Step-by-step explanation:
Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.
The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330
Solve for x:
0.06x(3)+0.075(18000−x)(3)=3330
Step 1: Simplify both sides of the equation.
0.06x(3)+0.075(18000−x)(3)=3330
0.06x(3)+−0.225x+4050=3330(Distribute)
0.18x+−0.225x+4050=3330
(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)
−0.045x+4050=3330
−0.045x+4050=3330
Step 2: Subtract 4050 from both sides.
−0.045x+4050−4050=3330−4050
−0.045x=−720
Step 3: Divide both sides by -0.045.
−0.045x/−0.045=−720/−0.045
x=16000
x=16000
So, the amounts borrowed are:
Bank at 6% = 16000
Bank at 7.5% = 2000
Already did the gradient a , just stuck on gradient B
The gradient of line B is (-1).
What is gradient?The gradient of a line is used to calculate the steepness of a line and determines how much it is inclined with reference to the x-axis. To calculate the gradient of any line, the x and y coordinates of a line are used. In other words, it is the ratio of the change in the y-axis to the change in the x-axis.
The gradient is the measure of the steepness of a straight line.
Given:
coordinates taken from line B is (5, 0) and (-2, 7)
we have [tex]y_2[/tex]= 7, [tex]y_1[/tex]= 0, [tex]x_1[/tex]= 5, [tex]x_2[/tex] =-2
now, substituting the values then,
The gradient is
=[tex]( y_2- y_1)/ (x_2 - x_1)[/tex]
=(7-0) / (-2 - 5)
=7 /(-7)
=-1
Hence, the gradient is -1
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The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.
The standard deviation of the response time is 1.2755 minutes.
How to illustrate the information?Based on the information, the response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.
The standard deviation of the response time will be illustrated thus:
It should be noted that the area under the one tailed standard normal curve is given as:
P(0 <= Z <= 1.96) = 0.475
The standards deviation will be:
= 2.5 / 1.96
= 1.2755
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The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes. What is the standard deviation of the response time?
Simplify each number. 32¹.²
The result of simplifying the number 32¹.² using the exponent rules is 1024
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(32¹)²
32⁽¹*²⁾ =
32² =
32 * 32 =
1024
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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If x is a binomial random variable with n = 20 and p = 0.25, the expected value of x is:_________
The expected value with a sample size of 20 and a probability of 0.25 will be 5.
What is the expected value?The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.
E(x) = 20 x 0.25
E(x) = 5
The expected value with n = 20 and p = 0.25 will be 5.
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Marcelo plays a carnival game six times he spent three tokens to play each game and he won 7 tokens each game write two different expressions that can be used to find the total profit in tokens that Marcelo made
The expressions that can be used to find the total profit in tokens that Marcelo made is (7 × 6) - (3 × 7) and 42 - 21.
How to illustrate the information?From the information, Marcelo plays a carnival game six times he spent three tokens to play each game and he won 7 tokens each game.
The appropriate expression will be:
= (7 × 6) - (3 × 7)
= 42 - 21
= 21
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If m<2=9x+7 and m<3 = 5x + 5, what is m<1?
The value of m<1 is 65 degrees
How to determine the angleFrom the diagram shown, we have that;
m<2=9x+7 m<3 = 5x + 5It is important to note that angles on a straight line sum up to 180 degrees
Also, corresponding angles are equal
Then, we have that;
m<2 + m<3 = 180°
Substitute the values
9x + 7 + 5x + 5 = 180
collect like terms
14x = 180 - 12
14x = 168
Make 'x' the subject
x = 168/ 14
x = 12
We have that;
m<3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65
But m<3 = m<1
m<1 = 65
Thus, the value of m<1 is 65 degrees
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jada and mai are trying to decide what type of sequence this could be
Since the difference between consecutive terms is the same, the sequence is an arithmetic sequence, hence Mai is correct.
