The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.
How to calculate the value?From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:
= 10 × 12 = 120 months
The difference in the amount paid as a result of the credit score will be:
= ($840 × 120) - ($771 × 120)
= $100800 - $92520
= $8280
Therefore, the amount is $8280.
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Your friend says that the solutions to the inequality 9x-12x≤9 are xs-3. Solve the inequality correctly. What error did your friend
make?
holow and fill in the answer box to complete your choice
Answer:
[tex]9x - 12x \leqslant 9[/tex]
[tex] - 3x \leqslant 9[/tex]
[tex]x \geqslant - 3[/tex]
The inequality sign must be reversed when multiplying or dividing each side of an inequality by a negative number.
Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces
the brakes. He works no more than 54 hours a week. He routinely completes at least 2 shocks replacements and 6
brake replacements a week. If he charges $400 for labor replacing shocks and $250 in labor for replacing brakes, how
many jobs of each type should he complete a week to maximize his income?
Answer:
18 Shocks replacments and 0 Brakes
Step-by-step explanation:
if he did That he will make 7200$ a week
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 54%.
A. What is the probability that they win both contracts?
B. What is the probability that they lose both contracts?
C. What is the probability that they win only one contract?
A) The probability that the Aerospace Company wins both contracts is 29.04%.
B) The probability that the Aerospace Company loses both contracts is 70.96%.
C) The probability that the Aerospace Company wins only one contract is 23.76%.
What is the probability?Probability describes the chance or likelihood of an expected event occurring out of many outcomes.
Probability is a ratio of an outcome versus many possible events.
Probability is represented as a percentage, fraction, or decimal, like a ratio.
How the probabilities are calculated:The probability of winning the first contract = 44%
The probability of losing the first contract = 56% (1 - 44%)
The probability of winning the first and the second contract = 66%
The probability of losing the first and the second contract = 34% (1 - 66%)
The probability of losing the first contract and winning the second = 54%
A) The probability that they win both contracts = the probability of winning the first contract multiplied by the probability of winning the second contract.
= 29.04% (44% x 66%)
B) The probability that they lose both contracts = 1 minus the probability of winning both contracts.
= 70.96% (1 - 29.04%)
C) The probability that they win only one contract = the probability of winning the first contract multiplied by the probability of winning only the second contract.
= 23.76% (44% x 54%)
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{3}{8}-\frac{1}{6}
8
3
−
6
1
Step-by-step explanation:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly.
I hope this helps.
Step-by-step explanation:
8/3
8-3=6
6/3
6-3=
3find f(g(2)) if f(x)= 4x^2-1 and g(x) = 3x+2
The value of the function f(g(2)) is 255.
The two function given is f(x) = 4x^2 - 1 and g(x) = 3x + 2
We have to find the value of the function f(g(2)).
First we will find the function f(g(x))
f(g(x)) = f(3x+ 2)
=4[tex](3x +2)^{2}[/tex] - 1
= 4( 9[tex]x^{2}[/tex] + 12x + 4) - 1
= 36x² + 48x + 16 - 1
= 36x² + 48x + 15
Now we have to find f(g(2)) for which we have to put the value of x as 2.
f(g(2)) = 36(2)² + 48 (2) + 15
= 36× 4 + 48 ×2 + 15
= 144 + 96 + 15
= 255
Therefore the value of the function f(g(2)) is 255.
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Mathataur weighs 230,998,888,201 grams, and Mathamoth weighs 44,002,156 grams. About how many times greater is the weight of the Mathataur than the weight of the Mathamoth?
Answer:234534 pounds greater
Step-by-step explanation: 230,99987389x7=76
Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me
Answer:
see explanation
Step-by-step explanation:
(a)
the angles shown are alternate interior angles and are congruent
(c)
since they are congruent , then
- 1 + 8x = 7x + 11 ( subtract 7x from both sides )
- 1 + x = 11 ( add 1 to both sides )
x = 12
(d)
then
7x + 11 = 7(12) + 11 = 84 + 11 = 95
- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95
a balloon is released from the top of a platform that is 50 m tall the balloon Rises at the rate of 4 meters per second identify the input variable output variable initial value and rate of change
Let's begin by identifying key information given to us:
Height = 50 m
velocity = 4m/s
The input variable is the number of seconds
The output variable is the theight of the ballon
The equation:
[tex]\begin{gathered} y=4x+50 \\ \text{Comparing this equation with the standard equation,}y=mx+b \\ \Rightarrow m=4,b=50 \\ m=4 \end{gathered}[/tex]Therefore, the rate of change equals 4
Which expression is equivalent to 3w-4-w-93w−4−w−9?
