To solve this problem, all we have to remember is that fractions also mean division. Therefore this means that:
4 / 7 = 4 divided by 7
We can use either a calculator to solve for this or do the long division method of division (your choice). Now to solve this simply, I used the calculator and got the answer:
4 / 7 = 0.571428571
However, the problem asked us to round this to the nearest thousandth. We know that the decimal places are:
0.(tenths)(hundredths)(thousandths)
So we are to round this into 3 decimal numbers which gives us:
4 / 7 = 0.571
Use complete sentences to describe the range of the sine function.
(4.05 LC)
The graph shows y as a function of x:
Graph of x against y shows 4 segments. Segment A is a horizontal line parallel to the x-axis. Segment B is a slanting straight line going up. Segment C is a horizontal line parallel to the x-axis. Segment D is a slanting straight line going down that touches the x-axis.
In which segment is the function increasing?
A
B
C
D
Answer: I think the answer is A.
Step-by-step explanation:
I think this because its the only time that It could stay the same.
Graph the functions and approximate an x-value in which the quadratic function exceeds the exponential function. y = 4x y = 7x2 + 4x - 2
x = -0.5
x = 0
x = 0.5
x = 2
Answer:
Option 3th is correct
x = 0.5
Step-by-step explanation:
The given functions are:
Function 1: [tex]y = 4^x[/tex]
Function 2: [tex]y=7x^2+4x-2[/tex]
The values of function at x = -0.5, 0, 0.5 and 2 are as follow:
x values Function 1 Function 2
-0.53 0.5 -2.25
0 1 -2
0.53 2.086 2.0863
2 16 34
From the above table. It is clear that the quadratic function [tex]y=7x^2+4x-2[/tex] exceeds the exponential function [tex]y = 4^x[/tex] at x = 0.53
Therefore, the approximate x-value in which the quadratic function exceeds the exponential function at x = 0.5
A parallelogram has vertices E(−4, 6), F(1, 3), G(3, −4), and H(−2, −1). What are the coordinates of the midpoint of each diagonal?
(−3.5, 2.5)
(−0.5, −1)
(−0.5, 1)
(0.5, −1)
85 is 20% of what number? Enter your answer in the box.
Josh has 40 minutes to complete a government exam. There are 15 multiple-choice questions worth 3 points each. There are also 5 short-answer questions worth 11 points each. It takes about 2 minutes for Josh to answer the multiple-choice questions m and about 8 minutes to complete the short-answer questions s. The system of inequalities that represents this problem is graphed below. Which ordered pair is not a vertex of the feasible region?
The feasible vertices of the system representing Josh's exam are (0,0), (12,5), and (15,1.25). The non-feasible vertices are (15,0), (0,5), and (20,0). Therefore, the ordered pair (15,0) is not a vertex of the feasible region.
1. System of Inequalities:
- Time constraint: [tex]\(2m + 8s \leq 40\)[/tex]
- Number of multiple-choice questions: [tex]\(m \leq 15\)[/tex]
- Number of short-answer questions: [tex]\(s \leq 5\)[/tex]
2. Feasible Vertices:
- (0,0), (12,5), (15,1.25)
3. Non-feasible Vertices:
- (15,0), (0,5), (20,0)
So, the ordered pair (15,0) is not a vertex of the feasible region.
Can you square both sides of an inequality
Squaring both sides of an inequality can be valid if you know both sides are non-negative, but it can introduce extraneous solutions. Therefore, it's important to check any solutions against the original inequality to ensure their validity, especially in cases involving negative numbers or functions with restricted domains.
When you're working with inequalities, you have to be careful when performing operations like squaring both sides. Unlike equalities, where multiplication or division by the same number on both sides does not change equality, with inequalities, the effect can be more complex due to the direction of the inequality sign and the possibility of dealing with negative numbers.
