The probability that a patient would have a depression score greater than 60 is 0.9878.
The probability that a patient would have a depression score greater than 60 in a pain clinic when the mean depression score on a sample of patients is 78 with a standard deviation of 8 can be calculated using z-score.
Z-score formula
Z-score = (x - μ) / σ
Where,
x = the value to be standardized
μ = the mean of the population
σ = the standard deviation of the population
Given data,
Mean = 78
Standard deviation, σ = 8
Let x be the depression score.
To find the probability that a patient would have a depression score greater than 60, we need to find the z-score first.
Using the formula,
z-score = (x - μ) / σ = (60 - 78) / 8 = -2.25
Now, the probability can be calculated using the z-score table which gives the probability that a value will be less than z.
To find the probability that a value will be greater than z, subtract the probability from 1.
Probability of Z < -2.25 = 0.0122
Probability of Z > -2.25 = 1 - 0.0122 = 0.9878
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In a car park,
the number of cars: the number of vans = 7:4
the number of vans: the number of lorries = 3:2
The total number of cars, vans and lorries in the car park is 205
How many vans are in the car park?
Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.
What is an unitary method?It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.
Here,
Let's begin by giving the unknowns variables:
x = number of vehicles
Van count = 4 times
Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).
The value of x can be determined using the second bit of knowledge:
=> 4x/3 = (205 - 11x)/2
When we simplify this solution, we obtain:
=> 8x = 3(205 - 11x)
=> 8x = 615 - 33x
=> 41x = 615
=> x = 15
We can now determine the quantity of vans:
Van count = 4x = 4(15) = 60
Consequently, the parking lot has 60 trucks.
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State the coordinates of the point.
The sum of two numbers is 18. Their difference is -8. Find the two numbers.
Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
When we write out the system of equations, we will get:
[tex]x+y=18[/tex]
[tex]x-y=-8[/tex]
We can then use elimination to get just one variable.
[tex]x+y=18[/tex]
[tex]x-y= -8[/tex]
Which gives us: [tex]2x=10[/tex]
We then divide by 2 and get: [tex]x=5[/tex]
We next plug that into one of the two equations and solve for the other variable: [tex](5)+y=18[/tex]
We subtract 5 from both sides and get: [tex]y=13[/tex]
So the two numbers are 13 and 5.
I need help show work
Based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.
What is population and sample?The population in statistics refers to the total set of people or things that we are attempting to analyse and make conclusions about. Typically, this group is too big to see or measure directly, so we use statistical methods to infer some of its features from a smaller collection of people or things, known as a sample. A representative portion of the population was selected for the sample in order to learn more about the population as a whole. The purpose of statistical analysis is to draw conclusions about the population using data from the sample.
The number of weeks in a month= 4.
Using the given table the estimated number of sales for the month are:
Salted caramel: 51 x 4 = 204
Gingerbread: 31 x 4 = 124
Mint: 99 x 4 = 396
Hence, based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.
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GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
a bag contains 13 balls numbered 1 through 13. what is the probability of selecting a ball that has an even number?
The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.
To calculate the probability, we use the formula:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.
Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.
To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.
In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.
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SOMEBODY HELP ME PLEASE
Answer:
The volume is 1474.45 mm^2
Step-by-step explanation:
First, you have to find the radius. To do this, you divide the diameter by 2. This means that the radius is 8.
Then you use the formula V=3.14*r^2*(h/3)
V=3.14*8^2*(22/3)=1474.45 mm^2
What is the measure of <7?
Answer:
120
Step-by-step explanation:
Angels family is driving to their grandmothers house, which is 325 miles away.
After they drive 26 miles, what percent of the distance have they traveled?
Answer:
8%
Step-by-step explanation:
[tex]= .08[/tex]
This is the answer as a decimal. To change a decimal to a perfect multiply the decimal by 100%
[tex].08 \times 100\% = 8\%[/tex]
you work as a cashier in a supermarket. on saturday, you had 135 customers. on sunday, you had 90 customers. what is the approximate percent decrease
The approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%
To find the approximate percent decrease in the number of customers from Saturday to Sunday, we first need to calculate the decrease in the number of customers:
Decrease = Saturday customers - Sunday customers
Decrease = 135 - 90
Decrease = 45
The percent decrease can be found by taking the decrease as a percentage of the original value (Saturday customers):
Percent decrease = (Decrease / Saturday customers) x 100%
Percent decrease = (45 / 135) x 100%
Percent decrease = 33.33%
Rounding to the nearest percent, we get that the approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%.