The most appropriate choice for simplification of algebraic expression will be given by -
-92w -17 is the correct answer
What is simplification of algebraic expression?
At first it is important to know about algebraic expression. Algebraic expression consist of numbers and variable connected by addition, subtraction, multiplication, division.
Simplification of algebraic expression is the process of calculating the algebraic expression into lower form by combining all the like terms together. Here, BODMAS rule is used. B stands for bracket, O stands for of, D stands for division, M stands for multiplication, A stands for addition, S stands for subtraction.
3w - 4 - w - 93w - 4 -w - 9
3w - w - 93w -w -4 - 4 - 9
-92w -17
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Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the phrases below to explain how to use positive or negative integers to represent income and expenses.
You would use
Choose...
integers to represent income because it is a
Choose...
amount.
You would use
Choose...
integers to represent expenses because they are
Choose...
income.
The positive integer represents an addition to the income while.a negative integer represents a subtraction.
How to illustrate the information?Positive integers are used to represent income since they indicate an increase rather than a decrease in the financial value of the company. In other words, cash is coming in rather than leaving. A positive number 10 is used as an example to illustrate an increase in operating revenue when there is profit on items sold, say $10.
When you express an expense with a negative number, you're actually subtracting money value rather than adding it. In other words, money is leaving the company rather than being brought in. For instance, when a transportation expense is incurred to deliver items to the customer, it is recorded as an expense deducted from, let's say, the business' revenue sales. Since they are already identified and recognized as expenses and deducted nonetheless, they are typically shown in brackets in accounting to signify negative worth.
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Can you help me with this please!!
Let us find the third side of the right triangle using the Pythagora's theorem
The missing side is the opposite side because it is facing the angle
[tex]\begin{gathered} 13^2=5^2+x^2 \\ \\ x^2=169-25 \\ \\ x^2=144 \\ \\ x=\sqrt[]{144} \\ \\ x=12 \end{gathered}[/tex][tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ \\ sin\theta=\frac{12}{13} \end{gathered}[/tex]At the neighborhood grocery, 0.5 pounds of chicken thighs cost $3.14 Taub spent $29.83 on chicken thighs. How many pounds of chicken thighs did she buy, to the nearest hundredth of a pound?
Taub bought 4.75 pounds of chicken thighs at the neighborhood grocery.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
0.5 pounds of chicken thighs = 3.14 dollars
X pounds of chicken thighs = 29.83 dollars
Cross-multiplying, we have:
3.14X = 0.5 × 29.83
3.14X = 14.915
X = 14.915/3.14
X = 4.75 pounds of chicken thighs.
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Share:
Share £20 pounds in the ratio 2:3
Share 15cm in the ratio 1:2
Divide £24 in the ratio 1:3
Share 35 sweets in the ratio 4:3
The share base on the ratio are as follows:
The share is £8 to £12The share is 5 cm to 10 cmThe share is £6 to £18The share is 20 sweet to 15 sweet.How to find the share base on the ratio?A ratio compares values. A ratio says how much of one thing there is compared to another thing.
Therefore, lets use the ratios to share the items.
Share £20 pounds in the ratio 2:3
2 / 5 × 20 = 40 / 5 = 8
Therefore, the share is £8 to £12
Share 15cm in the ratio 1:2
1 / 3 × 15 = 15 / 3 = 5 cm
Therefore, the share is 5 cm to 10 cm
Divide £24 in the ratio 1:3
1 / 4 × 24 = 24 / 4 = 6
Therefore, the share is £6 to £18
Share 35 sweets in the ratio 4:3
4 / 7 × 35 = 20 sweets
Therefore, the share is 20 sweet to 15 sweet.
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If Alejandra estimates that one outfit welghs two pounds and one pair of shoes welghs three pounds, which graph represents the number of
outfits and shoes that Alejandra can pack while staying under the weight limit?
A graph which represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, the x-axis represents the number of outfits while the y-axis represents the number of shoes. Additionally, since one pair of shoes weighs three (3) pounds and one outfit weighs two (2) pounds, the x and y coordinates would be given by this inequality:
2x + 3y < 30
Making y the subject of formula, we have:
3y < -2x + 30
Dividing all through by 3, we have:
3y/3 < -2x/3 + 30/3
y < -2x/3 + 10
Note: For 30 pounds, there would be 10 shoes (0, 10) while for 30 pounds, there would be 15 outfits (15, 0).
In conclusion, the boundary line is dashed or dotted to indicate that the boundary is not part of the solution because the inequality symbol is less than (<).
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What are the next two terms in the sequence? 2, 12, 22, 32, ...
