simplify the expression
ab – 2ac + cb
Answers
Answer:2
Step-by-step explanation:
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Math pls patulong
You are a bank financier. Your bank pays an annual interest rate of 3% compounded
quarterly. If the initial deposit (or principal), of your client is Php 50 000, find the
balance after 5 years.
You have to show the balance of Php 50 000 after 5 years if the bank pays an interest
rate of 3% compounded annually. Which gives a higher interest between the two?
Explain.
Answers
Using compound interest, it is found that:
With interest compound quarterly, the balance is of Php 5,804.With interest compound annually, the balance is of Php 5,796.Due to the higher balance, the quarterly compound gives the higher interest.Compound interest:\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.
In this problem:
Rate of 3%, hence \(r = 0.03\).Compounded quarterly, hence \(n = 4\).Initial deposit of 50000, hence \(P = 50000\).Five years, hence \(t = 5\).Then, the balance is:
\(A(5) = P\left(1 + \frac{r}{n}\right)^{nt}\)
\(A(5) = 5000\left(1 + \frac{0.03}{4}\right)^{4(5)}\)
\(A(5) = 5804\)
With interest compound quarterly, the balance is of Php 5,804.
Now, with annual interest, we have that \(n = 1\), and:
\(A(5) = P\left(1 + \frac{r}{n}\right)^{nt}\)
\(A(5) = 5000\left(1 + \frac{0.03}{1}\right)^{1(5)}\)
\(A(5) = 5796\)
With interest compound annually, the balance is of Php 5,796.
Due to the higher balance, the quarterly compound gives the higher interest.
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calcula correctamente cada una de las ecuaciones de la recta.
pasa por los puntos a(4,-6) y b(-5,3)
Answers
The equation of straight line of the points is given as y = -x - 2
Equation of Straight LineTo solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.
In the given points;
A = (4, -6)B = (-5, 3)The formula of slope of a line is given as
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Substituting the values into the equation;
\(m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1\)
The slope of the line is equal to 1.
Let's find the intercept of the line
\(y = mx + c\)
Taking point A;
\(y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2\)
The equation of the line is y = -x - 2
Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).
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Chris bought 12.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closetsto the number of liters of gasoline Chris bought? A 11.44 L B 2.74 L C 47.12 L D 14.20 L2
Answers
Answer:
C 47.12 L
Step-by-step explanation:
1 gallon = 3.8 liters
12.4 gallons = x
Cross Multiply
= 12.4 × 3.8
47.12 liters
Option C is correct
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
A.
y = 3x + 4
B.
y = 3x − 14
C.
y = 3x − 4
D.
y = 3x + 12
Answers
Answer:
A. y = 3x + 4
Step-by-step explanation:
got it correct!
How to do this question plz
Answers
Answer:
Aproximately 25 days
Step-by-step explanation:
so he goes 15.12 mph and rides for 8 hours so 15.12*8=120.96
3069.25/120.69
=25.374091 round it to nearest whole number so its 25days
you take 6 steps forward and 8 steps backwards how many steps have you taken?
It’s a subtracting integer question.
So would it be 6-(-8)?
Answers
Answer:
I think it would be simply 6-8
Step-by-step explanation:
becuase 6-(-8) is really 6+8, which isn't correct. It could also be 6-(8), but I'm not sure.
Lamont made a scale drawing of the elementary school. The scale of the drawing was 1 millimeter : 4 meters. The actual width of the school yard is 36 meters. HOW WIDE IS THE SCHOOL YARD IN THE DRAWING?
Answers
Answer:
36 meters
Step-by-step explanation:
hope it helps bye
Answer: 9 millimeters
Step-by-step explanation:
A golf cart priced at $5,600 was on slae for 20% off.The sales tax rate is 6%.What is the sale price of the golf cart,including tax?
Answers
Answer:
$4748.80
Step-by-step explanation:
First, find the cost with 20% off, by multiplying the price by 0.8
5600(0.8)
= 4480
Find the cost with tax, by multiplying this by 1.06
4480(1.06)
= 4748.8
So, the sale price, including tax, is $4748.80
80/100 x $5600 = $4,480 (same as 80% times $5600)
6/100 x $4,480= $268.80 (sales tax price)
$4,480+$268.80=$4748.80
Some species have earned the names dog vomit slime and wolf’s milk slime. Through research, biologists have determined that these single-celled organisms live on mulch or wet decayed wood, have membrane-bound organelles, do not have chitin in their cell walls, and do not contain chlorophyll. In which kingdom do these organisms most likely belong?
