Answer:
56 pages per hour
Step-by-step explanation:
Penny reads 14 pages in 1/4 of an hour.
An hour is 4 times more than 1/4 of an hour (you could think of it as 15 minutes compared to 60 minutes)
Multiply the amount penny reads in 1/4 of an hour (14 pages) by 4 to get the rate she reads in 1 hour.
14 x 4 = 56
Now add the rate of time (per hour) to get that she reads a total of 56 pages per hour.
Hope this helps!
1 secX + 3 = cosX + tanX (2+ sinX)
The solution for X is X ≈ [tex]tan^{(-1)(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
Given: 1 secX + 3 = cosX + tanX (2 + sinX)
To simplify the equation, let's express secX and tanX in terms of sinX and cosX:
1/cosX + 3 = cosX + sinX/cosX (2 + sinX)
Now, multiply both sides by cosX to eliminate the denominators:
[tex]1 + 3cosX = cos^2X + sinX(2 + sinX)[/tex]
Expanding the equation:
[tex]1 + 3cosX = cos^2X + 2sinX + sin^2X[/tex]
Since [tex]sin^2X + cos^2X[/tex] equals 1 (based on the Pythagorean identity), we can substitute it into the equation:
[tex]1 + 3cosX = 1 + 2sinX + sin^2X[/tex]
Rearranging the terms:
[tex]3cosX = 2sinX + sin^2X[/tex]
Now, let's express cosX in terms of sinX using the Pythagorean identity:
cosX = √(1 - [tex]sin^2X[/tex])
Substituting this into the equation:
3√(1 - [tex]sin^2X) = 2sinX + sin^2X[/tex]
Squaring both sides to eliminate the square root:
[tex]9(1 - sin^2X) = (2sinX + sin^2X)^2[/tex]
Expanding the right side:
[tex]9(1 - sin^2X) = (2sinX)^2 + 2(2sinX)(sin^2X) + (sin^2X)^2\\9 - 9sin^2X = 4sin^2X + 4sin^3X + sin^4X[/tex]
Rearranging the terms:
[tex]sin^4X + 4sin^3X + 4sin^2X + 9sin^2X - 9 = 0[/tex]
Combining like terms:
[tex]sin^4X + 4sin^3X + 13sin^2X - 9 = 0[/tex]
Unfortunately, this equation does not have a simple algebraic solution. It needs to be solved numerically or graphically. Using numerical methods or a graphing calculator, we can find that one solution to this equation is sinX ≈ 0.7429.
Taking the inverse tangent (arctan) of both sides, we have:
X = arctan(0.7429)
Therefore, the solution for X is X ≈ t[tex]an^{(-1)}(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
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What’s the lateral area of this
Answer:
240 in²
Step-by-step explanation:
You want the lateral area of a triangular prism with triangular base having sides 6 in, 8 in, and 10 in, and a distance between them of 10 in.
Lateral areaThe lateral area of a triangular prism is the area of the three rectangular faces. The width of those faces is the "height" of the prism, given as 10 in. The total length of those faces is the perimeter of the base:
6 in + 8 in + 10 in = 24 in
The lateral area is ...
A = LW = (24 in)(10 in) = 240 in²
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helpppppppppp meeeeee please
Answer: D. <4 and <7
Step-by-step explanation:
Consecutive means one after the other
Interior means within the parallel lines
So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side
D. <4 and <7
Explain what is meant by a positive relationship between two variables and a negative relationship between two variables. Give an example of a situation in which you would expect to find a positive relationship and when you would expect to find a negative relationship.
Answer: A positive relationship between two variables means that as the value of one variable increases, the value of the other variable also increases. In other words, there is a direct association or correlation between the two variables. Graphically, a positive relationship is represented by an upward-sloping line or curve.
For example, let's consider the relationship between studying time and exam scores. In general, if a student spends more time studying for an exam, their exam score is likely to increase. This implies a positive relationship between studying time and exam scores.
