The vertex of the parabola is in the form of coordinates is (h, k). The standard equation can be used to find the vertex.
What is Parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curvesGiven is to find the vertex of the parabola.
The vertex of the parabola is the point of intersection of the parabola and the axis of symmetry.
The Standard Form of a Parabola is y = a(x-h)² + k. To find the vertex in this form, you will use identify h and k from the standard form and put it into the vertex point (h, k).
Therefore, the vertex of the parabola is in the form of coordinates is (h, k). The standard equation can be used to find the vertex.
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2 friends share 1 melon each friend gets ____ of the melon. pls answer
Answer: 1/2
Step-by-step explanation:
Answer:
Each friend will get half of the melon
Step-by-step explanation:
If the two friends have one melon, they will each get half. There are two people, so you cut it in half. They will each get 0.5 or 1/2 of the melon.
The equation y = 2.4x represents the number of miles, y, biked by Aaron in x days. The table shows the number of miles biked by Sara in a certain number of days.
Select all of the statements that are true based on the equation and the table above.
a. Aaron bikes twice as many miles as Sara does each day.
b. On day 3, Sara will have biked 7.2 more miles than Aaron.
c. Sara bikes twice as many miles as Aaron does each day.
d. Aaron bikes faster than Sara.
e. Aaron bikes fewer miles than Sara each day.
The statements that are true ; b. On day 3, Sara will have biked 7.2 more miles than Aaron. d. Aaron bikes faster than Sara.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that equation y = 2.4x represents the number of miles, y, biked by Aaron in x days.
0.5 10
1 10
1.5 10
2 10
2.5 10
Since x = 2 then
y= 2.4 (2)
y = 4.8
The statements that are truly based on the equation and the table above;
b. On day 3, Sara will have biked 7.2 more miles than Aaron.
d. Aaron bikes faster than Sara.
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Find the mean 12, 13, 15, 16, 24, 15, 22, 10, 9, 13, 13, 18, 16, 25, 23, 24
Round to two decimals
Answer:24
Step-by-step explanation:
because
how do these each of these coefficients (a, b, c) theoretically relate to quantities position x, velocity v and acceleration a?
The coefficients (a, b, c) in a polynomial equation is relate to the position x, velocity v, and acceleration a of an object.
Position (x): The position of the object can be represented by the x-coordinate of its position in space. This can be related to the coefficients in the equation by setting the x-coordinate equal to x and solving for the corresponding y-coordinate.
Velocity (v): The velocity of an object is the rate at which its position is changing. This can be related to the coefficients in the equation by taking the first derivative of the equation with respect to time. The result is a linear equation that represents the velocity as a function of time.
Acceleration (a): The acceleration of an object is the rate at which its velocity is changing. This can be related to the coefficients in the equation by taking the second derivative of the equation with respect to time. The result is a constant value that represents the acceleration of the object.
In summary, the coefficients (a, b, c) can be related to the position, velocity, and acceleration in equation for x, taking derivatives of the equation with respect to time, and interpreting the results as the position, velocity, and acceleration of the object.
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A special truck cleans the surface of the ice rink shown below.
The figure is composed of a square and two semicircles.
30 m
30 m
If the truck cleans the entire surface, how many square meters of
ice will the truck
clean? Use 3.14 for p. Round your answer to the nearest tenth.
Answer: The area is 1660.41.
Geometry
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Given
The combination of circle and rectangle of length, width, and radius are 30.5, 30.5, and 15.25.
To find
The area of the geometry.
How to find the area of geometry?
Area = Area of rectangle and area of two semi-circle
Length = 30.5
Width = 30.5
Radius = 15.25
Then
Thus the area is 1660.41.
A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space for the original random experiment of selecting three failed beams and denoting the type of failure along with each outcome's associated value of x.
The probability of each outcome can be calculated using basic probability formulas, such as the multiplication rule and the addition rule is 1/2
Probability is the branch of mathematics that deals with the likelihood of events occurring. In this scenario, we are looking at the probability of a concrete beam failing by shear or flexure.
When three failed beams are randomly selected, the type of failure is determined for each one. We want to find the probability of each possible outcome, where X represents the number of beams among the three selected that failed by shear.