Answers
The organisms that have earned the names dog vomit slime and wolf's milk slime, which live on mulch or wet decayed wood, have membrane-bound organelles, do not have chitin in their cell walls, and do not contain chlorophyll most likely belong to the Kingdom Fungi.
Kingdom Fungi is one of the five kingdoms in which living organisms are classified based on their characteristics and taxonomy. Fungi are unicellular or multicellular eukaryotic organisms that are heterotrophic and obtain food through the absorption of nutrients from the environment.
Fungi are known for their ability to break down complex organic matter, such as wood and other plant materials, and convert it into simpler compounds that can be used by other organisms. They play a crucial role in the ecosystem, serving as decomposers, mutualists, and parasites. The organisms mentioned in the question share several characteristics with fungi, including their mode of nutrition and their habitat, which is why they are most likely to belong to the Kingdom Fungi.
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You can infer causality from a correlational result, but only when the r value is greater than ?A. 0B. 5C. 1
Answers
You can infer causality from a correlational result, but only when the r value is greater than:
C. 1
Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.
However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.
In addition, there are other factors that need to be considered when assessing causality from a correlational result.
For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.
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Are the ratio 1 is to 2 is to 3 equivalent?
Answers
the ratio 1 is to 2 is equivalent to 3: 6
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Mark draws one card from a standard deck of 52. He receives $ 0.50 for a heart, $ 0.65 for a jack and $ 0.85 for the jack of hearts. How much should he pay for one draw
Answers
The value of Mark should pay $ 0.210 for one draw.
Mark draws one card from a standard deck of 52. He receives $ 0.50 for a heart, $ 0.65 for a jack and $ 0.85 for the jack of hearts.
The probability of drawing a heart out of a standard deck of 52 cards is 13/52 or 1/4. If Mark draws a heart, he receives $ 0.50.
There are 4 Jacks in a standard deck of 52 cards. The probability of drawing a Jack out of a standard deck of 52 cards is 4/52 or 1/13.
If Mark draws a Jack, he receives $ 0.65.The Jack of hearts is the only one of its kind in a standard deck of 52 cards. The probability of drawing the Jack of hearts out of a standard deck of 52 cards is 1/52.
If Mark draws the Jack of hearts, he receives $ 0.85.
Therefore, the expected value of a single draw for Mark is:
(1/4)($ 0.50) + (1/13)($ 0.65) + (1/52)($ 0.85) = $ 0.144 + $ 0.050 + $ 0.016 = $ 0.210.
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Find the volume of the pyramid with a square base where the perimeter of the base is 8. 7cm and height of the pyramid is 6. 3cm round your answer to the nearest tenth of the cubic centimeter
Answers
Answer:
9.9\(cm^{3}\)
Step-by-step explanation:
Formula:
1/3(area of the base x height)
1/3 [2.175(2.175)(6.3)]
1/3(4.730625)(6.3)
1/3(29.8029375)
9.9343125
Is the perimeter of the base is 8.7, we need to divide that by 4 (2.175) to find out the side length of the square. The area of the square, we need to multiply 2.175 by 2.175.
9.9343125 rounded to the nearest tenth is 9.9
Helping in the name of Jesus.
just the linked questions, thanks . 8.4 similar triangles unit 8 practice a
Answers
The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;
8. \(\overline {ST}\) is parallel to \(\overline{PR}\)
9. \(\overline{ST}\) is parallel to \(\overline{PR}\)
10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)
11. x = 57.6
12. x = 25.8
13. x = 11
14. x = 10
15. x = 5
16. x = 17
What is Thales theorem?Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.