On the other hand, a negative relationship between two variables means that as the value of one variable increases, the value of the other variable decreases. In this case, there is an inverse association or correlation between the two variables. Graphically, a negative relationship is represented by a downward-sloping line or curve.
For instance, let's consider the relationship between hours of sleep and levels of fatigue. As the number of hours of sleep decreases, the level of fatigue tends to increase. This indicates a negative relationship between hours of sleep and levels of fatigue.
It's important to note that these examples describe typical scenarios, but individual variations and other factors can also influence the relationships between variables.
A track coach recorded the time it took for each of her athletes to run a mile. She plans to display the results with a histogram. Which of the following will it show? Select all that apply. (please help as soon as possible. thanks :))
The histogram will show the distribution of the athletes' mile running times. It will provide a visual representation of the frequency or count of athletes falling within different time intervals.
1. Determine the time intervals or "bins" for the histogram. For example, you might have bins of 5-second intervals, such as 0-5 seconds, 5-10 seconds, and so on.
2. Count the number of athletes who fall within each bin. For instance, if three athletes completed the mile in the 0-5 second bin, and five athletes completed it in the 5-10 second bin, record those counts.
3. Plot the bins on the x-axis of the histogram and the corresponding frequency or count on the y-axis.
4. Draw rectangles (or bars) on the histogram, with the height of each bar representing the frequency or count of athletes within each bin.
5. Label the axes and add a title to the histogram for clarity.
The resulting histogram will provide a visual representation of how the athletes' mile running times are distributed, allowing you to observe any patterns or trends.
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Triangle ABC is shown. Use the graph to answer the question.
triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2
Determine the coordinates of the image if triangle ABC is translated 5 units down.
A′(−4, −2), B′(4, −2), C′(0, 2)
A′(1, −7), B′(9, −7), C′(5, −3)
A′(1, 3), B′(9, 3), C′(5, 7)
A′(6, −2), B′(14, −2), C′(10, 2)
If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.
The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).
To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.
The new coordinates of the vertices after the translation are:
A': (1, -2 - 5) = (1, -7)
B': (9, -2 - 5) = (9, -7)
C': (5, 2 - 5) = (5, -3)
Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of sin θ is 9/13.
Option A is the correct answer.
We have,
In trigonometry,
The sine function (sin) represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
The cosecant function (csc) is the reciprocal of the sine function, meaning it is equal to 1 divided by the sine of an angle.
In this case,
We are given that csc θ (the cosecant of θ) is equal to 13/9.
To find the value of sin θ (the sine of θ), we can take the reciprocal of csc θ. So,
sin θ = 1/(csc θ) = 1/(13/9) = 9/13.
Therefore,
The exact value of sin θ is 9/13.
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Please help!!! Correct answer gets brainliest!!!
Ashley got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13 cents per yard. If after that purchase there was $25.06 left on the card, how many yards of ribbon did Ashley buy?
Answer:
38 yards
Step-by-step explanation:
First, subtract to find out how much money was spent.
30 - 25.06
= 4.94
Then divide to find out how many groups of $0.13 are in $4.94.
4.94 ÷ .13
= 38
Ashley bought 38 yards of ribbon.
38 × .13 = 4.94
4.94 + 25.06 = 30
This answer does not consider tax at all. Because it wasn't mentioned in the question and it complicates the problem. So probably don't worry about tax. Unless your teacher /book/program said to consider it. I can edit the answer.
Also, if they said to write an equation:
Let x = yards of ribbon
30 - .13x = 25.06
subtract 30
-.13x = -4.94
divide by -.13
x = 38
Which graph has the same end behavior as f(x)=(10x^(3)+x^(2)+3)/(2x^(2)+1)?
The graph that has the same end behavior as f(x)= (10x³+x²+3)/(2x²+1) is Option A. See the attached.