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Your question is incomplete, but probably the complete question is :
You work as a cashier in a supermarket. On Saturday, you had 135 customers. On Sunday, you had 90 customers. What is the approximate percent decrease in the number of customers from Saturday to Sunday?
33%
45%
50%
90%
225%
Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below.
a. The probability that a randomly selected adult female has a pulse rate less than 82 beats per minute is 0.7123.
b. The probability that 25 randomly selected adult females have a pulse rate with a mean less than 82 beats per minute is 0.9974.
c. The normal distribution can be used in part (b), even though the sample size does not exceed 30 as Option D: Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. Using the z-score formula, z = (x - μ) / σ, where x = 82, μ = 75, and σ = 12.5, we get -
z = (82 - 75) / 12.5
z = 0.56
Using a standard normal distribution table or calculator, we can find the probability that z is less than 0.56 is 0.7123.
Therefore, the probability value is obtained as 0.7123.
b. The central limit theorem states that as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the original population distribution.
Therefore, we can use a normal distribution to approximate the sampling distribution of the sample mean, even if the sample size is less than 30.
The mean of the sampling distribution of the sample mean is the same as the mean of the original population, which is 75.
The standard deviation of the sampling distribution of the sample mean, also known as the standard error, can be calculated as σ / sqrt(n), where n = 25 is the sample size.
standard error = 12.5 / √(25) = 2.5
Using the z-score formula again, we can find the z-score for a sample mean of x' = 82 -
z = (x' - μ) / (σ / √(n))
z = (82 - 75) / (2.5)
z = 2.8
Using a standard normal distribution table or calculator, we can find the probability that z is less than 2.8 is 0.9974.
Therefore, the probability value is obtained as 0.9974.
c. The correct answer is the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.
The requirement of a sample size greater than 30 applies to using a normal distribution to approximate the population distribution, not the sampling distribution of the sample mean.
Therefore, the correct option is D.
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Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute.
The probability is ___.
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.
The probability is ___.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.
B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.
C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.
D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Question 5(Multiple Choice Worth 2 points)
The median of 20 is the most accurate to use, since the data is skewed.
What is histogram?A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. It is a bar graph-like structure where the bars represent the frequency or proportion of data in specific intervals or ranges of values. The x-axis represents the range of values, and the y-axis represents the frequency or proportion of data in each range. Histograms are commonly used in statistical analysis to represent the distribution of data, especially when dealing with large datasets.
Here,
The data is not evenly distributed, as there are many donations at the lower end and fewer donations at the higher end. Therefore, the median, which represents the middle value in the data set, is a better measure of center than the mean, which can be influenced by extreme values. The median donation in this data set is $20.
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Can someone help I’ll give 10 points
Answer:
Hey Sweetheart!
z=4
4x4x4= 64
Hope this Helps!!!
11. Rectangles and trapezoids
Sides:
Angles:
Relationship:
12. Squares and rhombi
Sides:
Angles:
Relationship:
13. Squares and trapezoids
Sides:
Angles:
Relationship:
14. Rhombi and trapezoids
Sides:
Angles:
Relationship:
The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.
How do quadrilaterals relate ?Rectangles and trapezoids
Sides: A rectangle has two pairs of parallel sides, where both pairs are equal in length. A trapezoid has one pair of parallel sides and the other pair of non-parallel sides are not equal in length.Angles: A rectangle has four right angles, each measuring 90 degrees. A trapezoid has two acute angles and two obtuse angles.Relationship: A rectangle is a special case of a trapezoid, where both pairs of non-parallel sides are equal in length.Squares and rhombi
Sides: A square has four equal sides, where each side intersects at a 90-degree angle. A rhombus has four equal sides, but opposite sides intersect at an acute angle and the other pair at an obtuse angle.Angles: Both a square and a rhombus have four equal angles, each measuring 90 degrees.Relationship: A square is a special case of a rhombus, where all angles are right angles.Squares and trapezoids
Sides: A square has four equal sides, while a trapezoid has two parallel sides of unequal length and two non-parallel sides of unequal length.Angles: A square has four right angles, while a trapezoid has two acute angles and two obtuse angles.Relationship: A square is not a trapezoid since it does not have parallel sides of different lengths.Rhombi and trapezoids
Sides: A rhombus has four equal sides, while a trapezoid has two parallel sides of unequal length and two non-parallel sides of unequal length.Angles: A rhombus has four equal angles, while a trapezoid has two acute angles and two obtuse angles.Relationship: A rhombus is not a trapezoid since it has two pairs of parallel sides, both of which are equal in length.Find out more on trapezoids at https://brainly.com/question/4458080
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which of the following best describes the chord of a circle? a chord is any segment in which the end points are found on the arc of the circle. a chord is a triangle inside of a circle. a chord is the arc formed from the segment. a chord is a square inside of a circle.