To list the outcomes in the sample space, we can use the following notation: S for shear failure and F for flexure failure. The possible outcomes are:
SSS, where all three beams failed by shear. In this case, X = 3.
SSF, where two beams failed by shear and one by flexure. In this case, X = 2.
SFS, where two beams failed by shear and one by flexure. In this case, X = 2.
FSS, where two beams failed by shear and one by flexure. In this case, X = 2.
SFF, where one beam failed by shear and two by flexure. In this case, X = 1.
FSF, where one beam failed by shear and two by flexure. In this case, X = 1.
FFS, where one beam failed by shear and two by flexure. In this case, X = 1.
FFF, where all three beams failed by flexure. In this case, X = 0.
Each outcome has a different value of X, which represents the number of beams that failed by shear.
Then the probability is calculated as,
=> 1/2
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This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
x =
Two rectangles of different sizes. The first rectangle has a longer side labeled 6.4 inches and a shorter side labeled 3.6 inches. The second rectangle has a longer side labeled 1.6 inches and a shorter side labeled x inches.
Answer: 0.9 is the answer hope I helped.
Step-by-step explanation:
The require value of side of rectangle(x) is equal to 0.9 in.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to question:We have;
length of longer side = 6.4 in and loneger side of small rectangle = 1.6 in.
Then,
Scale factor = 6.4/1.6 = 4
It means Sides of big rectangle is 4 times of small rectangle.
We also have smaller side of big rectangle = 3.6 in
3.6 = 4x
x = 3.6/4
x = 0.9
Thus, required value of x is 0.9 in.
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Find a function whose domain is the set of all integers and whose target is the set of all positive integers that satisfies each set of properties.
(a) Neither one-to-one, nor onto.
(b) One-to-one, but not onto.
(c) Onto, but not one-to-one.
(d) One-to-one and onto.
a) This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one
b) This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs.
c) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.
d) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs
(a) One example of a function that is neither one-to-one nor onto is:
[tex]f(x) = \begin{cases} x+1 & \text{if } x \text{ is even} \ x & \text{if } x \text{ is odd} \end{cases}[/tex]
This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one because, for example, f(2) = f(4) = 3. It is not onto because no positive even integer is in the range of f.
(b) One example of a function that is one-to-one but not onto is:
[tex]f(x) = \begin{cases} 2x & \text{if } x > 0 \ -2x+1 & \text{if } x \leq 0 \end{cases}[/tex]
This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs. However, it is not onto because no odd positive integer is in the range of f.
(c) One example of a function that is onto but not one-to-one is:
[tex]f(x) = \begin{cases} x/2 & \text{if } x \text{ is even} \ -(x+1)/2 & \text{if } x \text{ is odd} \end{cases}[/tex]
This function maps even integers to positive integers, and maps odd integers to negative integers. It is onto because every positive and negative integer is in the range of f. However, it is not one-to-one because, for example, f(2) = f(-2) = 1.
(d) One example of a function that is both one-to-one and onto is:
f(x) = x
This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.
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Hello please help me w this question
Answer: so u do the e then f to get z
Step-by-step explanation:
The Smith family is selling their home for $250,000 with a required down payment of 5%. Find the amount of the required down payment and the mortgage.
Down Payment:
Mortgage:
Answer:
Down payment is $12,500.
Mortgage = $237,500
Step-by-step explanation:
The required down payment is 5% of the selling price of the house, which is $250,000.
Down payment = 5% of $250,000 = 0.05 x $250,000 = $12,500
Therefore, the required down payment is $12,500.
To find the amount of the mortgage, we need to subtract the down payment from the selling price of the house.
Mortgage = Selling price of the house - Down payment
Mortgage = $250,000 - $12,500
Mortgage = $237,500
Therefore, the amount of the mortgage is $237,500.
An airplane on a transatlantic flight took 2 hours 30 minutes to get form New York to its destination, a distance of 3,000 miles. To avoid a storm, however, the pilot went off his course, adding a distance of 600 miles to the flight. How fast did the plane travel?
