Answer:
Step-by-step explanation:
Use the formula
[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]
where A(t) is the amount after all the compounding is done, P is the initial investment, r is the interest rate as a decimal, n is the number of times the investment is compounded each year, and t is time in years. For us,
P = 6050
r = .046
n = 4
t = 6
A(t) = ?
Filling in our given info:
[tex]A(t)=6050(1+\frac{.046}{4})^{(4)(6)}[/tex]
which simplifies to
[tex]A(t)=6050(1+.0115)^{24}[/tex]
which simplifies a bit more to
[tex]A(t)=6050(1.0115)^{24}[/tex] and
A(t) = 6050(1.31577397) so
A(t) = $7960.43
which is choice C
Final answer:
The balance after 6 years is $6810.53 that is option A is correct.
Explanation:
To find the balance after 6 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt).
Given that the initial principal (P) is $6050, the interest rate (r) is 4.6% (or 0.046 in decimal form), and it is compounded quarterly (n=4 times per year), we can plug in the values and solve for A.
A = $6050(1 + 0.046/4)^(4*6) = $6810.53
Therefore, the balance after 6 years is $6810.53, which corresponds to answer choice A.
can anyone help to find the answer to this:
17x - 2x/3
Answer:
49x
Step-by-step explanation:
Can someone help me solve this question I can't seem to manage it
Answer:
LA=6 WA=4 LB=6 WB=2
Step-by-step explanation:
Its a square so the sides are 6cm. 2:1 ratio means A is 6*4=24 cm while B is 6*2=12cm.
What are the solutions to the equation
[tex] |x - 8| + 2 = 20[/tex]
Answer:
Solutions are -10 and 26
Step-by-step explanation:
( - the abolute sign I'm using
( x - 8 ) + 2 = 20
( x - 8 ) = 18
x - 8 = 18 (postive case)
x - 8 + 8 = 18 + 8
x = 26
( x - 8 ) = 18
x - 8 = -18 (negative case)
x - 8 + 8 = -18 + 8
x = -10
People at the state fair were surveyed about which type of
lemonade they preferred. The results are shown below.
Pink lemonade: 156 males, 72 females
Yellow lemonade: 104 males, 48 females
Answer:
Step-by-step explanation:
You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.
Pink Lemonade Yellow Lemonade TOTAL
Male 156 104 260
Female 72 48 120
TOTAL 228 152 380
P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6
P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6
Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6
Answer:
P(pink lemonade | female) = P(pink lemonade) = 0.6.
Step-by-step explanation:
Sarah and George wanted to buy some sweets so they decided to buy brownies and banana bread Sarah bought four boxes of brownies and six loaves of banana bread George bought five boxes of brownies and three loaves of banana bread is Sarah spent $44 and George spent $37 determine how much the cost is for a box of brownies and a loaf of banana bread
Answer:
Cost of a box of brownies = $5
Cost of a loaf of banana bread = $4
Step-by-step explanation:
Let, x= box of brownies.
y=loaf of banana bread.
Now,
Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-
[tex]4x+6y=44[/tex] --------------------------(equation 1)
And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-
[tex]5x+3y=37[/tex] --------------------------(equation 2)
Now,
[tex]4x+6y=44[/tex]
[tex]4x=44-6y[/tex]
[tex]x=\frac{44-6y}{4}[/tex]
[tex]x=11-\frac{6}{4}y[/tex]
[tex]x=11-\frac{3}{2}y[/tex]------------------(equation 3)
Now substituting equation 3 in equation 2 we get,
[tex]5x+3y=37[/tex]
[tex]5(11-\frac{3}{2}y)+3y=37[/tex]
[tex]55-(\frac{15}{2}\times y) +3y=37[/tex]
[tex]55-37=(\frac{15}{2}\times y)-3y[/tex]
[tex]18=7.5y-3y[/tex]
[tex]18=4.5y[/tex]
[tex]y=4[/tex] ----------------------------------(Equation 4)
Now putting value of y from equation 4 in equation 3
i.e. [tex]x=11-\frac{3}{2}y[/tex]
[tex]x=11-\frac{3\times 4}{2}[/tex]
[tex]x=11-6[/tex]
[tex]x=5[/tex]
Therefore the cost of a box of brownies = $5
the cost of a loaf of banana bread = $4
On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount. Which inequality can be used to find the possible weight, w, of each gift.
(A) x + 32 < 50
(B) 5x + 32 < 50
(C) 5 + x + 32 < 50
(D) x/5 + 32 < 50
Answer:
5x + 32 < 50
Step-by-step explanation:
On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount.
If each gift weighs w pounds, then the weight of five gifts will be 5w pounds and an additional 32 pounds of clothes will make it total (32 + 5w) pounds.
