Identify the slope and y-intercept.
y=2x−8
Enter your answers in the boxes in simplest form.
M=
B=
Identify the converse of the following conditional:
If a point is in the fourth quadrant, then its coordinates are negative.
A. If a point is in the fourth quadrant, then its coordinates are negative.
B. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
C. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
D. If the coordinates of a point are negative, then the point is in the fourth quadrant.
How many pounds does 64 ounces weigh?
Answer:
4 lbs
Step-by-step explanation:
There are 16 ounces in a pound, so divide 64 by 16 to get the number of pounds. 64 ÷ 16 = 4 lbs
Solve the equation.
–2 3/7 + b = 6 1/7
A.
b = 3 5/7
B.
b = 4 2/7
C.
b = 8 2/7
D.
b = 8 4/7
How to simplify and expression by combining like terms?
Need help ASAP
Will upvote!
I think it's A but i'm not sure
Lines A and B are represented by the equations given below:
Line A: x + 2y = 3
Line B: x + y = 3
Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round to the nearest integer).
FIRST GRAPH
A) 20 units^2
B) 30 units^2
C) 40 units^2
D) 50 units^2
A quadrilateral has angles that measure 74°, 93°, and 117°.
Six different written driving tests are administered by the Motor Vehicle Department. One of these six tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
(b) What is the probability that the two women will take the same test?
To find the probability that exactly two of the five will take the same test, we use combinations. The probability is 2/3 or 0.667. To find the probability that the two women will take the same test, we use combinations. The probability is 1/2 or 0.500.
To find the probability that exactly two of the five will take the same test, we can use the concept of combinations. There are six different tests, and we need to choose two of them to be taken by two people. The total number of ways to select two tests out of six is given by the combination formula C(6,2) = 6!/(2!(6-2)!) = 15. Now, for each of these two selected tests, there are two people (either two men or two women) who can take the test, resulting in a total of two possibilities. Therefore, the number of favorable outcomes is 2 * 15 = 30. Finally, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 6!/(2!3!) = 15. So the probability is 30/15 = 2/3 or 0.667 (rounded to three decimal places).
To find the probability that the two women will take the same test, we can use similar reasoning. There are six different tests, and we need to choose one of them to be taken by both women. The total number of ways to choose one test out of six is given by the combination formula C(6,1) = 6!/1!(6-1)! = 6. Now, for the chosen test, there are three possible ways both women can take it, since they can be the first two applicants, the last two applicants, or the middle two applicants. Therefore, the number of favorable outcomes is 3. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is also 6. So the probability is 3/6 = 1/2 or 0.500 (rounded to three decimal places).
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Final answer:
The probability that exactly two of the five will take the same test is 0.00463. The probability that the two women will take the same test is 1.167.
Explanation:
To find the probability that exactly two of the five will take the same test, we can use combinations. There are 6 different tests and we want to select 2 of them for the same test. Since order doesn't matter, we can use combinations. The number of ways to choose 2 tests out of 6 is 6 choose 2 = 15.
Now, for each pair of tests, we have 5 people who can take those tests. The probability that exactly 2 of the five will take the same test is the probability that exactly 2 people are randomly assigned to the same test out of the 5 people. The total number of possible outcomes is 6^5 since each person has 6 choices for which test to take, and there are 5 people.
So, the probability that exactly two of the five will take the same test is 15/6^5, which is approximately 0.00463.
To find the probability that the two women will take the same test, we consider the different possibilities. The two women can take the same test out of the 6 tests, or they can take different tests.
If they take the same test, there are 5 possible tests for them to choose from. The probability of this happening is 5/6.
If they take different tests, there are 5 possible tests for each of them to choose from. The probability of this happening is (5/6) * (4/5) = 2/3.
Therefore, the probability that the two women will take the same test is (5/6) + (2/3) = 7/6, which is approximately 1.167.
Sara tells Michael she is 160 centimeters tall, while Michael says he is 60 inches tall. If there
are 2.54 centimeters in an inch, who is taller?
x + 2 > -8
a. x > -6
b. x > -10
c. x <-10
d. x < -6
Which input value produces the same output value for the two functions on the graph?
x = -3
x = -2
x = -1
x = 3
What is the formula that relates circumference and radius?