Answer:
To solve this problem, we can use the formula:
Speed = Distance / Time
The total distance traveled by the plane is 3,000 + 600 = 3,600 miles. The total time taken is 2 hours 30 minutes, or 2.5 hours.
So, the speed of the plane is:
Speed = 3,600 miles / 2.5 hours = 1,440 miles per hour
Therefore, the answer is 1440 mph
Let X denote the amount of time a book on two-hour reserve is actually checked out, asuppose the cdf is the following.
0 x<0
F(x) = x^2/16 0?x?4
1 4?x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X ? 1)
The CDF at P(X > 1) is 1/16.
CDF stands for the cumulative distribution function. It is a function that maps each possible value of a random variable X to the probability that X takes a value less than or equal to that value.
The cdf given is:
F(x) =0 for x < 0
x^2/16 for 0 <= x < 1
1 - (3-x)^2/16 for 1 <= x < 4
1 for x >= 4
P(X <= 1)
Using the definition of the cdf, we have:
P(X <= 1) = F(1)
Since 0 <= 1 < 1, we have:
F(1) = 1^2/16 = 1/16
So, P(X <= 1) = F(1) = 1/16.
P(X > 2)
Using the definition of the cdf, we have:
P(X > 2) = 1 - P(X <= 2)
Since 0 <= 2 < 4, we have:
P(X <= 2) = F(2) = 2^2/16 = 1/4
Therefore:
P(X > 2) = 1 - P(X <= 2)
=> 1 - 1/4
=> 3/4.
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One couple and four individuals have been invited to a dinner party where dinner will be served promptly at 8pm. The chance any individual arrives late to the party is 10%. The chance the couple arrives late is 30% (the couple will arrive together) Let X = the number of guests arriving late Note: suppose I wanted to find the probability that 3 people arrive late to the party. This can happen in two ways ° (a) any combination of 3 individuals arive late (all others on time) » (b) any 1 individual and the couple arrive late (all others on time) or We consider in the following table all ways that (a) any combination of 3 individuals are late, the couple is on-time, and the remaining individual is on-time
Probability of 3 people arriving late is 0.34%.
The probability of 3 people arriving late to the party is the probability of a combination of 3 individuals arriving late and the couple and remaining individual arriving on time. This can be expressed mathematically as P(X = 3) = P(3 individuals arrive late)P(Couple arrives on time)P(Individual arrives on time).
We can calculate this probability as follows:
P(X = 3) = (0.1 x 0.1 x 0.1) x (0.7 x 0.7) = 0.00343
This means that there is a 0.34% chance that 3 people arrive late to the party. Probability of 3 people arriving late is 0.34%.
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4x-(-4x³ + 11)-(2x + x³) + 7x
Answer: 3x³+ 9x + -11
Step-by-step explanation: Combine Like Terms: 4x + 4x³+-11+-2x+-x³+7x
=(4x³+-x³) + (4x + -2x +7x) + (-11)
=3x³+ -9x+ -11
jaly has 241 times greater of gummys than deens who has 463 but jaly gave 50 away than recived 3542 write this in a sentence in fraction and decimal useing these fractions
6/2 and 4/8
WILL MARK AS BRAINLEST PLSSS HELP
This final result as a fractiοn and a decimal 115075 using the given fractiοns 6/2 and 4/8
What is fractiοn?A fractiοn is a mathematical representatiοn οf a part οf a whοle οr a ratiο between twο quantities. It is typically represented as a tοp number (numeratοr) divided by a bοttοm number (denοminatοr), separated by a hοrizοntal line.
Fοr example, the fractiοn 3/4 represents three parts οut οf fοur equal parts οf a whοle. The numeratοr (3) represents the number οf parts, while the denοminatοr (4) represents the tοtal number οf parts that make up the whοle.
Accοrding tο the questiοn:
Let's first find hοw many gummys Jaly has:
Jaly has 241 times greater number οf gummys than Deens, whο has 463. Sο Jaly has:241 x 463 = 111583 gummys Jaly then gave 50 away and received 3542 gummys.
Therefοre, the tοtal number οf gummy's Jaly nοw has is:111583 - 50 + 3542 = 115075We can express this final result as a fractiοn and a decimal using the given fractiοns 6/2 and 4/8.
