Question 7 of 10
For an exponential regression equation in the form ý = ab*, which of the
following values of b will cause ý to get smaller as x gets larger?
Answers
The correct answer is option D which is 0.798
The complete question is given below:-
For an exponential regression equation in the form y=ab^x which of the following values of b will cause y to get smaller as x gets larger?
a.) 1.526
b.) 1.798
c.) 2.526
d.) 0.798
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Since we know that an exponential function is in the form:y= ab\(.^x\) where,
a= Initial value,
b = For growth b is in form (1+r), where r is the rate in decimal form.
b = For decay or regression b is less than 1 and in form (1-r), where r is the rate in decimal form.
Upon looking at our given choices we can see that options a, b and c are in form 1+r, while the choice provided in option d is less than 1 and in form 1-r, therefore, option d is the correct choice.
Therefore the correct answer is option D which is 0.798
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Related Questions
7(4p+2q+3r) apply the distributive property to create an equivalent expression
Answers
Answer:
28p + 14q + 21r
Step-by-step explanation:
7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside
= 28p + 14q + 21r
If a function f(x) is defined as 3x2 + x + 2, what is the value of Lim h-0 f(x+h)-f(x)/h? A. 3x + 1 B. 3x + 2 C. 6x + 1 D. 6x + 2
Answers
Answer:
\( f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2\)
\(f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2\)
And replacing we got:
\( lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}\)
And if we simplfy we got:
\( lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h \)
And replacing we got:
\(lim_{h \to 0} 6x + 1 +3h = 6x+1\)
And the bet option would be:
C. 6x + 1
Step-by-step explanation:
We have the following function given:
\( f(x) = 3x^2 +x+2\)
And we want to find this limit:
\( lim_{h \to 0} \frac{f(x+h) -f(x)}{h}\)
We can begin finding:
\( f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2\)
\(f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2\)
And replacing we got:
\( lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}\)
And if we simplfy we got:
\( lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h \)
And replacing we got:
\(lim_{h \to 0} 6x + 1 +3h = 6x+1\)
And the bet option would be:
C. 6x + 1
Answer:
6x+1
Step-by-step explanation:
Plato :)
Which equation is true?
A) 4/-9=-4/9
B) 4/-9=2/-3
C) 4/-9=4/9
D) 4/-9=2/3
Answers
Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.
Answers
The image showing the complete question is attached.
Answer:
1) Scale factor = 2
2) Scale factor = 4
3) Scale factor = ½
4) Scale factor = 2
5) Scale factor = 1
6) Scale factor = ¼
7) Scale factor = 1
Step-by-step explanation:
Scale factor is a number by which the dimensions of an object are multiplied in order to create an enlarged or reduced object.
Now, from the image attached;
1) From P to Q, we see that the length of Q seems to be double that of P. Similarly, the width of Q seems to be double that of P. Thus, each dimension of P is said to be multiplied by 2 to achieve the enlarged dimensions of Q.
Thus, scale factor = 2
2) From P to R, we see that the length of R seems to be 4 times that of P. Similarly, the width of R seems to be 4 times that of P. Thus, each dimension of P is said to be multiplied by 4 to achieve the enlarged dimensions of R.
Thus, scale factor = 4
3) From Q to S, we see that the length of S seems to be half of that of Q. Similarly, the width of S seems to be half of Q. Thus, each dimension of Q is said to be multiplied by ½ to achieve the reduced dimensions of S.
Thus, scale factor = ½
4) From Q to R, we see that the length of R seems to be double that of Q. Similarly, the width of R seems to be double that of Q. Thus, each dimension of Q is said to be multiplied by 2 to achieve the enlarged dimensions of R.
Thus, scale factor = 2
5) From S to P, we can see that the dimensions of both rectangles remain the same. Thus, S was multiplied by a factor of 1 to get P. Scale factor = 1
6) From R to P, we see that the length of P seems to be a quarter that of R. Similarly, the width of P seems to be quarter of R. Thus, each dimension of R is said to be multiplied by ¼ to achieve the reduced dimensions of P.