Find the product.
(b-na)(4b+9na)
Enter the correct answer.
The product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
How do you find the product of an expression?Algebraic expressions can be multiplied using the following procedures. You can start by calculating the algebraic sum of the like and unlike terms, multiplying the term coefficients, and adding the variable powers with the same base.
Given:
To find the product of (b-na)(4b+9na).
To determine the product, multiply each term of the first expression by each term of the second expression.
(b-na)(4b+9na)
= 4b² + 9abn - 4abn - 9a²n²
= 4b² + 5abn - 9a²n²
Therefore the product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
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To make orange paint he must mix yellow and red paint in the ratio 6:4 if he uses 9 litres of yellow paint how much red paint should he use
Answer:6 liters of red paint
Step-by-step explanation:
Calculate the first two terms: 34÷6
Calculate the first two terms: 6
Answer:6
Write a quadratic function given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
y=(x+3)(x=2)
y=(x-3)(x+2)
y=3(x-3)(x-2)
y=3(x-3)(x+2)
Quadratic function is 3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
What is quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:
f(x) = ax² + bx + c in standard form, where a 0.
Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.
The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.
Given Data
Roots (-3,0) and (2,0)
Point (1,-12)
y = a(x-(-3) (x-2)
y = a(x+3)(x-2)
Equating points
-12 = a(1+3)(1-2)
-12 = a(4)(-1)
-12 = -4a
a = 3
f(x) = 3(x+3)(x-2)
Function is 3(x+3)(x-2).
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What is the correct conjunction identity for tan 0?
A. csc (90 ° - 0)
B. sec (90 ° - 0)
C. sin (90 ° - 0)
D.cos (90 ° - 0)
E. cot (90 ° - 0)
The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.
These trigonometric identities includes;
SineCosineTangentCotangentSecant CosecantIt is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.
The cofunction identities are represented thus;
sin θ = cos(90 - θ)
cos θ = sin(90 - θ)
cot θ = tan(90 - θ)
tan θ = cot(90 - θ)
csc θ = sec(90 - θ)
sec θ = csc(90 - θ)
For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)
Thus, the identity is cot (90 ° - 0)
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The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E.
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.These trigonometric identities includes; sine,cosine, tangent, cotangent, secant cosecant.
It is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.The cofunction identities are represented thus;
sin θ = cos(90 - θ)cos θ = sin(90 - θ)cot θ = tan(90 - θ)tan θ = cot(90 - θ)csc θ = sec(90 - θ)sec θ = csc(90 - θ)For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)Thus, the identity is cot (90 ° - 0)
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Given the two rectangles below. Find the area of the shaded region.10, 2, 4, 2
Applying the formula for the area of a rectangle, the area of the shaded region is calculated as: 42 units².
What is a Rectangle?A rectangle has two pairs of opposite sides that are of equal length, one pair is the length, while the other is the width.
How to Find the Area of a Rectangle?The area of a rectangle = the product of its length and its width = (length)(width).
The area of the shaded region = area of the larger rectangle - area of the smaller rectangle
Dimensions of the larger rectangle:
Length of the larger rectangle = 10 + 2 = 12 units
Width of the larger rectangle = 9 + 2 = 11 units
Area of the larger rectangle = (12)(11) = 132 units²
Dimensions of the smaller rectangle:
Length of the smaller rectangle = 10 units
Width of the smaller rectangle = 9 units
Area of the smaller rectangle = (10)(9) = 90 units²
The area of the shaded region = 132 - 90
The area of the shaded region = 42 units²
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Line ℓ has equation y=
–x–3. Find the distance between ℓ and the point I(2,5).
The distance between line y= -x-3 and the point (2,5) is 5√2units.
The distance(d) between the line ax+by+c=0 and point (x₁,y₁) is calculated using the formula
d= |ax₁+by₁+c|/√a²+b² , where a and b are the coefficients of x and y .
In the question ,
the equation of the line ℓ is given by y = -x-3
rewriting the equation in standard form x+y+3=0
So the distance between the line x+y+3 and the point (2,5) can be calculated by substituting the values in the formula, we get
d=|1(2)+1(5)+3|/√1²+1²
= |2+5+3|/√2
= 10/√2
Simplifying further , we get
= 5√2
Therefore , the distance between line y= -x-3 and the point (2,5) is 5√2 units.
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A rectangle is 4 meters longer than it is wide. Find the dimensions of the rectangle if its area is 165 sq-meters.