8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625
Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)
9. The ratio of the sides the parallel side to the base divides the other two sides are;
33/41.8 = 15/19
45/(102 - 45) = 45/57 = 15/19
Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)
10. The ratio of the sides the segment \(\overline{ST}\) bisects the other two sides are;
24/57 and 19/38
24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)
Second part; To solve for x
11. x/30 = 48/25
x = (48/25) × 30 = 57.6
x = 57.6
12. x/34.4 = (49 - 28)/28
x = 34.4 × (49 - 28)/28 = 25.8
x = 25.8
13. (2·x + 6)/52.5 = 32/60
(2·x + 6) = 52.5 × (32/60)
x = (52.5 × (32/60)) - 6)/2 = 11
x = 11
14. (x - 3)/21 = (x - 1)/27
27·x - 27 × 3 = 21·x - 21
27·x - 81 = 21·x - 21
6·x = 60
x = 60 ÷ 6 = 10
x = 10
15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)
15/20 = (4·x - 2)/(7·x - 11)
15 × (7·x - 11) = 20 × (4·x - 2)
105·x - 165 = 80·x - 40
105·x - 80·x = 165 - 40 = 125
25·x = 125
x = 125/25 = 5
x = 5
16. (x - 3)/35 = 4/(x - 7)
(x - 3) × (x - 7) = 35 × 4 = 140
x² - 10·x + 21 = 140
x² - 10·x - 119 = 0
(x - 17) × (x + 7) = 0
x = 17 or x = -7
Therefore, the possible value of x is 17
x = 17
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What is the simplified version for 2^2×2^3/2^4?
A 2^0
B 2^1
C 2^2
D 2^3
Answers
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lorenzo is a kickboxing instructor who will be teaching classes at a local gym. to get certified as an instructor, he spent a total of $94. lorenzo will be earning a base salary of $79 per month from the gym, plus an additional $3 for every class he teaches. if lorenzo teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. how many classes will that take? how much will lorenzo's expenses and earnings be?
Answers
Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.
Given that:
Amount he spends = $94
His base salary = $79/ month
Additional amount = $ 3
Let x represents the money he earn for every one class.
we can no put it in a equation:
79(1) + 3x = 94
⇒ 79 +3x = 94
⇒ 3x = 15
⇒ x = 15/3
⇒ x = 5
Therefore, Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.
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Please help due in 10mins
Answers
Answer:
(2,7), (6,-2),
Step-by-step explanation:
After finding the points you plug them in to the distance formula:
d=√((x2-x1)²+(y2-y1)²)
d=√[(6-2)²+(-2-7)²]
Jack paid $46 for 4 pizzas. How much did he pay per pizza?
Answers
Answer:
$11.50
Step-by-step explanation:
46/4=11.5
In money have to make it the hundredths, so it's $11.50.
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Answer:
$11.50
Step-by-step explanation:
$46 ÷ 4 = 11.5
I need help asap im having a test on it
Answers
Answer:
Triangle ABC is congruent to triangle DFE.
Write the equation of a line given the following information:26) The line has a slope =and passes through (8.-1)27) TH
Answers
Answer:
The equation of the line is;
\(y=-\frac{3}{4}x+5\)Explanation:
Given that the line has a slope of;
\(m=-\frac{3}{4}\)And passes through the point;
\((8,-1)\)Applying the point-slope equation of straight line;
\(y-y_1=m(x-x_1)\)substituting the given values and solving;
\(\begin{gathered} y-(-1)=-\frac{3}{4}(x-8) \\ y+1=-\frac{3}{4}x-\frac{3}{4}(-8) \\ y+1=-\frac{3}{4}x+6 \\ y=-\frac{3}{4}x+6-1 \\ y=-\frac{3}{4}x+5 \end{gathered}\)Therefore, the equation of the line is;
\(y=-\frac{3}{4}x+5\)when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
Answers
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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In a study of speed dating, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 equals=not attractive; 10 equals=extremely attractive). find the range, variance, and standard deviation for the given sample data. can the results be used to describe the variation among attractiveness ratings for the population of adult males
Answers
Answer:
hello the data is missing but it is included in the explanation below
missing data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6
Answer :
A) range = 9 , variance = 8.3015, standard deviation = 2.8812
B) The results cannot be a representative of the variation of attractiveness among the population of adult males
Step-by-step explanation:
A ) calculate the Range, variance and standard deviation
The given data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6
i) Range = difference between largest and smallest values
= 10 -1 = 9
ii) variance = summation of ; (xi − x)^2/n-1
= 207.5385/26−1 ≈ 8.3015
iii) standard deviation = \(\sqrt{variance}\)
= \(\sqrt{8.3015}\) = 2.8812
B) The results cannot be a representative of the variation of attractiveness among the population of adult males
guuuysse please help me with this ASAP
Answers
hello
the answer to the question is:
EB² = AB² + AE² ----> EB² = 8² + 9² = 64 + 81 = 145
----> EB = 12
Draw an area model to represent 4x^2+12x+9 = (2x+3)^2. Label the length and width of the whole square and label each individual small square and rectangle.