Thus, scale factor = ¼
7) From P to S, we can see that the dimensions of both rectangles remain the same. Thus, P was multiplied by a factor of 1 to get S. Scale factor = 1
A rectangular room is 1.6 times as long as it is wide, and its perimeter is 34 meters. Find the dimensions of the room.
Answers
Answer:
Step-by-step explanation:
x=1.6w and 2w+2x=34.
Simply substitute for x in the perimeter equation, and solve for w. Now compute x.
Solve each of the following equations and show how you checked your answers 2y+4y=6-3y
Answers
Answer:
y=2/3
Step-by-step explanation:
2y+4y=6-3y
⇔ 2y+4y+3y=6
⇔ 9y=6
⇔ y=6/9=2/3
The answer is:
y = 2/3
Work/explanation:
For now, I focus on the left side and combine the like terms:
\(\bf{2y+4y=6-3y}\)
\(\bf{6y=6-3y}\)
Add 3y to each side
\(\bf{6y+3y=6}\)
Combine like terms
\(\bf{9y=6}\)
Divide each side by 9
\(\bf{y=\dfrac{6}{9}}\)
\(\bf{y=\dfrac{2}{3}}\)
Hence, the answer is 2/3.
I WILL GIVE 5 STARS
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answers
Part A: The average rate of change of each section are,
Section A = 8, Section B = 32.
Part B: There are 4 times greater is the average rate of change of Section B than Section A.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and divi
The function is given by,
⇒ f (x) = 4 (2)x
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = 8
And in section B, the average rate of change is = 32
Part B:
Therefore, the average rate of change of section B is greater than section A is,
⇒ 32 / 8 = 4
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Find the ordered triple $(p,q,r)$ that satisfies the following system:
\begin{align*}
p - 2q &= 3, \\
q - 2r &= -2, \\
p + r &= 9.
\end{align*}
Answers
The ordered triple (p, q, r) that satisfies the given system of linear equations is (7, 2, 2).
To solve the given system of equations:
Start with the first equation: p - 2q = 3.
Multiply this equation by 2 to eliminate the coefficient of q: 2p - 4q = 6.
Next, we'll combine this equation with the second equation: q - 2r = -2.
Add the two equations together: (2p - 4q) + (q - 2r) = 6 + (-2).
Simplifying, we get: 2p - 3q - 2r = 4.
Now, let's consider the third equation: p + r = 9.
Rearrange this equation: p = 9 - r.
We can substitute this value for p in the equation we obtained in step 3:
2(9 - r) - 3q - 2r = 4.
Simplify the equation: 18 - 2r - 3q - 2r = 4.
Combining like terms, we have: -4r - 3q = -14.
We now have a system of two equations with two variables:
-4r - 3q = -14, (Equation 1)
q - 2r = -2. (Equation 2)
To solve this system, we can use various methods such as substitution or elimination. Here, we'll use the substitution method.
From Equation 2, we can solve for q:
q = 2r - 2.Substituting this value for q in Equation 1, we have:
-4r - 3(2r - 2) = -14.
Simplify and solve for r:
-4r - 6r + 6 = -14,
-10r = -20,
r = 2.
Now, substitute the value of r back into Equation 2 to solve for q:
q - 2(2) = -2,
q - 4 = -2,
q = 2.
Finally, substitute the values of q and r into Equation 3 to solve for p:
p + 2 = 9,
p = 7.
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if a(x) = 3x+1 and b(x) = \(square root of x-4\), what is the domain of (boa)(x)
Answers
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
\(b(x) = \sqrt{x-4}\)
Therefore, the composite function (boa)(x) is given by;
\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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![if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/gGe6IRGOQUF4aKHR4HvpxeklJAqlYD78.png)
Place the numbers in the correct boxes.
Answers
Answer:
Step-by-step explanation:
Top left answer:
-4 4/5
Top right answer:
-7.5
Bottom left answer:
1.5
Bottom right answer
-2 2/5
An Airplane travels at a constant speed 320 miles per hour. How far, in miles, will the airplane travel in 15 minutes?