Now, this total weight has to be less than 50 pounds.
Therefore, the inequality equation that can be used to find the possible weight of each gift, w is
5x + 32 < 50 (Answer)
BRAINIAC IN LAW OF SINES?? Ill give brainlest and extra points
Answer:
[tex]x \approx 31.8[/tex]
Step-by-step explanation:
[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]
Cross multiply:
[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]
Divide both sides by 22:
[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]
Take [tex]\sin^{-1}( )[/tex] of both sides:
[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]
Put left hand side into a calculator now:
[tex]31.7941 \approx x[/tex]
To the nearest tenth that is: [tex]x \approx 31.8[/tex]
Factor completely 6x^2 − 11x − 10.
(6x + 2)(x − 5)
(6x − 2)(x + 5)
(3x + 2)(2x − 5)
(3x − 2)(2x + 5)
Answer:
(3x+2)(2x-5)
Step-by-step explanation:
you can use process of elimination on this one just distribute the equations:
3x(2x-5)+2(2x-5)
6x^2-15x+4x-10 <------ Combine like terms
6x^2-11x-10
Final answer:
Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).
Explanation:
When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.
Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.
Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)
The completely factored form of the quadratic equation is (3x + 2)(2x − 5).
Two of the angles in a triangle measure 18° and 72°. What is the measure of the third angle?
Final answer:
To find the third angle of a triangle, add the two known angles and subtract from 180 degrees. In this case, the third angle measures 90 degrees since the sum of the two given angles is 90 degrees.
Explanation:
When determining the measure of the third angle in a triangle, we utilize the fundamental property that the sum of all angles in a triangle equals to 180 degrees. Given that two of the angles measure 18° and 72°, we can find the third angle by subtracting the sum of these two angles from 180°.
The calculation is as follows:
Add the two known angle measures: 18° + 72° = 90°.Subtract this sum from the total sum of angles in a triangle: 180° - 90° = 90°.Therefore, the measure of the third angle in the triangle is 90 degrees.
25. Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
the trip to Scenic Lake Park?
DATA
Trip to Scenic
Lake Park
10:15 A.M. to 2:30 P.M.
Slide show
4:15 P.m. to 5:10 P.M.campfire 7;55p.m.to 9;30p.m
26. How much longer is dinner than the
Paulo's family has 1 hour and 45 minutes before the trip to Scenic Lake Park after their arrival at the reunion.
Explanation:The question asks how long Paulo's family has before the trip to Scenic Lake Park if they arrived at a family reunion at 8:30 A.M. and the trip is scheduled to start at 10:15 A.M. To solve this, we need to calculate the time difference between 8:30 A.M. and 10:15 A.M.
Here's how you calculate the time difference:
Start by noting the start time which is 8:30 A.M.The end time is 10:15 A.M.To find the difference, consider how many whole hours are between the times: There is 1 full hour from 8:30 A.M. to 9:30 A.M.Then, we need to account for the remaining time from 9:30 A.M. to 10:15 A.M., which is 45 minutes.Adding the full hour and the remaining 45 minutes, we find that there is a 1 hour and 45 minutes gap between the arrival time and the departure for the trip.
Write the definition of midpoint, provide a supporting figure
Step-by-step explanation: Using the diagram shown which I have provided in the image attached, the definition of a midpoint states that M is the midpoint of segment LN, then segment LN ≅ to MN.
The definition of a midpoint can also be stated the other way around. using the diagram shown, if segment LN ≅ to segment MN, then M is the midpoint of segment LN.
We can use hash marks in the figure to show that are 2 segments are congruent.
if (x-a) is a factor of (x^3-4x^2-4x+7), what is the value of the remainder?
Answer:
0
Step-by-step explanation:
When any number or expression is divided by one of its factors, the remainder is zero.
Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the
ground and the top of the lighthouse is 41", How tall is the lighthouse?
Question:
Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41° How tall is the lighthouse?
Answer:
The height of lighthouse is 52.2 yards
Solution:
Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41 degree
The diagram is attached below
Consider a right angled triangle ABC
AB is the height of the lighthouse
BC is the distance between the base of a lighthouse and Photographer
As per given, BC = 60 yards
Angle between the ground and the top of the lighthouse is 41 degree
Angle ACB = 41 degree
To find: height of lighthouse i.e AB = ?