What is the missing information?The sequence is missing, and has these following information:
The first term is of 2.The second term is of 6.The fifth term is of 18.We also have that:
Jada says that the sequence is geometric.Mai says that the sequence is not geometric.What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the values os the function, we have that:
d = a2 - a1 = 4.4d = a5 - a1 -> 4d = 16 -> d = 4.3d = a5 - a2 -> 3d = 18 - 6 -> 3d = 12 -> d = 4.The rate of change is the same, hence sequence is an arithmetic sequence, and Mai is correct.
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Ryan has 1.75 meters of satin ribbon. Which fraction correctly represents the length of ribbon Ryan has?
Answer: Papst blue ribbon
Step-by-step explanation:
Ryan lives in a trailer park. He likes to drink papst blue ribbon and not wear satin robes.
Plane H contains four points. Points A, C, and D form a diagonal line on the left. Point B is to the right of point C.
Which points are coplanar and noncollinear?
points A and D
points C and D
points A, C, and D
points A, B, and D
Answer:
Points A B D
Step-by-step explanation:
I am assuming in the plane, all the points are inside. For it to be non- collinear, I am pretty sure there has to be points not on the line. In this Case, only A C D are actually on a line. Since B is to the right of C, I don't think that will make a good line. So that is the answer I am going with.
Answer:
d)a ,b,d
Step-by-step explanation:
Expand each logarithm. State the properties of logarithms used. log₄x²y³
log₄x²y³ = log x² + log y² is solution of this logarithmic function.
What is an example of a logarithmic function?
For instance, 2y = 8 can be used in instead of y = log2 8. We have y = 3 since 8 = 23. Y stands for the exponent and the logarithm, as was discussed at the outset of this session. A logarithm is an exponent, therefore.What distinguishes exponential from logarithmic growth?
The opposite of exponential functions are logarithmic functions. The exponential function y = ax has the inverse, x = ay. The exponential equation x = ay is defined as being identical to the logarithmic function y = logax.we use property [ log ( mn) = log + log n ] in equation -
log₄x²y³ = log x² + log y²
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Evelyn is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has 18 stuffed cats and 12 stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Evelyn can place her stuffed animals into?
The greatest number of groups Evelyn can place her stuffed animals into
= 6 Groups.
We have been given that
Evelyn should donate her collection of stuffed animals in which
No. of stuffed cats = 18
No. of stuffed dogs = 12.
We have to find out number of groups with no stuffed animals left over.
for solving this question we can use GCF
What is GCF (Greatest Common Factor)?
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
How can we find GCF?
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.
18 and 12 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 12.
The common factors of 12 and 18 are 1, 2, 3 and 6. The greatest common factor of them is 6.
In each groups no. of cats and dogs are (3cats , 2 dogs)
Hence , 6 is the greatest number of groups Evelyn can place her stuffed animals into.
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<, >, or =
-3.625 ___ -3.62
Answer:
-3.625 < -3.62
Step-by-step explanation:
If you add 1 to an even number, the answer will be even.
A. True
B. False
Answer:
the answer is false
Step-by-step explanation:
this is an example: 22+1=23 23 is not an even number
Answer:
B. False
Step-by-step explanation:
Let the even number be x_e and odd be x_o
[tex]{ \tt{ = x _{e} + 1}}[/tex]
Assume the range is 2 ≤ x ≤ 4
[tex]{ \tt{x _{2} = 2 + 1}} \\ { \tt{x_{2} = 3 \: (odd)}}[/tex]
[tex]{ \tt{ x_{4} = 4 + 1}} \\{ \tt{x _{4} = 5 \: (odd)}}[/tex]
Therefore:
[tex]{ \tt{x _{n + 1} = x _{e} + n \: \: gives \: odd}}[/tex]
Hence;
[tex]{ \tt{ x_{e} + 1 = x _{o} }}[/tex]
A triangle has vertices on a coordinate grid at R(-3,3)R(−3,3), S(-3,-9)S(−3,−9), and T(-9,-9).T(−9,−9). What is the length, in units, of \overline{RS}
RS
?