The statement that best describes the chord of a circle is a chord is any segment in which the end points are found on the arc of the circle. (option a).
A chord of a circle is a line segment that connects two points on the circle. The two endpoints of the chord are called the endpoints of the chord, and they lie on the circumference of the circle.
Therefore, option (a) that states that a chord is any segment in which the endpoints are found on the arc of the circle is the correct answer.
It is important to note that a chord does not have to pass through the center of the circle. If a chord passes through the center of the circle, it is called a diameter. A diameter is the longest chord of a circle, and it divides the circle into two equal parts called semicircles.
The correct answer to the question is option (a), which states that a chord is any segment in which the endpoints are found on the arc of the circle.
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Complete Question:
which of the following best describes the chord of a circle?
a) a chord is any segment in which the endpoints are found on the arc of the circle.
b) a chord is a triangle inside of a circle.
c) a chord is the arc formed from the segment.
d) a chord is a square inside of a circle.
10. BUILD PERSEVERANCE Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2. Write the coordinates of T'.
Answer:
(-3, 6.4)
Step-by-step explanation
First draw a line across the y axis about 4.2 blocks in
Then go to doing your reflections with ease
If Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The line y = 4.2 is a horizontal line that is 1.8 units above the x-axis (since the y-coordinate of T is 2).
When a point is reflected across a horizontal line, its y-coordinate is negated with respect to the line.
So, the y-coordinate of the reflected point T' will be:
y-coordinate of T' = (-3, 6.4)
Hence, if Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)
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we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution. group of answer choices true false
The statement "we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution" is true because when dealing with continuous data representing time between events, it is common to evaluate a histogram to determine if it follows an exponential distribution.
If the data represents the time between events and it is a continuous variable, it is common to evaluate the histogram to see if it follows an exponential distribution. The exponential distribution is often used to model the waiting time between independent events that occur at a constant average rate, and it has a continuous range of values that can be plotted as a histogram.
To evaluate whether the data follows an exponential distribution, you can plot a histogram and visually check if it has a single peak and a decreasing tail, which are characteristic of the exponential distribution. You can also use statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test to assess the goodness-of-fit between the data and the exponential distribution.
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this one, i suck at the hypotenuse and i learned it yesterday and this is due today please help break it down for me
The right triangle has a 90-inch perimeter.
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.
To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.
We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:
40² + b² = 41²
1600 + b² = 1681
b² = 1681 - 1600
b² = 81
b = √81
b = 9
Hence, the other leg is 9 inches long.
We can now determine the triangle's perimeter:
Perimeter = a + b + c
Perimeter = 40 + 9 + 41
Perimeter = 90 inches
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2) After fuel prices rose by 15%, a
family's annual heating bill was £1654.
What would the bill have been without
the price increase?
Therefore , the solution of the given problem of percentage comes out to be the initial annual heating cost was about £1438,26 before the 15% increase.
What precisely is a percentage?A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.
Here,
Assume that the annual heating expense was x prior to the 15% increase.
=> x + 0.15x = 1.15x was the new bill after the 15% price rise.
We can write: Because we are aware that the new price following the increase is £1654:
=> 1.15x = 1654
We must find x in order to determine the initial bill before the increase:
=> x = 1654/1.15
=> x ≈ 1438.26
Therefore, the initial annual heating cost was about £1438,26 before the 15% increase.
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Let sin 60° =
√3
2
Find the measure of angle 3, in degrees, for cos
√√3
2
Answer/Step-by-step explanation:
We know that sin 60° = √3/2, and we can use this information to find cos 60°:
cos 60° = √(1 - sin^2 60°) = √(1 - 3/4) = √(1/4) = 1/2.
To find the measure of angle 3, we can use the formula:
cos(180° - 2x) = -cos(2x)
We want to solve for x when cos 2x = √(√3/2) = √3/2 * 1/√2 = √3/2√2
cos(180° - 2x) = -cos(2x)
cos(2x) = √3/2√2
180° - 2x = 150° or 210°
x = 15° or 35°
Therefore, the measure of angle 3 can be either 15° or 35°.
find the perimeter
side A: x+10y units
side B:7x^2-x+9y units
Step-by-step explanation:
2(x+10y)+2(7x^2-x+9y)
= 2x+20y+14x^2-2x+18y
= (14x^2+38y) units^2
X
Y
3
12
6
-3
q
- 18
12
-33
Is this linear or non-linear
Explain.