Answers
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
What are area models?Area models are shapes used to model or illustrate products, multiplications, divisions and quotients
How to draw the area model?The equation is given as:
4x^2+12x+9 = (2x+3)^2
Express (2x+3)^2 as the product of (2x+3) and (2x+3)
4x^2+12x+9 = (2x+3) * (2x+3)
The above means that the area model is a square.
So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
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At the toy store you could get 7 board games for $40.25. Online the price for 4 board games is $23.04. Which place has the highest price for a board game?
Answers
The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go ip in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 motnhs is estimated to be
Answers
The probability that either house sales or interest rates will increase in the next 6 months is estimated to be 0.79.
To find the probability that either house sales or interest rates will go up in the next 6 months, we can use the concept of union in probability theory. The union of two events A and B, denoted as A ∪ B, represents the event that either A or B or both occur.
Given the probabilities that house sales will increase (0.25) and interest rates on housing loans will go up (0.74), we need to calculate the probability of the union of these two events. However, we must consider that the events are not mutually exclusive, meaning that it is possible for both house sales to increase and interest rates to go up simultaneously.
To calculate the probability of the union, we can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of both events A and B occurring.
Substituting the given probabilities into the formula, we have P(A ∪ B) = 0.25 + 0.74 - P(A ∩ B). Since we do not have the information regarding the joint probability of both events occurring (P(A ∩ B)), we cannot determine the exact probability of the union. However, we can say that the probability of either house sales or interest rates going up is estimated to be 0.79, assuming that the joint probability is not significant.
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find equation of parabola given vertex and point calculator
Answers
The equation of the parabola having vertex at (1,4) and passing through the point (3,8) is y = (x - 1)² + 4 .
There are different methods to find the equation of a parabola,
We use the standard form of the equation of a parabola:
which is : y = a(x - h)² + k;
Where (h, k) = vertex and a = constant which determines shape and orientation of parabola.
we know that, vertex of the parabola is (1, 4),
So, we substitute h = 1 and k = 4 in the equation above:
we get,
⇒ y = a(x - 1)² + 4,
Now, To determine the value of a,
We know that parabola passes through point (3, 8).
So, we substitute x = 3 and y = 8 in the equation above,
We get,
⇒ 8 = a(3 - 1)² + 4,
⇒ 8 = 4a + 4
⇒ 4a = 4
⇒ a = 1
Substituting this value of "a" in equation for parabola,
We get,
⇒ y = (x - 1)² + 4,
Therefore, the equation of the parabola y = (x - 1)² + 4.
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The given question is incomplete, the complete question is
Find equation of parabola with the vertex at (1,4) and passes through the point (3,8).
What scale factor was used in the dilation?
Answers
The scale factor used in the dilation of the triangle ABC is 3.
What is the dilation of a triangle?Dilation is a method for generating analogous figures decreasing or increasing their dimensions by some scaling factors.
By dividing distances by the scale factor, each point is stretched outward from the central point D if the scaling factor is more than 1 or inwards if the scale factor is less than 1.
Considering the triangle ABC:
The length of the side AB is 2 units
Compared with triangle DEF, the length of the similar side DE is 6 units
The scaling factor = length of side DE /length of the side AB
The scaling factor = 6 / 2
The scaling factor = 3
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how do you do this , i need help!!
Answers
Answer:
i dont know
Step-by-step explanation:
Answer:
112º
Step-by-step explanation:
(you may need a calculator for this)
first let's start with what we know, we know a triangle has 180º. We also know a line has 180º. if you know the line has 180º, then ? + 126 º = 180º. so if you subtract 126 from 180, you get 54. now lets look at the triangle, we know the triangle has 180º in total. we already know one angle is 58º, and we just figured out the other is 54º. if you do 54+58, you get 112. remember, the triangle has 180 degrees in total, and two of them equal 112º, so 180 - 112 is 68. almost there! now we have to do the line trick again, because on the line, 68 + x = 180. 180- 68 is 112, so the answer is 112º. Hope this helps :D
Find f(6) if f(x)=x²÷3+x.
4
10
18
Answers
Answer:Answer:
The value of f(6) is, 18
Step-by-step explanation:
Given the function:
.....[1]
We have to find the value of.
Put x = 6 in [1] we have;
⇒
⇒
Simplify:
Therefore, the value of f(6) is, 18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
we fill in where x is and make it 6
And I will use pemdas
f(6)=6^2÷3+6
f(6)=36÷3+6
f(6)=12+6
f(6)=18
Hopes this helps please mark brainliest