The length of the side RS in triangle RST as required to be determined in the task content is; 12 units.
What is the distance between two points?The distance between two points defined by pairs of coordinates on the Cartesian plane can be determined by a modification of the Pythagoras theorem.
Hence, the distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:
AB= √{(y₂ - y₁)² + (x₂ - x₁)²}
Given that the vertices R and S of the triangle is at R(−3,3), S(-3,-9), hence:
RS= {( -9-3 )² + ( -3-(-3))² } = 12 units.
The length of the side RS in triangle RST is 12 units.
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Line g has an equation of y = -2/9x + 6. Parallel to line g is line h, which passes through the point (3, 2). What is the equation of line h? Write the numbers in the equation of line h
Two parallel lines have equal slope.
Therefore, slope of line y = -2/9x + 6 is equal to the slope of the line joining the points (3,2).
Slope of line is given by :
m= -[(coefficient of x) / (coefficient of y)]
Where m= slope,
Slope of line y = -2/9x + 6
2/9x + y = 6
(m1) slope of equation g = -x/y
= -(2/9)/1
= -2/9
Since equation h is parallel to g
So, m1=m2
That is slope of equation h=slope of equation g
We know,
Equation of the line h having slope=m2= -2/9
passing through the slope of the point (3,2) is,
y-y1=m(x-x1)
Replace with values x1,y1=(3,2) and m=-2/9
y-2=(-2/9)(x-3)
We can solve it :
9y-18=-2x+6
2x+9y=6+18
2x+9y=24
2x+9y-24=0
Hence,
2x+9y-24=0 is the equation of h.
Therefore,
Line g has an equation of y = -2/9x + 6. Parallel to line g is line h, which passes through the point (3, 2), then the numbers in the equation of line h is 2x+9y-24=0
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calculate the area of ABC and the area of ABDE for each of these diagrams
Step-by-step explanation:
ED || AB
E is the midpoint of AC.
therefore, D is the midpoint of BC, and AB is 2×ED.
but also the height of ABC is 2×height of EDC.
now, we know, the area of a triangle is
baseline × height / 2
area EDC = baseline × height / 2 = 18 cm²
area ABC = 2×baseline × 2×height /2 =
= 4 × (baseline × height / 2) =
= 4 × area EDC = 4 × 18 = 72 cm²
the area of ABDE = area ABC - area EDC =
= 72 - 18 = 54 cm²
Based on the results express the probability that the next chew Lamonte removes from the bag will be apple chew as a percent to the nearest whole number
An apple chew was selected 13 times.
A strawberry chew was selected 6 times.
A like chew was selected 15 times.
Solve. Check for extraneous solutions. √5-x -√x=1
x = 4 is an extraneous solution.
√(5-x) -√x=1
√(5-x) = 1 + √x
Squaring both sides of the equations, we get
(√(5-x))² = (1 + √x)²
5 - x = 1 + x + 2√x
4 - 2x = 2√x
Squaring again both sides of the equations, we get
(4 - 2x)² = (2√x)²
16 + 4x² - 16x = 4x
4x² - 20x + 16 = 0 ...(1)
By middle term splitting equation (1) can be written as
4x² - 16x - 4x + 16 = 0
4x(x - 4) -4(x - 4) = 0
(x - 4) (4x - 4) = 0
4x - 4 = 0 and x - 4 = 0
x = 1 and 4
Check for Extraneous solution by putting value of x in the original equation -
Let x = 1
√(5-1) -√1=1
√4 - 1 = 1
2 -1 = 1
1 = 1
Since, LHS = RHS, so, x = 1 is not an extraneous solution
Let x = 4
√(5-4) -√4=1
√1 - 2 = 1
1 - 2 = 0
-1 = 0
which is a contradiction, so, x = 4 is an extraneous solution.