Answer:
linear
Step-by-step explanation:
gradient 1 = [tex]\frac{-3-12}{6-3}[/tex] = -5
gradient 2 = [tex]\frac{-18+3}{9-6}[/tex] = -5
therefore, the graph is linear as the gradient is constant
3. Jermiah is raising money for tickets to go to the school dance. To do this, he is buying a large number of candy
bars to sell. Bulk candy bars cost $55 for a box, but this is on sale for 10% off the original price. He also has a coupon
for $7 off the total cost before the percent discount is taken. If he has $300 to spend, which of the following
equations will help him determine how many boxes of candy, x, he can buy?
A. 55x0.9(7) = 300
B. 55(0.9x - 7) = 300
C. 0.9(55x) 7= 300
D. 0.9(55x-7)= 300
Answer:
The answer is D, I'm not sure but I believe it's supposed to be
0.1(55-7)= 300
Step-by-step explanation:
know what it is but needs to know how to do it
5x+75=180
Answer:21
Step-by-step explanation:
5x=180-75
5x=105
x=105/5
x=21
Ross is trying to make the target number 10. Using the numbers 6,7,8, and 9, how can ross make an equation out of those numbers that equals 10? Each number can be used only once, in any order, with any operations
One possible equation Ross can make is 9 - 7 + 8 = 10
Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.
One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.
Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.
Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.
One possible equation Ross can make is:
9 - 7 + 8 = 10
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9.6 8.4 7.2 6.0 4.8 3.6 2.4 1.2 0 1 2 3 4 5 6 7 8 9 10 ➤X The equation of the line of best fit for the nine points is determined. Then, three more points are added to the scatter plot, but the equation of the original line of best fit remains unchanged. Which three ordered pairs are most likely the added data points?
i need help
A (4,4), (5,5), (6,6)
b (4,10), (4,11), (4,12)
c (8,9), (8,10), (8,11)
d (10,10), (10,11), (10,12)
The three ordered pairs that are most likely the added data points are:
B: (4,10), (4,11), (4,12)
C: (8,9), (8,10), (8,11)
D: (10,10), (10,11), (10,12)
How to determine the added data pointsIn order to determine the added data points, we first need to note that the data points have a slightly linear pattern with a negative slope. Also, a linear regression on the points will give us: linear regression on the given data points, we obtain the equation: y = -1.2x + 10.8
In selecting the three added data points, a good criterion will be for the points to be as close as possible to the original line of best fit. The data points in option A are close to slope 1 so adding them will significantly shift the line of best fit. The data points in options B, C, and D are in a vertical line and will not shift the line of best fit. So, they are most likely the best data points to add.
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How tell what the equation is if the vertical line is going through the y-axis?
Answer:
The equation of a vertical line in the graph, which is parallel to y-axis is x = a. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero.
Step-by-step explanation:
14 , 28, 56 as product of their prime factors
Answer:
14 = 2 x 7
28 = 2² x 7
56 = 2³ x 7
If two sets of numbers have the same mean, which of the following must always be true: A) The two sets must have the same variance B) The two sets of numbers must have the same standard deviation. C) The two sets of numbers must be identical. D) None of these statements must be true
None of these statements must be true
=========================================
Explanation:
Let's go through the answer choices one at a time.
----------------
A)
Consider the set {4,5,6}. It has a mean of (4+5+6)/3 = 15/3 = 5. We add up the values and then divide by the number of values (3 in this case).
Now consider the set {3,5,7}. I've added 1 to the largest element and subtracted 1 from the smallest. This will spread the data set out further. The mean is still 5 because (3+5+7)/3 = 15/3 = 5. The center hasn't changed. But the data is more spread out so the variance is larger for this new set.
Therefore, the sets {4,5,6} and {3,5,7} do NOT have the same variance. We cross choice A off the list.
----------------
B)
Recall that
[tex]\text{standard deviation} = \sqrt{\text{variance}[/tex]
For example, if the variance is 36 then the standard deviation would be [tex]\sqrt{36} = 6[/tex]
Because of the connection of the standard deviation and variance, both measure how spread out a set is. Furthermore, it means the sets {4,5,6} and {3,5,7} do NOT have the same standard deviation. We can cross choice B off the list.
----------------
C)
This statement is clearly not true because the sets {4,5,6} and {3,5,7} are not the same, but they produce the same mean. We can cross choice C off the list.
Choice D is the only thing left so it must be the final answer.
write the equation of an exponential decau function with a range of (-inifinage,10) verticlal shrink of 3/4 and vertical shift up 10 units
The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.
We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
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