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Please subtract and simplify.
Subtract (9x+8)-(3x + 5)
6x + 13
2x + 13
6x + 3
6x - 3
Answer:
The expression (9x+8)-(3x + 5) simplifies to 6x + 3. Therefore, the answer is option C: 6x + 3.
To learn the probabilities in graphical models, which of the following may be used? (Select all that apply.) Use relative frequency to estimate probability. Make proper assumption about the priors. Use the MLE principle for estimation.
All of the options are correct regarding the probabilities in graphical models.
Use relative frequency to estimate probability: This is a common approach for estimating probabilities in graphical models, especially when we have a large amount of data. We can count the number of times a certain event occurs in the data and divide it by the total number of events to get an estimate of the probability.
Make proper assumption about the priors: Priors represent our knowledge or beliefs about the probabilities before observing any data. By making appropriate assumptions about the priors, we can incorporate additional information into the model and improve our estimates of the probabilities.
Use the MLE principle for estimation: Maximum Likelihood Estimation (MLE) is a commonly used approach for estimating the parameters of a graphical model. The goal of MLE is to find the parameter values that maximize the likelihood of observing the data. This approach is often used when we have limited data and need to estimate the parameters of the model.
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Please help me bro.
Answer:
b
Step-by-step explanation:
The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 15 square inches and a height of 7 inches?
The volume of a pyramid with a base area of 15 square inches and a height of 7 inches is, 35 cubic inches.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
If the volume of a pyramid varies jointly with its base area and height, we can write this relationship as:
V = k[Ah/3]
To find the value of k, we can use the given information that the volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Plugging these values into the formula, we get:
24 = k(24)(3)/3
Simplifying, we get:
k = 1
Now we can use the formula to find the volume of a pyramid with a base area of 15 square inches and a height of 7 inches:
V = kAh/3
V = (1)(15)(7)/3
V = 105/3
= 35
Therefore, the volume of the pyramid is 35 cubic inches.
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Rita collected a total of 14 gallons of sap in one day if she distributes all of the sap equally between five jars how much sap will be in each jar
Answer: in decimal form = 2.8 gallons
in fraction = [tex]2\frac{4}{5}[/tex]
the fraction in simplest form = [tex]\frac{14}{5}[/tex]
Step-by-step explanation:
14 divided by 5 which gives 2.8, which means that there are 2.8 gallons in each jar.
1.Do 4x and 15+x have the same value when x is 5?
2.Are 4x and 15+x equivalent expressions?
Answer:
Step-by-step explanation:
1.Do 4x and 15 + x have the same value when x is 5?
To determine if 4x and 15 + x have the same value when x is 5, we can substitute 5 for x in both expressions and see if they equal the same value:
4x = 4 * 5 = 20
15 + x = 15 + 5 = 20
So, when x is 5, 4x and 15 + x both have the same value of 20.
2. Are 4x and 15 + x equivalent expressions?
Two expressions are considered equivalent if they have the same value for all possible values of the variables they contain. In this case, for all values of x, 4x and 15 + x will have the same value, so we can say that 4x and 15 + x are equivalent expressions.
Also:
When we substitute x = 5 into both expressions 4x and 15 + x, we find that:
4x = 4 * 5 = 20
15 + x = 15 + 5 = 20
As we can see, both expressions have the same value of 20 when x = 5. This means that the value of the expression 4x is equal to the value of the expression 15 + x when x = 5.
However, just because the values of the expressions are equal when x = 5, this does not necessarily mean that the expressions are equivalent for all values of x. To determine if two expressions are equivalent, we need to consider their values for all possible values of the variables they contain. In this case, since 4x and 15 + x have the same value for all values of x, we can conclude that these two expressions are equivalent.
In general, equivalent expressions are expressions that have the same value for all values of the variables they contain. Equivalent expressions can be transformed into each other through operations such as adding or subtracting the same value, multiplying or dividing by the same non-zero value, or using the distributive property.
What is the area of this composite shape?
Enter your answer in the box.
in²
The combined area of the given figure will be 40 square inches.