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If 8x+7y=6 is a true equation, what would be the value of 5+8x+7y?
If the equation 8x+7y=6 is a true equation, then the value of the equation 5+8x+7y is 11
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of the equation?The equation is given as
8x + 7y = 6
The above equation is said to be true
The next step is to add 5 to both sides of the equation 8x + 7y = 6
So, we have
5 + 8x + 7y = 6 + 5
Evaluate the sum of the like terms
So, we have
5 + 8x + 7y = 11
Hence, if the equation 8x+7y=6 is a true equation, then the value of the equation 5+8x+7y is 11
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Bob has a window that is 114 square feet. The window is in the shape of a square. Which of the following expresses the length of one of the sides of the window? A 1142 B √57 C √114 D√111 E 1143 answer as soon as possible :)
The expression of the length of one of the sides of the window is √114
What are areas?The area of a shape is the amount of space on the shape
Which of the following expresses the length of one of the sides of the window?The area of the window is given as
Area = 114 square feet
The shape of the window is a square
The area of a square is calculated as
Area = Length^2
So, we have
114 = Length^2
Take the square root of both sides
Length = √114
Hence, the expression of the length of one of the sides of the window is √114
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Solve
please show all steps
Answer:
10m + 100 = 15m
20 movies
Step-by-step explanation:
Hello!
Let the number of movies watched be m.
The equation for the first movie club would be 10m + 100, as you pay 10 dollars per movie (10*m) and you add the original membership fee (100).
The equation for the second movie club is 15m, 15 dollars per movie. Set the equations equal to each other and solve for m, the number of movies, so the price would be equal.
Solve for m10m + 100 = 15m 100 = 5m (subtract 10m)20 = m (Divide by 5)Therefore, you would need to watch 20 movies in each movie club for the total price to be equal.
2 nm = _____ cm
WHAT IS THE FORMULA I CANT --
2nm = 2e-7 cm or written out 0.0000002 cm
To convert nm to cm, you have to divide the value by 1e+7 (10000000).
the quotient of y and 27
y ÷ 27
27 ÷ y
y ÷ 27 + y
y × 27
im literally so confused pls explain how you got the answer bc someone told me and means multiplication and math but apparently it doesnt so
It should be noted that the quotient of y and 27 will be y ÷ 27. The correct option is A.
How to illustrate the information?It should be noted that quotient simply means the quantity that's produced when two numbers are divided. A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio. The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8, while the divisor is 4.
When we divide a number, the result we ultimately get is the quotient. The mathematical symbol (÷ ) denotes division, a technique for allocating items equally among groups.
In their case, the quotient of y and 27 simply means the division of the numbers. This will be y ÷ 27.
Therefore, the correct option is A.
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Write each expression in simplest form. 5+√3 / 2-√3
The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.
An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.
Consider the expression,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]
Rationalizing the denominator,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]
Using the identity,
( a + b )( a - b ) = a² - b²
Therefore,
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]
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here are the first two terms of some different arithmetic sequences
The best there terms of the sequence will be:
a. 10, 16
b. 211, 311
c. 10 , 12.5
d. -13, -22
How to illustrate the information?It should be noted that in an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term.
We find the constant difference for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.
a. 4 - (-2) = 6
3rd term: 4 + 6 = 10
4th term: 10 + 6 = 16
b. 111 - 11 = 100
3rd term: 111 + 100 = 211
4th term: 211 + 100 = 311
c. 7.5 - 5 = 2.5
3rd term: 7.5 + 2.5 = 10
4th term: 10 + 2.5 = 12.5
d. -4 - 5 = -9
3rd term: -4 + (-9) = -13
4th term: -13 + (-9) = -22
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Here are the first two terms of some different arithmetic sequences:
a. -2,4
b. 11, 111
C. 5, 7.5
d. 5,-4
What are the next three terms of each sequence?