Group of answer choices
Answers
Answer:
80 miles
Step-by-step explanation:
1 hour is equivalent to 60 minutes. Because 15/60 is just 1/4, 1/4 * 320 is the same as 320 divided by 4. Thus, the answer is 80.
Last week, the price of oranges at the farmers market was $1.75 per pound. This week, the price has decreased by 15%. What is the price of
oranges this week?
Answers
Answer:
11.6 (6 is repeating)
Step-by-step explanation:
1.75 divided by 15% of 75
There are two gyms in town. We Run For Fun a $63 starting fee plus $12 per class. Yoga For All charges no starting fee and $15 per class. Write and solve an equation to find the number of classes for which the cost will be the same at both places.show ALL work please!
Answers
Let be "x" the number of classes for which the cost will be the same at both places.
According to the information given in the exercise, a person must pay $12 per class plus a starting fee of $63 in the gym We Run For Fun . Based on this, you can set up the following expression to represent this situation:
\(12x+63\)In the gym Yoga For All there is no starting fee. A person must pay $15 per class. Then, you can set up the following expression to represent this situation:
\(15x\)Since you need to find the value of "x" for which the cost will be the same, you must set up the this equation:
\(12x+63=15x\)Now you have to solve for "x":
\(\begin{gathered} 63=15x-12x \\ 63=3x \\ \\ \frac{63}{3}=x \\ \\ x=21 \end{gathered}\)The answer is:
Equation:
\(12x+63=15x\)Number of classes:
\(x=21\)how do you simplify this\(( {3}^{2} - {2}^{2} ) {}^{3} + 42 \div 6 \times {3}^{2} - 9\)
 {}^{3} + 42 \div 6 \times {3}^{2} - 9[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/FhVG1QRTWTOhSmQhAMr8z7aUJ955N0GU.png)
Answers
Given:
\(\frac{(3^2-2^2)^3+42}{6\times3^2-9}\)First simplify the numerator and denominator,
Which of the following rational functions is graphed below?
Answers
The rational function that represents the graph attached is; f(x) = 1/(x + 5)²
How to interpret the graph of the rational function?There is a vertical asymptote -5. Vertical asymptotes are present where x on the denominator is equal to 0. The value of -5 sets x equal to 0 in the denominator, so it is a horizontal asymptote.
For the given graph it can be observed that the function is undefined for the value of x as -5.
This means that the function can be expressed as;
f(x) = 1/(x + 5)²
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A map has a scale of 1 inch:18 km, three distances on the map are listed in the chart below drag an actual distance into each box to match the corresponding distance on the map
Answers
Answer:
A map has a scale of 1 inch:18 km, three distances on the map are listed in the chart below drag an actual distance into each box to match the corresponding distance on the map
Step-by-step explanation:
1-18
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
<\(\sqrt{74}\)
Answers
The inequality is -8 < √74 < 9. A mathematical expression that's values on the left and right are not equal is referred to as having an inequality.
A mathematical expression that's values on the left and right are not equal is referred to as having an inequality. In essence, an inequality analyses any two values that demonstrates whether one is bigger than, less than, or neither greater nor equal to the other quantity. Numbers are compared using inequalities to determine a range of quantities that are contained inside the parameters of a variable.
Let A = √74
A² = 74
8² < A² < 9²
Hence, the inequality is -
8 < √74 < 9
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a number changed to 3.25 after it was rounded to what place was the number rounded
Answers
Answer: hundredths place
Step-by-step explanation:
Hundredths place is the second number after the decimal point
Because the second number after the decimal (overall the third number) was the number that was rounded
A physical therapy facility is building a new pool that is 90 feet long and 6 feet deep. They have ordered enough tile for a 340 -foot-long border around the edge. How wide should the pool be to ensure that all tiles are used?
Answers
The width of the pool should be 80 feet.
What should the width of the pool be?The pool would have the shape of a rectangular prism. The edge of the pool would have the shape of a rectangle. A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has a width and a length of different sizes.
The border that goes around the edge of the pool is equal to the perimeter of the pool. Perimeter is the distance round an object.
