Answer:
x = 3, -5/2
Step-by-step explanation:
First, you move the 15 onto the left of the equation by subtracting it from both sides.
Second, you plug your info into the quadratic equation. (1 +- sqrt(1+4*15*2))/4
ACTIVITY 4: Solve the following inequalities.
The solutions of the inequalities are shown below
x [tex]\geq[/tex] 5
x< 13
x[tex]\geq[/tex]1
x> 1
How do you solve inequalities?Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.
[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]
[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]
[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]
[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]
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For f(x)=3x+4 and g(x)=x^2 find the following composite functions and state the domain of each.
The composite functions are:
a) f ∘ g = 3x² + 4, with domain of all real numbers.
b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.
c) f ∘ f = 9x + 16, with domain of all real numbers.
d) g ∘ g = x⁴, with domain of all real numbers.
To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.
a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:
f(g(x)) = 3g(x) + 4 = 3x² + 4
The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:
g(f(x)) = (3x + 4)² = 9x² + 24x + 16
The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:
f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16
The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:
g(g(x)) = (x²)² = x⁴
The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
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NASA launches a rocket at
t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t^2+43t+339
.
(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)
The rocket splashes down after
seconds._______
(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)
The rocket peaks at _____
meters above sea-level._____
Answer:
(A)
[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]
[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]
[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]
The rocket splashes down after 13.79 seconds.
(B) h'(t) = -9.8t + 43 = 0
t = 43/9.8 = 215/49 = 4.39 seconds
h(4.39) = 433.34 meters
At t = 4.39 seconds, the rocket peaks at
433.34 meters above sea level.
Level E: The repair department of the bicycle shop repairs three things: flat tires, bent handle bars and ripped seats. Today in the repair department, 25% of the bikes had flat tires only, 5% had bent handlebars only, and 10% had ripped seats only. Just 1/12th of the bikes had all three repairs to do: flat tires, bent handlebars and ripped seats. No bikes were completely fixed and there are a total of 101 repairs to be made. How many bikes are in the repair department? How many bikes need two repairs? If less than half of all the bikes have a ripped seat, what is the range of bikes that need both the tires and handlebars repaired without needing to fix the seat?
Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.
Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:
P(F) = 0.25
P(H) = 0.05
P(S) = 0.10
P(F ∩ H ∩ S) = 1/12
We want to find the number of bikes in the repair department and the number of bikes that need two repairs.
Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:
Flat tires: 0.25N
Bent handlebars: 0.05N
Ripped seats: 0.10N
The number of bikes that need all three repairs is:
P(F ∩ H ∩ S)N = (1/12)N
The number of repairs needed for these bikes is:
3P(F ∩ H ∩ S)N = (1/4)N
The number of repairs needed for bikes that need only two repairs is:
2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N
The number of repairs needed for bikes that need only one repair is:
[P(F) + P(H) + P(S)]N = 0.4N
The total number of repairs needed is given as 101, so we have:
(1/4)N + (5/12)N + 0.4N = 101
Simplifying this equation gives:
N = 60
Therefore, there are 60 bikes in the repair department.
The number of bikes that need two repairs is:
(5/12)N = 25
Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).
We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:
P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)
= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)
= 2(5/12) - 1/12
= 5/12
So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.
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Find the slope of the line that passes through A (3, 7) and B (7, 10).
Answer:
[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]
A manager of Furniture store has compiled a list of written complaints during the past three months. The complaints were categorized as follows. Type and Frequency Error in billing, Rudeness by store personnel, Late delivery, Questions not answered during telephone inquiry,and Other 42 14 8 6 5 Total 75 Present the above data using pie-chart(put the relative frequencyand the central angle measure toeach categoryon a table)
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
Here, we have,
H0 : μ ≥ 6
H1 : μ < 6
Test statistic :
n = 20
Sample Mean, x = 3
σ = 1.5
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (3 - 6) ÷ 1.5/sqrt(20)
Test statistic = - 3 / 0.3354101
Test statistic = −8.944271
Since, sample size is < 30 ;
Obtaining the Critical value using the from T;
Tcritical at 0.05, df = 19 = - 1.729
Tstatistic < Tcritical
−8.944271 < - 1.729
Hence, we reject the Null:
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
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(40 POINTS)
Data based on past observations can sometimes predict future performance.
a. Give an example where past performance does predict future performance. Explain your reasoning.
b. Give an example where past performance does not predict future performance. Explain your reasoning.
An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.
An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.
What does the data show on volcanoes ?Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.
However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.