For instance, squaring both sides of an inequality is not always a valid operation because if one or both sides of the inequality are negative, squaring could lead to incorrect results. When you square a negative number, it becomes positive, which could potentially reverse the inequality's direction. However, if you know that both sides of the inequality are non-negative, then squaring both sides is permissible. This concept is similar to solving quadratic constraints without introducing square roots, using identities like |(1 + ix)²|² = ([1 + ix|²)².
To avoid introducing solutions that were not there originally (extraneous solutions), it is important to check the solutions obtained after squaring against the original inequality. An example where squaring both sides might be questioned is when solving trigonometric inequalities, where a common mistake is to square both sides without considering the domain of the original function.
I need all the answers for question 2 and please explain each step to get the answer, thanks
A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.
Hello : let
A(2,-1) B(8,4)
the slope is : (YB - YA)/(XB -XA)
(4+1)/(8-2) = 5/6
Answer: Equation of line in point slope form,
[tex]y + 1 = 5 ( x - 2 )[/tex]
And, Equation of line in standard form,
[tex]5 x - 6 y = 16[/tex]
Step-by-step explanation:
Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,
Then the equation of line,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]
Thus, the equation of the given line,
[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)
⇒ [tex]6(y+1)= 5(x-2)[/tex]
⇒ 6 y + 6 = 5 x - 10
⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )
⇒ 6 + 10 = 5x - 6y ( By adding 10 on both sides )
⇒ 16 = 5x - 6y
⇒ 5 x - 6 y = 16 ------(2)
Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]
Thus, equation (1) shows the in slope form of the line.
And, standard form of the line is ax + by = c where a, b and c are the integers.
Thus, equation (2) shows the standard form of the given line.
The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. find the first quartile, q1.
The 1st quartile q1 is also called the 25th percentile (the bottom 25% of a data set). In this case, if we choose 100 light bulbs, then the 1st quartile will be the 25 bulbs with shortest useful life.
To solve this problem, we would have to use the z statistic.
Using the standard distribution tables for z, we locate for the value of z at P
= 0.25:
z = - 0.674
Then to calculate for the 1st quartile, we use the
formula:
Q1 = x + z * s
where x is the mean, and s is the standard deviation, therefore:
Q1 = 392 + (- 0.674) (9)
Q1 = 385.934
To find the first quartile of a normal distribution, use the z-score corresponding to an area of 25%. For these lightbulbs with a mean of 392 hours and standard deviation of 9 hours, the first quartile is approximately 386 hours.
Explanation:In statistics, the quartiles of a dataset divide the data into four equal parts. The first quartile, Q1, is the value below which 25% of the data fall. To determine Q1 for the lifetime of a certain type of lightbulb, we use the properties of the normal distribution.
First, realize that 25% of data falls below Q1, and hence using the z-table, we find that z=-0.675 corresponds to an area of 0.25. We then use the formula for a z-score in a normal distribution, z = (X - μ)/σ. Solving for X we find X = z*σ + μ.
Plugging in the known values we get Q1 = -0.675*9 + 392 = 386.025 hours. So, for these lightbulbs, 25% will have failed by around 386 hours.
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what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?
Answer:
The answer is 3 for A P E X
Step-by-step explanation:
Use the given graph to determine the limit, if it exists. A
Find limit as x approaches three from the left of f of x..
What is the factorization of the polynomial below?
x²+12x+27
A. (x+3)(x+9)
B. (x+9)(2x+9)
C. (12x+1)(x+2)
D. (3x+3)(x+9)
A giraffe can run 40 meters per second what is its speed in miles per hour
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.
options for the first blank are: 20.22, 35.08, 50.07, or 100.11
options for the second blank are: 2, 4, 6 or 8
The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
Given :
Flask can be modeled as a combination of a sphere and a cylinder.
The volume of Sphere is given by the:
[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]
Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.
Now, the volume of sphere of radius 2.25 inches will be:
[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]
[tex]\rm V_s = 47.71\; inches^3[/tex]
The volume of Cylinder is given by the:
[tex]V_c = \pi r^2h[/tex]
Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.
Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:
[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]
[tex]\rm V_c = 2.35\; inches^3[/tex]
Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].
Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:
Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches
Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch
Height of cylinder = [tex]3\times 2[/tex] = 6 inches
Now, the volume of sphere when radius is 4.5 inches will be:
[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]
[tex]\rm V_s' = 381.70\; inches ^3[/tex]
And the volume of cylinder when radius is 1 inch and height is 6 inches will be:
[tex]V_c' = \pi \times (1)^2\times 6[/tex]
[tex]\rm V_c'=18.85\;inches^3[/tex]
Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].
Now, divide volume with dilation by theorginal volume of the flask.
[tex]\dfrac{400.55}{50.06}=8[/tex]
Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
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Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2.
Answer:
Sequence 1 is arithmetic and Sequence 2 is geometric.
Solve the system of equations: 2x + 9y = 0 and 3x + 5y = 17.
Which linear inequality is represented by the graph? y ≥ 1/3x – 4 y ≤ 1/3x – 4 y ≤ 1/3x + 4 y ≥ 1/3x + 4
Answer:
[tex]y\leq \frac{1}{3}x-4[/tex]
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line
The slope of the line is positive
The y-intercept of the solid line is equal to [tex]-4[/tex]
therefore
The inequality must be
[tex]y\leq \frac{1}{3}x-4[/tex]
Are rational numbers always, sometimes or never natural numbers?
Answer:
SOMETIMESStep-by-step explanation:
this the picture for my question
Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?
Answer:
[tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Given : Two 6-sided dice are rolled.
To find : what is the probability the sum of the two numbers on the die will be 4.
Solution : We have given
Two 6-sided dice are rolled.
Dice have number { 1,2,3,4,5,6} { 1,2,3,4,5,6} .
[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].
sum of the two numbers on the die will be 4.
Case (1) : first dice rolled 3 and second dice rolled 1.
{3,1}
3 +1 = 4 .
Case (2) : first dice rolled 1 and second dice rolled 3 .
{1,3}
1 + 3 = 4 .
Case (3) : first dice rolled 2 and second dice rolled 2.
{2,2}
2 + 2 = 4.
Then there are 3 possible outcomes where the sum of the two dice is equal to 4.
The number of total possible outcomes = 36.
[tex]Probability =\frac{3}{36}[/tex].
[tex]Probability =\frac{1}{12}[/tex].
Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].
Therefore, [tex]\frac{1}{12}[/tex].
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?
The sum of two rational numbers will always be
Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.
What percentage is the fraction 2/4 equal to?
system of equations with different slopes and different y-intercepts have one solution.
A. Always
B. Sometimes
C. Never
I think it is A but I am not sure and it is impossible for system of equations with different slopes and different y-intercepts to be parallel or infinite.
How could the relationship of the data be classified?
scatter plot with points loosely scattered going down to the right
A positive correlation
A causation
A negative correlation
No correlation
Answer: A negative correlation
Step-by-step explanation:
If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.
With the increase of one quantity or variable there is decrease in the other quantity or variable.
Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.
Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
a. 3in, 4in, 5 in
b. 5in, 6in, 7in
c. 8in, 9in, 12in
From the information, A is a right angle, B is an acute triangle and C is an acute angle.
How to solve the triangleIt will be a right triangle if a² + b² = c². It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².
For the first one,
a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25
This is a right triangle.
For the second one,
a² + b² = 5² + 6²
= 25 + 36 = 61
c² = 7² = 49
61 > 49 = аcute triangle.
For the third one,
a² + b² = 8² + 9²
= 64 + 81 = 145
c² = 12² = 144
145 > 144 = аcute triangle.
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how to write 314,207 in word form
Answer: three hundred fourteen thousand, two hundred seven
explanation for the comma after thousand: I’m used to putting one there because it says 314, not just 314 so I added one. Hope I helped !
A video game club charges a fixed annual membership fee of $18 and $3 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $20 the next year?
Answer:
The correct answer is f(n)=3n+38
Step-by-step explanation:
Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.