What is an area?The area is defined as the space covered by the object in two-dimensional space.
The area of a rectangle with a length of 7 inches and a width of 5 inches is given by:
Area of rectangle = length x width = 7 in x 5 in = 35 square inches
The area of a triangle with a base of 5 inches and a height of 2 inches is given by:
Area of triangle = (1/2) x base x height = (1/2) x 5 in x 2 in = 5 square inches
Therefore, the combined area of the rectangle and triangle is:
35 square inches + 5 square inches = 40 square inches
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Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5, y=1,
and the y-axis about the line y=−2
.
The volume of the solid obtained by rotating the region in the first quadrant bounded by [tex]$y=x^5$[/tex], y = 1, and the y-axis about the line y = −2 is 29.0359321.
The region is bounded in the xy plane and is said to be bounded in between the curve, line and y-axis as given by
Curve: [tex]$y=x^5$[/tex]
Line: y = 1
y-axis: x = 0
The curve and line intersect at [tex]x^5=1[/tex] and x = 1
The region bounded can be expressed as
[tex]x^5 \leq y \leq 1 \\[/tex]
0 ≤ x ≤ 1
Here we have to determine the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5, y=1
Now if the solid is obtained by the rotation of the region about the line y = -2 then the volume of the solid is evaluated by the method of the rings/washers as
Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{A}(\mathrm{x}) \mathrm{dx}[/tex]
Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \pi\left[\text { (outer radius) }^2-\text { (inner radius }^2\right] \mathrm{dx}[/tex]
Volume [tex]$=\pi \int_0^1\left[(1-(-5))^2-\left(x^5-(-5)\right)^2\right] d x[/tex]
Volume [tex]$=\pi \int_0^1\left[(1+5)^2-\left(x^5+5\right)^2\right] d x[/tex]
Volume [tex]$=\pi \int_0^1\left[(6)^2-\left(x^5+5\right)^2\right] \mathrm{d} x[/tex]
Volume = [tex]$\pi \int_0^1\left[(36)-\left(x^{10}+10 x^5+25\right)\right] d x$$[/tex]
Volume = [tex]$\pi \int_0^1\left(36-x^{10}-10 x^5-25\right) d x[/tex]
Volume [tex]$=\pi \int_0^1\left(11-x^{10}-10 x^5\right) d x[/tex]
Volume [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-10\left(\frac{x^6}{6}\right)\right]_0^1$$$$[/tex]
Volume [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-\frac{5}{3} x^6\right]_0^1$$$$[/tex]
Volume [tex]$=\pi\left(11(1-0)-\frac{1}{11}\left(1^{11}-0\right)-\frac{5}{3}\left(1^6-0\right)\right)[/tex]
Volume [tex]=\pi\left(11(1)-\frac{1}{11}(1)-\frac{5}{3}(1)\right)[/tex]
Volume [tex]=\pi\left(11-\frac{1}{11}-\frac{5}{3}\right)$$[/tex]
Volume = [tex]$\frac{305}{33} \pi[/tex]
Therefore the volume of the solid is
V [tex]=\frac{305}{33} \pi \approx[/tex] 29.0359321
Therefore the volume of the solid is 29.0359321
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in a sample of 28 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 182.5 degrees with a sample standard deviation of 14.1 degrees. what would be the 95% confidence interval for the temperature of your cup of coffee? homework help: 5ve. confidence intervals with sample standard deviation links to an external site.(1:37) group of answer choices (177.03, 187.97) (168.40, 196.60) (177.28, 187.72) (148.40, 176.60)
The Confidence interval starts at 177.28 and the Confidence interval ends at 187.72. Thus option c is correct.
The given data is as follows:
Number of coffee, N = 28
Mean, µ = 182.5
Standard deviation, α = 14.1
Confidence Level, CL = 95%
z-value for 95% confidence interval = 1.96
The confidence interval is calculated by using the formula,
Confidence interval = μ ± Ζ (α/√n )
Confidence interval = 182.5 ± 1.96*(14.1/√28)
Confidence interval = 182.5 ± 5.22
Confidence interval = (177.28, 187.72)
Therefore we can conclude that the Confidence interval starts at 177.28 and the Confidence interval ends at 187.72.