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2. You have graduated and landed a good stable job (congratulations!) which requires a commute by car (meh). Your daily drive to work takes about 20 minutes or so with plenty of stoplights and left turns, so it varies day to day. Just out of curiosity you want to find out how long it usually takes to get from home to work, so you accurately time for four weeks. On four of those mornings you stopped for gas or coffee and a bagel or whatever, so you recorded 16 usable results. The mean of these results is 21.4 minutes and the standard deviation is 1.8 minutes. your commute Given these results find a 95% confidence interval for your true average commute time. Assume that these four weeks are a representative sample of your overall commuting experience.
Therefore , the solution of the given problem of unitary method comes out to be a 95% degree of certainty that the genuine average commute time falls within this range.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
We may use the following calculation to determine the 95% confidence interval for the actual average commute time:
=> CI = x' ± t*(s/√n)
Finding the essential t-value is the first step. We can apply a two-tailed t-test with a significance level of = 0.05/2 = 0.025 because we have 16 useable findings (sample size: n = 16) and
we require a 95% confidence interval. The crucial t-value, which we determine using a t-distribution table or calculator, is roughly 2.131.
=> CI = 21.4 ± 2.131*(1.8/√16)
=> 21.4 ± 0.95
The genuine average commute time has a 95% confidence interval of 20.45 to 22.35 minutes.
Based on our sample of 16 travel times, we can thus say with a 95% degree of certainty that the genuine average commute time falls within this range.
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A coach asked her athletes if they enjoy running. Fifty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
The tree diagram shows athletes branching off into two categories, enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories, enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two subcategories, enjoys cycling and does not enjoy cycling.
What is the total percentage of the athletes who enjoy cycling?
9%
25.5%
55%
74.5%
Answer:
75%
Step-by-step explanation:
To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.
According to the information provided:
55% of the team does not like to run.
Of those who do not like to run, 70% enjoy cycling.
Of those who enjoy running, 80% also enjoy cycling.
To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.
Percentage of athletes who do not like to run and enjoy cycling:
= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)
= 55% * 70% = 38.5%
Percentage of athletes who enjoy running and enjoy cycling:
= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)
= (100% - 55%) * 80% = 45% * 80% = 36%
Total percentage of athletes who enjoy cycling:
= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling
= 38.5% + 36% = 74.5%
Therefore, the correct answer is:
74.5%
5. Find x and y of a , b and c
The value of x and y will be
a) x= 48 y= 72
b) x= 10 y= 3
c) x= 18 y= 3
What is triangle proportionality theorem ?
Triangle Proportionality Theorem Statement
If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
DA/BD = EC/BE
How we can calculate the value of x and y from the figure ?
The value of x and y can be calculated as
a ) x/4 + 5 =x/2-7 y/3-6=66-2/3y
x/4- x/2 = -7-5 y/3+ 2y/3= 66 + 6
x-2x/4=-12 3y/3= 72
x= 48 y=72
b) x/5 +3 = 4x-35 2y + 1 = 5y-8
x/5 - 4x = -35-3 2y-5y= -8-1
x-20x/5 = -38 -3y=-9
-1 9x/5 = -38 y=3
x= 10
c) x/3 + 2= 2x/3-4 5y=7y/3+8
x/3-2x/3= -4-2 5y-7y/3=8
-x/3 = -6 15y-7y=8x3
x= 18 y=3
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A fair number cube is rolled twice. After 500 trials of the experiment, the experimental probability of rolling two 3s is 11/50. What is the difference between the number of expected outcomes and the number of actual outcomes?
I will give 30 points to whoever answers
|x +3| if x >5
|x +3| if x >2
|x +3| if x =2
|x − 3| if x >5
|120+x| if x < −120
|x − 120| if x < −120
|x − (−12)| if x > −12
|x − (−12)| if x < −12
|x − (−12)| if x = −12
|x ÷ 3| if x >0
|x ÷ 3| if x <0
|x ÷ 3| if x =0
These are absolute value expressions evaluated under different conditions:
How to solve|x + 3| if x > 5:
Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.
|x + 3| if x > 2:
Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.
|x + 3| if x = 2:
In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.
|x - 3| if x > 5:
If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.
|120 + x| if x < -120:
Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).
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Please help!!!
Natalie gathered a random sample of flower bouquets at the florist. She calculated data on different variables. For one data that she collected, she constructed a bar graph
Which of the following variables did she use?
O Type of flowers in each bouquet
O Amount of water needed for each bouquet
O Number of flowers in each bouquet
O Price for each bouquet
The variables that Natalie used in the data collected was C. Number of flowers in each bouquet.