Answer:
width = 11 and length = 15
Step-by-step explanation:
→ Find algebraic length and width
width = x ∴ length = x + 4
→ Find area
x ( x + 4 ) = x² + 4x
→ Equate to area
x² + 4x = 165
→ Solve
x = 11
→ Find length and width
width = 11 and length = 15
I need the answer for this question...
Expand and simplify the following 2(7s+ 4) + 6
Answer: 14s + 14
Step-by-step explanation:
- multiply in the 2 to the 7 and 4
14s + 8 +6
- add 8 + 6
14s + 14
Answer:
14s+14
Step-by-step explanation:
2(7s+4)+6
Simplify each term.
Apply the distributive property.
2(7s)+2x4 + 6
Multiply 7 by 2
14s +2 x 4 + 6
Multiply 2 by 4
14s + 8 + 6
Add 8 and 6
14+44
Find the converse and determine if it is true or false.
Statement : obtuse angles are not right angles.
The converse statement is 'If an angle is not a right angles, then it is obtuse' True. Option A
What is a converse statement?The converse of a conditional statement is formed when the hypothesis and conclusion are both reversed.
In this case, the hypothesis is taken as the conclusion and the conclusion made the hypothesis.
The conditional statement is written as: a → b
The converse is written as b → a
Where;
a is the hypothesisb is the conclusionGiven that:
Original statement :Obtuse angles are not right angles
The converse statement : If an angle is not a right angles, then it is obtuse
We can see that the converse statement is true because an obtuse angle is an angle greater than 90 degrees.
Hence, the converse statement is true
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5.) Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
6.)
Birth Rates and Populations around the World in 2011
Birth Rate
(per 1000 population per year)
15.53
Country
French Polynesia
Brazil
17.79
Australia
12.33
Sudan
36.12
Russia
11.05
India
20.97
Bulgaria
9.32
Source: http://www.indexmundi com/g
a.) Which country has a birth rate of 36.12?
b.) Which country has the largest birth rate?
c.) Which country has the smallest population?
Population
294,935
203,429, 800
21,766,710
45,047,500
138,739,900
1,189,173,000
7,093,635
Mello Yello
Sprite
We are spending $ 0.0263 less every Mello Yello can, therefore it is the better buy.
What is profit and loss?
Subtract the smaller value from the greater value in order to calculate the profit or loss. The selling price is always higher than the cost price when there is a profit. Selling price minus cost price is profit. In a loss scenario, the cost price is higher than the selling price. Loss = Price Cost
Given,
20 cans of Mello Yello for $4.75
Therefore cost of 1 can of Mello Yello = $4.75 / 20 = $ 0.2375
Also given,
36 cans of Sprite for $9.50
Therefore, cost of 1 can of Sprite = $9.50 / 36 = $ 0.2638
Therefore, per can we are paying $ 0.0263 less for Mello Yello.
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Complete Question:
Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
I need help with this please because I got answer C but I’m not sure I’m right
Since supplementary angles are two angles with a sum of 180°, then the supplement of ∠WTV is the angle ∠WTZ. Therefore, the answer is the option C.
(-8.8)(-9) = ? im confused?
Answer: 79.2
Step-by-step explanation: if you take -8.8 x -9 take out the negative completely because we are multiplying 2 negatives you never have to worry about the them. 8.8 x 9 = 79.2
side note: + x + = + - x - = + - x + = - + x - = -
6. A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a
higher interest rate, but you cannot access your investment for a specified length of time.
Suppose you deposit $3000 in a CD paying 6% interest, compounded monthly. How much will
you have in the account after 20 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]
The graph of y=f(x) is the solid black graph below. Whoch function represents the dotted line
The function that represents the dotted line of the graph using transformation rules is; f(x - 1) - 4.
How to Interpret Translation of Graphs?For the function f(x) of the given graph, when we look at the solid line, we see that it has a root at x = -1 which means it has a zero at x = -1.
However, when observing the dashed line, we see that it has a root at x = 0 which means it has a zero at x = 0.
Thus, we can deduce from transformation rules that the function was moved by 1 unit to the right to get the new function.
Secondly, we observe that the dashed line is also below the function f(x), and we observe further that 4 was subtracted. Therefore, when we use the transformation rules again for subtracting from a function, we get the final function as; f(x - 1) - 4.
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Leila is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories.Leila wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.(BOLD ANSWER WHEN FINISHED
Answer:
[tex]25f+100c<600[/tex]Step-by-step explanation:
Let f be the number of french fries in the lunch
Let c be the number of chicken wings.
Then, if Leila wants her child to eat less than 600 calories and each french fry has 25 calories and each chicken wing has 100 calories. The linear inequality that represents this situation:
[tex]25f+100c<600[/tex]