What is the end behavior of the above graph?the end behavior of the graph of f(x) is:
As x → +∞ , f(x) → +∞ (approaches positive infinity).
As x → -∞, f(x) → -∞ (approaches negative infinity).
End behavior of a function f defines the behavior of the function's graph at the "ends" of the x- axis.
In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x -axis (as x approaches - ∞ ).
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What half of 4 fourths in a decimal
Answer:
0.5
Step-by-step explanation:
So what do we mean by half? Half means there are two of the thing, and so all you need to do is divide it by two. Half of 4/4 is just another way of saying 4/4 divided by 2:
: 4/4 ÷ 2
Now we know that "half" means to divide by 2, how do we half 4/4? Remember that a fraction a part of the whole, so the higher the denominator is, the smaller the piece. The answer is that the numerator stays the same and we multiply the denominator by 2:
: 4/4 x 2 = 4/8
Here's a little bonus calculation for you to easily work out the decimal format of half 4/4. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:
: 4/8 = 0.5
The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.
The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .
How to find the probability ?The number of adults with some high school degree or some college would be :
= 3, 561 + 6, 058
= 9, 619 people
The probability that a random adult would have high school degree or some college is therefore :
= Adults with high school degree or some college / Total adults in the town
= 9, 619 / 17, 981
= 53. 50 %
In conclusion, the probability is 53. 50%.
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AC = 3x-10. BD = x+34. Solve for X.
The value of x in the figure is 22 as the diagonals are equal
Diagonals of a parallelogram are the line segments connecting two non-adjacent vertices of a parallelogram
Both the AC and BD are equal
AC=3x-10
BD=x+34
As two diagonals are equal
3x-10=x+34
We have to solve for x
3x-x=10+34
2x=44
Divide both sides by 2
x=22
Hence, the value of x in the figure is 22
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100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The given quadrilateral is a parallelogram by the theorem "The diagonals of a parallelogram bisect each other."
Given is a quadrilateral.
We have to determine that the quadrilateral is a parallelogram or not.
From the shape and the drawing given, the quadrilateral is a parallelogram.
A parallelogram has opposite sides parallel to each other.
Here it is parallel.
Here it is given that the diagonals are bisected by each other, that is two parts of the diagonals are of equal length.
We have a theorem that "The diagonals of a parallelogram bisect each other."
A square, rectangle, rhombus can be included in the group of parallelogram.
So this is a parallelogram.
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NO LINKS!! URGENT HELP PLEASE!!!
O is the center of the decagon below. Find its area. Round to the nearest tenth if necessary.
Answer:
752.4
Step-by-step explanation:
Here we are provided with a decagon which has 10 sides.
The total interior angle is 360°.
So each will have 360/10 = 36 degrees
Half of that is 18 degrees inside the triangle.
Refer to the attachment below.
opposite = 16sin(18)
adjacent = 16cos(18)
Find the area of this triangle:
= 1/2 × 16sin(18) × 16cos(18)
= 37.61825
There are 20 triangles just like this so the total area is (37.61825 × 20) = 752.365 ≈ 752.4 unit2
Arizona license plates are designed so there
are three letters followed by four digits.
How many different license plates are
possible if letters and digits cannot be
repeated?
A. 175,760,000
B. 47,174,400
C. 78,624,000
D. 115,316,136
78,624,000 different license plates are possible if letters and digits cannot be repeated.
For the letters:
There are 26 letters in the English alphabet, and we need to choose three of them without repetition.
This can be calculated as a permutation of 26 letters taken 3 at a time:
P(26, 3) = 26! / (26 - 3)!
= 26! / 23!
= 26 x 25 x 24
= 15,600
For the digits:
There are 10 digits (0-9), and we need to choose four of them without repetition.
This can be calculated as a permutation of 10 digits taken 4 at a time:
P(10, 4) = 10! / (10 - 4)! = 10! / 6!