A quality engineer selects 3 ipods from a box that contains 20 ipods of which 3 are defective. what is the probability that the first is defective and the others are not defective?
Answer:
0.119
Step-by-step explanation:
Based on the concept of conditional probability, the probability that the first iPod is defective and the others are not defective is approximately 0.1842
What is Conditional Probability?Conditional Probability is a term that is used to describe the chances that some outcome occurs given that another event has also occurred.
Generally, the functional probability is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening
In this case, to find the answer we break down the problem step by step:
Step 1: Find the probability that the first iPod is defective.
Since there are 3 defective iPods out of 20 total the probability of selecting a defective iPod on the first draw is 3/20.
Step 2: Find the probability that the second and third iPods are not defective.
After selecting a defective iPod there are 19 remaining iPods in the box out of which 17 are not defective.
Hence, the probability of selecting a non-defective iPod on the second draw is 17/19.
Also, given that the probability of selecting a non-defective iPod on the third draw (assuming the previous two iPods were not defective) is 16/18.
Step 3: Finding the overall probability.
The overall probability of the first iPod being defective and the second and third iPods being non-defective can be computed by multiplying the probabilities of each step:
Probability = (3/20) * (17/19) * (16/18)
= (51/380) * (16/18)
= 0.1842105
Therefore, in this case, it is concluded that the correct answer is approximately 0.1842 or 18.42%.
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Given f(x)=2x²+4, find the value of f(−1)
Answer:6
Step-by-step explanation:
when x is -1 y is 6. input -1 as x in the equation and solve, otherwise graph.
Write and solve an inequality to find the possible values of x. (Please answer ASAP)
The inequality is: 14.2 + 14.2 + x < 51.3
x < 22.9
How to Solve an Inequality?We are given the following:
Perimeter of the triangle < 51.3 in.
The sides are 14.2 in., x in., and 14.2 in.
Therefore, we would have the following inequality:
14.2 + 14.2 + x < 51.3
Solve for x
28.4 + x < 51.3
x < 51.3 - 28.4
x < 22.9
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Three cars are shown below, along with
their original prices.
The price of each car is then rounded to
the nearest £100.
a) Work out which car's price changes the
most.
b) By how much does this car's price
change?
Car X
£13,420
MATHS X
Car Y
£17,590
MATHS Y
Car Z
£12,860
MATHS Z
In linear equation , the car y's price changes the most.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.According to the question
a) Car x : £ 10320 ≈ £ 10300 10320 - 10300 = 20
Car y : £ 15430 ≈ £ 15400 15430 - 15400 = 30
Car z : £ 17490 ≈ £ 17500 17490 - 17500 = 10
10 < 20 < 30
so the car y's price changes the most.
b) this car's price change £ 30
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Order the numbers from smallest to largest:
\large \mid4\mid,\sqrt{9},-3,\mid-5\mid,-3^2,2^3
Reorder answers
1.
\large -3
Reorder answers
2.
\large -3^2
Reorder answers
3.
\large \sqrt{9}
Reorder answers
4.
\large \mid4\mid
Reorder answers
5.
\large \mid-5\mid
Reorder answers
6.
\large 2^3
The rational numbers ordered from smallest to largest are given as follows:
-3², -3, sqrt(3), 4, 5, 2³.
What are rational numbers?Rational numbers are numbers that can be represented by fractions, such as integers and terminating or repeating decimals.
They are ordered as follows:
negative infinity, ..., -5, ..., -3, ..., 0, ..., 3, ..., 5, ..., positive infinity.
That is, large negative are the smallest, and large positives are the greatest.
For this problem, the numbers are given as follows:
4.sqrt(9) = 3.-3.5.-3² = -9(as it is not inside the parenthesis, only 3 is squared and the negative sign stays).2³ = 8.Hence the ordering, from least to greatest, of the numbers is given as follows:
-3², -3, sqrt(3), 4, 5, 2³.
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