We know that,
[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]
Here Base is BC and perpendicular is AB
[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]
Substituting the values,
[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]
Thus the height of lighthouse is 52.2 yards
What equals the expression if a=2.4 b=0.237 c=9.49. c-2ab
8.3524 equals the expression c - 2ab if a = 2.4 b = 0.237 c = 9.49
Step-by-step explanation:
The given is:
a = 2.4b = 0.237c = 9.49We need to find the value of the expression c - 2ab
∵ The expression is c - 2ab
∵ a = 2.4
∵ b = 0.237
∵ c = 9.49
- Substitute the values of a , b and c in the expression to find its value
∴ 9.49 - 2(2.4)(0.237) = 9.49 - 2(0.5688)
∴ 9.49 - 2(2.4)(0.237) = 9.49 - 1.1376
- Subtract the two numbers
∴ 9.49 - 2(2.4)(0.237) = 8.3524
8.3524 equals the expression c - 2ab if a=2.4 b=0.237 c=9.49
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what interval contains a positive solution to the equation 0.2x^2-0.8x=1.6
Step-by-step explanation:
0.2x² − 0.8x = 1.6
Multiply both sides by 5.
x² − 4x = 8
Complete the square by adding 4 to both sides.
x² − 4x + 4 = 12
(x − 2)² = 12
x − 2 = ±√12
x = 2 ± √12
The positive solution is x = 2 + √12 ≈ 5.46.
15. At a school fair, 70% of the people are under 16 years old. One of the people
teachers. If there are 21 teachers at the fait, how many people are there at the air
Answer:
210 people.
Step-by-step explanation:
Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?
Now, solving to find total number people in the fair.
Lets assume total number of people in the fair is "x".
As given, there is 70% of total number of people are under 16 year old.
∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]
Next, finding the number of remaining people.
∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]
Number of remaining people is 0.3x
As given, One third of the people remaining are teachers.
∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]
As given there are 21 teachers at the fair.
⇒ [tex]0.1x= 21\ teachers[/tex]
∴ x= [tex]\frac{21}{0.1} = 210[/tex]
Hence, total number of people in the fair are 210.
Avery’s water bottle holds 300 milliliters. Dashawn’s container holds 3/4 as much water how much do both containers hold?
Answer: Avery's bottle holds 300 milliliters. If Dashawn's container holds 3/4 as much, then his container can hold 225 milliliters. Added together, both containers can hold 525.
Step-by-step explanation: 3/4 of 300 is 225. 300 + 225 = 525.
??????((((((((??????????
Answer:
G. 17.3
solution:
If the sum of a number and five is doubled, the results is one less than the number.find the number
The number is -11.
Step-by-step explanation:
Let,
the number be x.
According to given statement;
Sum of a number and five is doubled;
2(x+5)
is equals to one less than the number
= x-1
Combining both the sides and forming an equation
2(x+5)=x-1
[tex]2x+10=x-1\\2x-x=-1-10\\x=-11\\[/tex]
The number is -11.
Keywords: addition, subtraction
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geometry math thanks if you help
Answer: Option B.
Step-by-step explanation:
For this exercise it is important to remember that, by definition, a relation is a function if and only if each input value has an unique output value.
The input values are the values of the variable "x" and the output values are the values of the variable "y".
You can observe in the table shown in the picture, that the input value -2 has two different output values:
[tex]x=-2,y=3\\\\x=-2,y=-13[/tex]
Notice that the input vale -1 has two different output values too:
[tex]x=-1,y=-1\\\\x=-1,y=-9[/tex]
Therefore, based on this, you can conclude that the information given in the table is a relation but not a function.
Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas? Explain your work
Answer:
16 hours and 20 minutes.
Step-by-step explanation:
Please consider the complete question.
Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?
To find the time taken by van to reach Dallas, we will divide total distance by speed.
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}[/tex]
[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}[/tex]
[tex]\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}[/tex]
[tex]\text{Time taken to reach Dallas}=16.3333\text{ Hour}[/tex]
Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.
[tex]0.3333\times 60=19.998\approx 20[/tex]
Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.
Final answer:
To calculate the time it takes for the van to reach Dallas, divide the distance from Grand Junction to Dallas by the average speed of the van.
Explanation:
To calculate the time it takes for the van to reach Dallas, we need to divide the distance from Grand Junction to Dallas by the average speed of the van.
The distance from Grand Junction to Dallas is not provided in the question, so we cannot calculate the exact time taken. However, if we are given the distance, we can use the formula:
Time = Distance / Speed
For example, if the distance is 300 miles, and the van's average speed is 60 miles per hour, then the time taken would be:
Time = 300 / 60 = 5 hours
An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off. He wants to know the sale price of the service
The sale price of the service is $25.50.
Given that,
The city auto is regularly at $30.There is a 15% coupon off.We need to find out the sale price
So, the sale price is
= $30 - (15% of $30)
= $30 - $4.50
= $25.50
Therefore we can conclude that the sale price of the service is $25.50.
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9:
Which expressions equivalent to 3−83−4?
Select all that apply.
A
3−12
B
3−4
C
32
D
132
E
134
F
1312
The question asks for equivalent expressions to 3-8/3-4. After clarifying and simplifying the expression, we determined that the equivalent expressions are 3-12 (A) and 13/12 (F).