How to find the variable ?The bar graph that Natalie crafted utilized the variable "number of flowers in each bouquet." This particular type of graph reveals the frequency or count associated with every number of flowers contained within a single bouquet.
As an illustration, let us suppose there were 20 bouquets holding 5 flowers, 30 bouquets possessing 10 flowers, and 15 bouquets that had 15 flowers each; consequently, the bar chart would exhibit exactly three bars symbolizing the count for all three categories as outlined above.
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Can you help me answer this question?
The constant of proportionality of the line is slope m = 2/3
Given data ,
Let the line be represented as A
Now , the value of A is
Let the point on the straight line be P ( 2 , 3 )
Now , from the proportionality , we get
y = kx
Divide by x on both sides , we get
k = y/x
So , the slope of the line is k
k = 2/3
Hence , the proportion is y = ( 2/3 )x
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a train will travel 300 kilometers at a constant rate. write an equation that represents the trains rate in kilometers per hour (r) based on how mant hours the trip takes (t).
Answer:
distance = rate x time
where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:
rate = distance / time
Substituting the given values, we get:
r = 300 / t
Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.
Step-by-step explanation:
Determine the solution to the equation shown below.
3.2 - 1/2 (x+4) = 4.8x + 2 - 5.2x
Answer:x=-8
Step-by-step explanation:
3.2+(−1/2)x−2=4.8x+2−5.2x
−0.1x=0.8
x=-8
Answer:
x=-8
Step-by-step explanation:
x=-8
Find the trig ratio, reduce and enter your answer in the lowest terms. Please help!
The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.
What does the trigonometric ratio mean? a trigonometric ratioTrigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).
The given triangle is a right angle,
To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.
[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]
Therefore [tex]cosA= \frac{3}{5}[/tex]
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Which equation represents a line that passes through the point (−12, 6) and is perpendicular to the graph of the equation y = 34
x + 7?
A. y = 43
x + 18
B. y = 34
x + 15
C. y = −43
x − 10
D. y = −34
x − 3
Answer:
C
Step-by-step explanation:
If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C
Let's replace now.
For C,
Let's take y=-4/3x-10 into consideration at the point (-12,6)
Y should be equal to 6 when we replace x by -12
Let's try
Y = -4/3(-12) - 10 = 16 - 10 = 6
Yup. C is your answer.
A spherical balloon has a 20-in. diameter when it is fully inflated. Half of the air is let out of the balloon. What is the volume of the fully-inflated balloon?
The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.
What is a sphere?
The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.
We are given diameter as 20 inches.
So, the radius is half of the diameter which comes out to be 10 inches.
From this, we get the volume as
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]
⇒ Volume = [tex]\frac{4000}{3}[/tex] π
⇒ Volume = 4186.67 cubic inches
Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.
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ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.
Answer:
what arecrosses on line 2
Can anyone help me??
1. The coordinates of the vertices of the preimage in the first column of the table are; (2, 2), (-1, 2) (-1, 1) (-2, 1) (-2, -2) (1, -2) (1, -1) (2, -1).
2. The scale factor for the dilation is 3
3. The coordinates for the image are, (6,6) (-3, 6) (-3, 3) (-6, 3)(-6, -6) (3, -6) (3, -3)(6, -3)
4. The sketch has been attached below;
5. The dilation multiplies the length of line segments by the scale factor.
6. The dilation did not affect the angle measures. The angles in the image are the same as the angles in the preimage.
How to calculate the scale factor of the image?
To calculate the scale factor for the dilation, we look at what has been provided (x, y) → (3x, 3y)
x =1 x2 = 3
1 multiplied by what will give us 3
1×? = 3
1/1 = 3/1 = 3
If we multiply 3 to every vertices of the preimage, we will find the coordinated of the image.
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Find the length of the missing side
Step-by-step explanation:
This is a right triangle , so the Pythagorean theorem applies
c^2 = a ^2 + b^2 c is the hypotenuse a and b are the legs
15^2 = 9^2 + x^2
15^2 - 9^2 = X^2
x = 12 ft
Help with math problems
The surd forms are simplified to give;
21. 10√6 - 12√10
23. -56a - 5√2a - 25
25. -4√15x - 25x + 3
What are surds?Surds are described as values in square root that can no longer be simplified into whole numbers or integers
They are also seen as irrational numbers.
