question,
16 , 7 , -2 , -11 . . . .
First term of AP : a₁ = 16
Second term : a₂ = 7
Common difference : d = a₂ - a₁
=> d = 7 - 16
=> d = -9
The recursive formula of AP : aₙ = aₙ₋₁ + d
Here d = -9 , substituting d
The recursive formula of given AP : aₙ = aₙ₋₁ - 9
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A shape is picked at random from the group below.
2 circles, 4 triangles, and 2 squares.
Which event has a theoretical probability of exactly Three-fourths? Select three options.
not picking a square
picking a square
picking a triangle
picking a shape that has only straight edges
not picking a circle
*EDIT* sry about the first time I was trying to look it up and only had that part
The events that have probability of exactly three-fourths are
(a) not picking a square ,
(d) picking shape that has only straight edges ,
(e) not picking a circle .
In the question ,
it is given that ,
there are 2 circles , 4 triangles , 2 squares .
(a) probability of not picking a square = ( circles + triangles )/total
= 6/8 = 3/4
(b) probability of picking a square = number of square / total figure
= 2/8 = 1/4
(c) probability of picking up a triangle = 4/8 = 1/2
(d) probability of picking up shape with straight edge = ( triangle + square) / total
= 6/8 = 3/4
(e) probability of not picking a circle = ( triangle + square) / total
= 6/8 = 3/4 .
Therefore , The events that have probability of exactly three-fourths are
(a) not picking a square ,
(d) picking the shape that has only straight edges ,
(e) not picking a circle .
The given question is incomplete , the complete question is
A shape is picked at random from the group of 2 circles, 4 triangles, and 2 squares .
Which event has a theoretical probability of exactly Three-fourths? Select three options.
(a) not picking a square
(b) picking a square
(c) picking a triangle
(d) picking shape that has only straight edges
(e) not picking a circle
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The figures below show the top view and right-side view of a rectangular prism that is completely packed with unit cubes.
How many unit cubes would it take to completely fill the prism with no gaps between unit cubes?
The number of unit cubes it would take to completely fill the prism with no gaps between unit cubes is 72
Calculating the number of cubes required to fill a prismFrom the question, we are to determine how many unit cubes it would take to completely fill the prism with no gaps between unit cubes.
To do this, we will calculate the volume of rectangular prism
Assuming each cube is 1 cubic unit
Then,
From the top view,
The length of the rectangular prism = 9 units
The width of the rectangular prism = 2 units
From the Right-side view,
The height of the rectangular prism = 4 units
Thus,
The volume of the rectangular prism = 9 × 2 × 4
Volume of the rectangular prism = 72 cubic units
Now,
Number of cubes required to fill the rectangular prism = Volume of the prism / Volume of the cubes
Number of cubes required to fill the rectangular prims = 72 / 1
Number of cubes required to fill the rectangular prims = 72
Hence, the number of unit cubes it would take is 72
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Which graph represents the equation y^2? = -4x?
Answer:
[tex]x=-\frac{y^{2} }{4}[/tex]
Step-by-step explanation:
This graph is in terms of x.
To calculate control limits, 20 subgroups of ______ must be saved. Definition.
A. five sets.
B. five subsets.
C. five samples.
Answer:
C. five samples.
Step-by-step explanation:
If the area of a rectangle is 7y2 - 3y and the width is y, then what is the length of the rectangle?
The length of the rectangle is 7y - 3
What is a Rectangle?
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. The area of a rectangle A = L×W
Where,
A = Area of the rectangle which is 7y^2 - 3y
L = Length which is unknown
W = Width of the rectangle which is y
Substituting,
7y^2 - 3y = L × y
divide through by y
(7y^2 - 3y)/y = L
L = 7y - 3
Therefore the length of the rectangle is 7y - 3
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A car service charges $2.40 for driving 1 mile. How much does the company charge for
driving 12.45 miles?
Answer:
no se Perdóname
Answer:
since 1 mile charge is $2.40
Then 12.45 miles is
2.40×12.45
=$29.88
√(14)*(3 √(7) + √(32) - √(28) + 2 √(2))
Answer:
27√2 -2√7 ≈ 32.8923
Step-by-step explanation:
Apparently, you want to simplify the expression √(14)*(3 √(7) + √(32) - √(28) + 2 √(2)).
Rules of radicals(√a)(√b) = √(ab)
√(a²b) = a√b
Application[tex]\sqrt{14}\cdot3\sqrt{7}+\sqrt{32}-\sqrt{28}+2\sqrt{2}\\\\=3\sqrt{14\cdot7}+\sqrt{4^2\cdot2}-\sqrt{2^2\cdot7}+2\sqrt{2}\\\\=3\sqrt{7^2\cdot2}+4\sqrt{2}-2\sqrt{7}+2\sqrt{2}=(3\cdot7+4+2)\sqrt{2}-2\sqrt{7}\\\\=\boxed{27\sqrt{2}-2\sqrt{7}}[/tex]
This is confusing.
Gradient is???
For the given graph, the gradient of the given blue line in the graph is equal to 2.
As given in the question,
For the given graph,
Consider two pairs of coordinates on the blue line of the given graph,
( x₁ , y₁ ) = ( 2, 2 )
( x₂ , y₂ ) = ( 3, 4 )
Gradient is nothing but slope of the line
Formula to calculate the gradient of the given blue line of the graph is given by:
Gradient = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula we get,
Gradient = ( 4 - 2 ) / ( 3 - 2 )
= 2 / 1
= 2
Therefore, for the given graph, the gradient of the given blue line in the graph is equal to 2.
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can you substitute -4x-y=4 and y=2x+2
Answer:
yes, by x=-1, y=0
Step-by-step explanation:
y=-4x-4
y=2x+2
-4x-4=2x+2
6x=-6
x=-1
y=0
Is 24 simplified expression