= 10 x 9 x 8 x 7
= 5,040
To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total possibilities = P(26, 3) x P(10, 4)
= 15,600 x 5,040
= 78,624,000
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100 tickets are sold for $1 each. there’s a $25 prize and a $10 prize.what is the expected value for a person that buys a ticket? round to the nearest cent
The expected value for a person who buys a ticket is $0.35.
We have,
Number of tickets sold = 100
Price of each ticket = $1
Prize value (1st prize) = $25
Prize value (2nd prize) = $10
Let's calculate the expected value step by step:
Calculate the probability of winning each prize:
Since there is only one 1st prize and one 2nd prize, the probability of winning each prize is:
Probability of winning the 1st prize = 1/100
Probability of winning the 2nd prize = 1/100
Calculate the expected value:
Expected value = (Probability of winning 1st prize x Value of 1st prize) + (Probability of winning 2nd prize x Value of 2nd prize)
= (1/100 x $25) + (1/100 x $10)
= $0.25 + $0.10
= $0.35
Therefore, the expected value for a person who buys a ticket is $0.35.
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use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4
Answer:
Solution: x = 2, y = -3.
Step-by-step explanation:
Given system of equations:
Equation 1: 2x - 3y = 13
Equation 2: x + 2y = -4
Multiply Equation 2 by 2:
2(x + 2y) = 2(-4)
Simplified: 2x + 4y = -8
Add Equation 1 and Equation 3:
4x + y = 5
Solve Equation 4 for y:
y = 5 - 4x
Substitute y into Equation 2:
x + 2(5 - 4x) = -4
Simplify:
-7x + 10 = -4
Solve for x:
x = 2
Substitute x into Equation 5:
y = 5 - 4(2)
y = -3
Solution: x = 2, y = -3.
Question 8
Match each compound to its correct type.
8.1
CO
hydroxide
8.2
CO₂
carbonate
8.3
SO₂
8.4
CaCO
8.5
NaOH
oxide
trioxide
dioxide
The correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - carbonate
8.5 NaOH - hydroxide
Here is the correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
Compound 8.4, CaCO, is not correctly represented. It should have a subscript to indicate the number of atoms present in the compound.
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30 POINTS, MULTIPLE CHOICE, TIME SENSITIVE!!
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4
Answer: x= —5/9
Step-by-step explanation:
please help me solve for x image is attached ive been stuck on it for a few days now
The value of x will be 10.
Given a triangle we need to set a proportion to solve for the value of x,
Therefore, according to the definition of the similar triangles,
x / 5 = 15+5 / x
x² = 5 × 20
x² = 100
x = 10
Hence the value of x will be 10.
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HELPPP
MA.7.DP.1.2
A group of students in the book club are debating whether high school juniors or seniors
spend more time on homework. A random sampling of juniors and seniors at the local high
school were surveyed about the average amount of time they spent per night on homework.
The results are listed in the table below.
Average Amount of Time on Homework Per Night (in minutes)
Juniors 125 90 95
80 100 100 120- 85 95 120 95 85
Seniors 135 70 65 100 35 175 80 80 90 65 120 60
Part A. Calculate and compare the measures of center for the data sets.
Part B. Calculate and compare the variability in each distribution.
Part C. Does the data support juniors or seniors spending more time on homework?
Explain your reasoning.
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
How to solve for the median of centerJuniors: 125, 90, 95, 80, 100, 100, 120, 85, 95, 120, 95, 85
First, sort the data: 80, 85, 85, 90, 95, 95, 95, 100, 100, 120, 120, 125
Sum = 1085
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Seniors: 135, 70, 65, 100, 35, 175, 80, 80, 90, 65, 120, 60
First, sort the data: 35, 65, 65, 70, 80, 80, 90, 100, 120, 120, 135, 175
Sum = 1095
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
Variability
Juniors:
Range = max - min = 125 - 80 = 45
Seniors:
Range = max - min = 175 - 35 = 140
C. Based on the mean and median, it appears that seniors spend slightly more time on homework on average (mean ≈ 91.25) compared to juniors (mean ≈ 90.42).