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Given the function below, find p (-2).
p(x) = x² - 7x
Answer:
18
Step-by-step explanation:
to find p(-2), substitute it into the equation!
you can make this easier by factoring x out, so p(x) = x(x-7)
then, plug -2 in
p(-2)=-2(-2-7)
p(-2)=-2(-9)
p(-2)=18
Answer:
Step-by-step explanation:
p(x)=[tex]x^{2}-7x\\[/tex]
=>p(-2)=[tex](-2)^{2} -7.(-2)[/tex]
= 4+14=18
Two events are mutually exclusive:
a. if their intersection is 1
b. if they have no sample points in common
c. if their intersection is 0.5
d. Both a and c are correct
e. None of the above
option (b) if they have no sample points in common, then the two events are mutually exclusive
Probability is an essential concept in statistics and other related fields. It deals with the chance or likelihood of an event happening. In this context, we will discuss the concept of mutually exclusive events.
Two events are considered mutually exclusive if they cannot happen at the same time. That is, if one event occurs, the other cannot occur. For instance, if we flip a coin, it can either come up heads or tails, but not both at the same time. In mathematical terms, we can represent mutually exclusive events using the intersection of sets.
Suppose we have two events A and B. Their intersection is the set of all sample points that are common to both events. If the intersection of A and B is equal to 1, then the two events are not mutually exclusive. This means that both events can happen at the same time. On the other hand, if the intersection is equal to zero, the two events have no sample points in common. This implies that the events cannot happen together and are mutually exclusive.
Therefore the correct option is (b).
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Please help. Just answer the best you can.
1. the positive linear relationship is what is shown here
A reasonable estimate that can be given for a person that played for 80 minutes is 26
The mean absolute deviation is appropriate to describe the spread of data if the data distribution is symmetric
How to solve for the relative frequency2. this is in the attachment
15 + 35 = 50
those that like fishing = 35 + 21 = 56
those that dislike fishing = 15 + 24 = 39
for male that like fishing = 35 / 56 = 0.63
for male that dislike fishing = 15 / 39 = 0.38
for females total 45
for female that like fishing 45 - 24 = 21 / 56 = 0.38
females that dislike fishing = 24 / 39 = 0.62
c. the relative frequency that is shown tells us that most of the people that like fishing are the males. While the most people that dislike fishing are the females
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#7
An insect population after x months can be modeled by
the function g(x) = 11(1.2). Which statement is the
best interpretation of one of the values in this function?
The insect population increased by 12 insects each month
The insect population decreased by 12 insects each month
The insect population increased at a rate of 20% each month
The insect population decreased at a rate of 20% each
month
+
A person has already worked Monday. The table and chart below shows gross
pay for the week based on hours worked Tuesday.
Pay is in U.S. dollars.
Hours Gross Pay
0
1
2
3
4
5
6
58.45
66.8
75.15
83.5
91.85
100.2
108.55
For every
Dollars
120
100
80
60
40
20
0
0
Hours
1
2
Gross Pay
3
Options for answers: 8.35, 58.45, hour, hours, dollar, dollars.
11
y = 8.35x + 58.45
5
the person's gross pay has increased by
For every hour worked, the person's gross pay has increased by 8.35 dollars.
How to model the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when the input increases by one, the output increases by 8.35, hence the slope m is given as follows:
m = 8.35.
Hence the meaning of the slope is that for every hour worked, the person's gross pay has increased by 8.35 dollars.
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The law of sines states that the ratio of the ____ of an angle to the length of the side ________ that angle is ________ in any triangle.
The law of sines states that the ratio of the Sine of an angle to the length of the side opposite that angle is constant in any triangle.
The Law of Sines is defined as a relationship that applies to all triangles, not just right triangles.
The law states that the ratio of length of side of a triangle to sine of angle opposite that side is constant for all sides and angles in the triangle.
So , for any triangle, ratio of length of one side to the sine of angle opposite that side is = ratio of length of any other side to the sine of the angle opposite that side.
The Sine Law is also useful for solving problems which involves the angles and sides of triangles, especially when not all sides and angles are known.
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