Perimeter of a rectangle = 2(length + width)
340 = 2(90 + width)
340 / 2 = 90 + width
170 = 90 + width
Width = 170 - 90
= 80 feet
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What is 48% of 159 express your answer rounded correctly to one decimal place
Answers
Answer:
.48 * 159 = 76.32
Step-by-step explanation:
48%
=0.48
Step 2: multiply to find the percent
0.48*159=76.32
So 48% of 159 is 76.32
Step 3: Round to the nearest tenth (assuming the one decimal place means tenth place)
76.32
=76.3
Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ = 64 and o = 12; n = 9
Answers
The standard deviation of the data sample is 2.55.
What is the standard deviation of the data sample?The standard deviation of the data sample is calculated by applying the following formula;
S.D = √ (x - μ)²/(n - 1)
where;
μ is the mean of the distributionx is the sample datan is the number of sample dataThe given parameters;
mean, μ = 64
x, = 12
number of samples = 9
The standard deviation of the data sample is calculated as;
S.D = √ (12 - 64)²/(9 - 1)
S.D = 2.55
Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.
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50 POINTS. if needed rotate in top right corner
Answers
The length of the side of the square would be 12 inches.
What is a Square?A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90° angles. The characteristics of a rectangle and a square are somewhat similar, although a rectangle only has its opposite sides equal. As a result, a rectangle is only referred to as a square if its four sides are of the same length.
Given : side of the triangle = 16 inches
So, the perimeter of the triangle = 16+16+16
= 48 inches
Now, the wire is unbent and shaped into a square.
So, the length of the wire would be same.
Hence, we can say that:
Perimeter of triangle = perimeter of square
48 = 4 × side
So, side = 12 inches.
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Prove: The square of a number that is two more than a multiple of 3 is one more than a multiple of 3.
Answers
Step-by-step explanation:
x is the number
x = 3y + 2
the square
x² = (3y + 2)² = 9y² + 12y + 4
9y² is a multiple of 3 (because of the factor 9)
12y is a multiple of 3 (because of the factor 12)
4 is 1 more than a multiple of 3 (1×3).
so, the sum of all 3 terms is 1 more than a multiple of 3.
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for π, and do not round your answers.
Area=?
Circumference=?
Answers
Answer:
\(Area = 153.938040026m^2\)
\(Circumference= 43.9822971503m\)
Step-by-step explanation:
Area
\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)
Circumference
\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)
pls answer me this all question correctly pls I beg you pls friends pls pls pls pls
Answers
A) 4/5.
B) 3/10
C) 1/2
2:
A) 62/15 = 4 2/15.
B) 73/36 = 2 1/36.
Hope it helps!
5th grade math. correct answer will be marked brainliest
Answers
Answer:
4 pieces 1/3 of a yard left over
 Hey guys, I would really appreciate if one of you help me with this question
Answers
Answer: 28.25%
Step-by-step explanation:
113/400=0.2825=28.25%
Math Homework: Unit 3 Assignment
Answers
Find the area of the rectangle with measurements shown; reduce to lowest terms: Length: 13 1/2 feet; Width: 10 2/3 feet
Answers
Answer:
Step-by-step explanation:
A = l*w
13.5 * 10.67 = 144.045 or 144
Hope that helps!
● Blondies are squares with 3 inch sides. ● Brownies are squares with 6 inch sides. ● The tray that displays the blondies and brownies has an area of 648 square inches and is completely full. If she has 4 rows of blondies and 4 rows of brownies, what fraction of the area of the tray, in square inches, is blondies? Show your work.
Answers
The fraction of the area of the tray occupied by the blondies is 1/9.
To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.
Let's calculate the area of each individual blondie:
The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.
Now, let's calculate the area occupied by the blondies in each row:
Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.
So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.
Next, let's determine the area occupied by the brownies:
The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.
Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.
Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.
Now, let's calculate the total area of the tray:
Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:
Total area of the tray - Area occupied by the brownies = Area occupied by the blondies
648 square inches - 576 square inches = 72 square inches.
So, the fraction of the area of the tray occupied by the blondies is:
Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:
72 square inches / 648 square inches = 1/9.
Therefore, the blondies' percentage of the tray's surface area is 1/9.
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