However, the median time spent for seniors (80 minutes) is less than that of juniors (95 minutes), indicating that the data for seniors might be skewed by some outliers.
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A person buy a lot of tickets for Rs.136 each execution class ticket cost rupees12 and each local class ticket cost for Rs 4 each make an equation and fine explain possible solutions
Answer:
3.98
Step-by-step explanation:
Answer:
the second method may be through graph
can some one
factor 7a10 - 112a2
The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
How to find the factor 7a10 - 112a2To factor the expression [tex]7a^{10} - 112a^2[/tex] we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:
The coefficients 7 and 112 have a common factor of 7.
The lowest power of "a" in each term.
In this case, the lowest power of "a" is 2.
Factoring out [tex]7a^2[/tex] from both terms, we get:
[tex]7a^2(a^8 - 16)[/tex]
Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
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Southside High School found that 80% of last year's sold-out plays occurred
during weekend performances. Based on this information, the drama teacher
decided to add another performance time on Saturday. This decision is a
result of
OA. describing data
OB. making an inference
OC. creating involvement
D. collecting data
Answer:
B. making an inference.
Step-by-step explanation:
The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.
8. For positive real numbers a, b, and c, the expressions albici and Vabac are equivalent. What are the values
of p, q, and r?
Answer:
Step-by-step explanation:
To find the values of p, q, and r in the expression albici = Vabac, we need to equate the corresponding parts on both sides.
From the given equation, we have:
p * (a * b) * (c * i) = q * (a * b * a * c)
Comparing the exponents of a, b, and c on both sides, we get:
p = q * a^2
1 = q * c
To determine the value of r, we can use the fact that albici and Vabac are equivalent. The radical symbol (√) represents taking the square root.
√(a * b * c * i) = √(a * b * a * c)
This implies that:
√(a * b * c * i) = √(a^2 * b * c)
Comparing the exponents of a, b, and c on both sides, we get:
1/2 = 2 * p * q * r
Combining all the equations, we have:
p = q * a^2
1 = q * c
1/2 = 2 * p * q * r
To find the specific values of p, q, and r, we need additional information or equations involving a, b, and c. Without more context or equations, it is not possible to determine the exact values of p, q, and r.
The proportional relationship between cost and pints of blueberries is shown in the table. Blueberries (in pints) 4 10 Cost (in dollars) 18.40 46 Describe what a graph of the proportional relationship would look like.
The graph of the proportional relationship is a linear graph, with slope of 4.6 and intercept of zero.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
Hence the graph is a linear function with slope of k and intercept of zero.
The cost of 4 pints is of $18.4, and the cost of 10 pints is of $46, hence the slope of the relation is given as follows:
k = 46/10 = 18.4/4 = 4.6.
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Find the slope of the line.
A. 3/2
B. -2/3
C. 4/3
D. -3/4
Answer:
-3/4, answer D
Step-by-step explanation:
Slope = rise/run. The equation is (y2-y1)/(x2-x1).
So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.
slope = (2-(-4))/(-2-6)
slope = (2+4)/(-2-6)
slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.
slope = -3/4
Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.
Answer:
Step-by-step explanation:
Use 2 points from the line: (-2, 2) and (6, -4)
slope = y2 -y1 = -4 - 2 = -6 = - 3
x2 - x1 6 - -2 8 4
The slope is choice D -3/4
Use the image to determine the type of transformation shown.
A. Reflection across the x-axis
B. 90° clockwise rotation
C. Horizontal translation
D. Vertical translation
Answer:
the answer is C. Horizontal translation
Step-by-step explanation:
trust fr
If $850 is invested in an account that earns 2.6% yearly interested compounded quarterly, then which of the
following is the worth of this investment after 5 years?
(3) $967.60
(4) $968.25
(1) $960.50
(2) $966.40
[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 &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]