From the information given, we have that;
√15(2√10 - 4√6)
Expand the bracket and multiply the surd forms
2√150 - 4√90
Factorize the forms
2√25 ×√6 - 4√9 × √10
find the square root
10√6 - 12√10
23. (√2a - 5)(7√2a - 5)
expand the bracket
7√4a² - 5√2a - 35√4a² + 25
find the square root, we have;
7×2a - 5√2a - 35×2a + 25
collect the like terms
14a - 70a - 5√2a - 25
-56a - 5√2a - 25
25. (√3 + √5x)(√3 - 5√5x)
expand the bracket
3 - 5√15x + √15x - 5√25x²
find the square root
3 - 5√15x + √15x - 25x
collect the like terms
-4√15x - 25x + 3
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pls help with this geometry asap
Area of sector XYZ is 81.45 feet².
Define area of sectorThe area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.
The formula for the area of a sector is:
Area of sector = (central angle / 360°) x π x r²
where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.
n is the area of sector XYZ
n/360=115/255(X)
n/255=115/360(V)
(The same elements are proportional)
n=115/360×255
n=81.4583≈81.45 feet²
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Liz opened a savings account and deposited $1,000.00 as principal. The account earns 8% interest, compounded quarterly. What is the balance after 4 years?
After the first quarter, the interest earned would be:
$1,000.00 * 0.02 = $20.00
So the new balance would be:
$1,000.00 + $20.00 = $1,020.00
After the second quarter, the interest earned would be:
$1,020.00 * 0.02 = $20.40
So the new balance would be:
$1,020.00 + $20.40 = $1,040.40
After the third quarter, the interest earned would be:
$1,040.40 * 0.02 = $20.81
So the new balance would be:
$1,040.40 + $20.81 = $1,061.21
After the fourth quarter, the interest earned would be:
$1,061.21 * 0.02 = $21.22
So the final balance after 4 years would be:
$1,061.21 + $21.22 = $1,082.43
Therefore, the balance after 4 years would be $1,082.43.
Pls Help Parallelogram PQRS is shown in the coordinate plane below. What is the perimeter of parallelogram PQRS?
1) Find the missing side using the right triangle shown. 2) Then find the perimeter by adding all four sides of the parallelogram!
Note that the perimeter of the parallelogram is 42
How is this so?recall that opposite sides of a parallelogram are congruent always
We have to to find the distance between the points Q(6, 6 ) and R(1, -6) using the distance formula which is
d = √[(x2 - x1) ² + (y2 - y 1)²]
where d is the distance between two points with paris (x1 , y1)
and (x2, y2).
PS = QR = √(6-1)² + (6+6)²
= √5² + 12²
= √(25+144
= √(169)
= 13
PQ = SR = 8
Perimeter = 13 + 13 + 8 + 8
Perimeter = 42.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
50 Points! Multiple choice algebra question. Suppose you deposit $1000 in an account paying 4% annual interest, compounded continuously. Find the balance after 10 years. Photo attached. Thank you!
The balance after 10 years is equal to: A. $1491.82.
How to determine the balance after 10 years?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]A(t) = P_{0}e^{rt}[/tex]
Where:
A(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.When time, t = 10 years, the future value can be calculated as follows:
[tex]A(t) = 1000e^{0.04 \times 10}\\\\A(t) = 1000e^{0.4}[/tex]
A(t) = 1000(1.49182469764)
A(t) = 1491.82469764 ≈ $1491.82.
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99 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The solution to the exponential equation is given as follows:
x = 0.8.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
[tex]\left(\frac{1}{64}\right)^{0.5x - 3} = 8^{9x - 2}[/tex]
64 is the sixth power of two, while 8 is the third power of two, hence:
[tex]\frac{1}{64} = 2^6[/tex][tex]8 = 2^3[/tex]Applying the power of power rule, the equation can be given as follows:
[tex]2^{-6(0.5x - 3)} = 2^{3(9x - 2)}[/tex]
[tex]2^{-3x + 18} = 2^{27x - 6}[/tex]
Exponential functions are one-to-one, meaning that the solution is obtained as follows:
-3x + 18 = 27x - 6
30x = 24
x = 0.8.
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Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
A box in the shape of a right rectangular prism has a length of 8.5 inches, a width of 4.5 inches, and a height of 3.75 inches, What is the volume, in cubic inches, of the box?
The volume of the prism is 143.44 in³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces.
The general formula for the volume of a prism is expressed as;
V = base area × height
The prism is a rectangular prism, therefore the volume will be calculated as
V = l× w × h
where l is the length of the base and w is the width of the base
V = 8.5× 4.5 × 3.75
V = 143.44 in³
therefore the volume of the rectangular prism is 143.44 in³
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