Explanation:The question is asking us to determine which expressions are equivalent to 3−83−4. First, let's clarify this expression. The symbols − and − can stand for subtraction or negative signs, making the expression ambiguous. However, we can interpret this as a subtraction problem with mixed numbers, which would be processed as 3 minus 8 thirds minus 4. Converting the mixed numbers to improper fractions, we get: 3−(8/3)−4 which simplifies to (9/3)−(8/3)−(12/3). This simplifies to 1/3−(12/3), or 1/3− 4, which then further simplifies to −(⅔).
When we look for equivalent expressions, we have the following options:
A) 3−12 is correct because it is the simplified form of 3 minus 8/3 minus 4, which is −3 1/3.B) 3−4 is incorrect because it simplifies to −1, which is not the same as −3 1/3.C) 3² is incorrect as this represents 3 squared, or 9, which is not the same as −3 1/3.D) 13² is incorrect because it represents 1/3 squared, which is 1/9, not the same as −3 1/3.E) 13´ could be construed as 13 to the power of 4 or 1/3 to the power of 4, but both interpretations are incorrect.F) 13⅜ is correct because it represents 1/3 minus 8/3 minus 4, which is −3 1/3.
What is the slope? Help me please I really am stuck on this
based on the graph, what would be the slope for the line of best fit of scatter plot? A. 0 B. 1/2 C. 1 D.1 1/2 E. 2
Answer:
c
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
rise over run 4/4=1
y =( x + 3) 2 - 1 identify the vertex
Answer:
Step-by-step explanation:
The vertex is of the form (h, k). The general equation of a quadratic in vertex form is
[tex]y=(x-h)^2+k[/tex]
where h is the x coordinate of the vertex and k is the y coordinate of the vertex. The important thing to remember is that the "x -" part of the formula is constant, it doesn't change. So if our expression inside the parenthesis is
(x + 3), it is understood to be (x - (-3)) which indicates movement to the left. The "+ k" part is not taken literally. If we have a + 2 at the end of our equation we are moving up 2; if we have a -1 at the end, we are moving down 1. Our vertex then is located at (-3, -1)
Find the value of x and y.
Answer:
Step-by-step explanation:
CD and AB are parallel; DB transverse
∠D + ∠B = 180 {co interior angles}
112 + 27 + y = 180
139 + y = 180
y = 180 - 139
y = 41
In ΔABC,
49 + x + y = 180 ( sum of all angles of triangle}
49 + x + 41 = 180
90 + x = 180
x = 180 - 90
x = 90
Find an equation of the line. Write the equation using function notation.
Through (3,-3); perpendicular to 4y=x-8
The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:
[tex]y = -4x+9[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]4y=x-8[/tex]
We have to convert the given line in slope-intercept form to find the slope of the line
So,
Dividing both sides by 4
[tex]\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2[/tex]
Let m1 be the slope of given line
Then
[tex]m_1 = \frac{1}{4}\\[/tex]
Let m2 be the slope of line perpendicular to given line
As we know that produt of slopes of two perpendicular lines is -1
[tex]m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4[/tex]
The slope intercept form of line is given by:
[tex]y = m_2x+b[/tex]
Putting the value of slope
[tex]y = -4x+b[/tex]
to find the value of b, putting (3,-3) in equation
[tex]-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9[/tex]
Putting the value of b in the equation
[tex]y = -4x+9[/tex]
Hence,
The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:
[tex]y = -4x+9[/tex]
Keywords: Equation of line, slope
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Final answer:
The result is the equation f(x) = -4x + 9 in function notation.
Explanation:
To find the equation of a line that is perpendicular to another and passes through a given point, follow these steps:
First, determine the slope of the given line. The equation given is 4y = x - 8. To put this in slope-intercept form, divide everything by 4 to get y = ⅔x - 2. The slope (m) of this line is ⅔.To find the slope of a line perpendicular to this one, take the negative reciprocal of ⅔, which is -4.Now, using the point-slope form of a line equation, which is y - y1 = m(x - x1) where (x1, y1) = (3, -3) and m = -4, we get:Therefore, the equation of the line in function notation is f(x) = -4x + 9.
Find the value of x. Plz hurry
Answer:
x = 12
Step-by-step explanation:
both (x+5) and (2x-7) are corresponding angles formed by an intersection between a transversal and 2 parallel lines.
hence they are equal in value
x+5 = 2x-7
x - 2x = -7 - 5
-x = -12
x = 12
Answer: x=12
Step-by-step explanation:
Find the value of x when a = 7/2, h = 10, k = 15, If
Answer:
9
Step-by-step explanation:
x= hk/ (k+h)(a-2)
10*15 (15+10) (7/2-2)= 9