A. C = 2r
B. C = 2/r
C. C = 2D
D. C + 2 = r
Answer:
The formula that relates circumference and radius is [tex]C=2\pi r[/tex].
Step-by-step explanation:
The circumference of a circle is calculated by the formula
[tex]C=2\pi r[/tex]
Where,
C is circumference of the circle.
r is radius of the circle.
π is 22/7 or 3.14.
In the given options π is not missing. So, all the given options are incorrect.
Therefore the formula that relates circumference and radius is [tex]C=2\pi r[/tex].
Word Problem help please
1. The magician said "The average of seven numbers is 49. If 1 is added to the fisr number, 2 is added to the second number, 3 is added to the third number and so on up to seventh number". what is the new average ? ...?
Rate of Change , you are given the dollar value of a product in 2004 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value (v) of the product in terms of the year
(Let t=0 represent 2000.)
2004 value= $156 with $4.50 increase per year
...?
Answer:
The linear equation is v = 4.5t +138
The product had value of $138 in 2000.
Step-by-step explanation:
In 2004, dollar value(v) = $156 and rate of change (m) = $4.50
The linear equation is in the form of y = mx + b, where "m" is slope or rate of change, b is the y-intercept.
We can rewrite the equation as v = m(t) + b.
Now let's find the value of b, when t = 4, m = 4.5, v = 156
156 = 4.5(4) + b
b = 156 - 4.5(4)
b = 156 - 18
b = 138
So, the linear equation is v = 4.5t +138
When t=0, the dollar value (v) = 4.5(0) + 138
v = $138
So, the product had value of $138 in 2000
11 less than the product of a number y and -2 is z
You estimate that a baby pig weighs 20 pounds. The actual weight of the baby pig is 16 pounds. Find the percent error.
Answer:
It's mainly 25% as the percent error.
Step-by-step explanation:
what is the correct expansion of the binomial (x+y)^5
Answer: The correct expansion is,
[tex]x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Step-by-step explanation:
Since, by the binomial expansion,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r}(q)^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, p = x and q = y and n = 5,
By substituting values,
[tex](x+y)^5=\sum_{r=0}^{5} ^5C_r (x)^{n-r}(y)^r[/tex]
[tex] =^5C_0(x)^{5-0}(y)^0+^5C_1 (x)^{5-1}(y)^1+^5C_2 (x)^{5-2}(y)^2+^5C_3 (x)^{5-3}(y)^3+^5C_4 (x)^{5-4}(y)^4+^5C_5(x)^{5-5}(y)^{5}[/tex]
[tex]=1(x)^5(y)^0+\frac{5!}{4!(5-4)!}x^4y^1+\frac{5!}{3!(5-3)!}x^3y^2+\frac{5!}{2!(5-2)!}x^2y^3+\frac{5!}{1!(5-1)!}xy^4+\frac{5!}{5!(5-5)!}x^0y^5[/tex]
[tex]=x^5+\frac{5!}{4!1!}x^4y^1+\frac{5!}{3!2!}x^3y^2+\frac{5!}{2!3!}x^2y^3+\frac{5!}{1!4!}x^1y^4+\frac{5!}{5!0!}x^0y^5[/tex]
[tex]=x^5+\frac{5\times 4!}{4!}x^4y^1+\frac{5\times 4\times 3!}{3!2!}x^3y^2+\frac{5\times 4\times 3!}{2!3!}x^2y^3+\frac{5\times 4!}{4!}x^1y^4+\frac{5!}{5!}y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Which is the required expansion.
Enter the slope-intercept equation of the line that has slope -6 and y-intercept (0, 2).
The slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, the line that has slope -6 and y-intercept (0, 2).
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
Here, m=-6 and c=2
Substitute m=-6 and c=2 in y=mx+c, we get
y=-6x+2
Therefore, the slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
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mx+4y=3t, Solve for the value of x
To solve mx+4y=3t for x, subtract 4y from both sides to isolate the x term, giving mx = 3t - 4y. Then, divide both sides by m to solve for x, resulting in x = (3t - 4y) / m.
Explanation:To solve the equation mx+4y=3t for the value of x, follow these steps:
First, isolate the x term by moving the 4y to the other side of the equation. This gives us:mx = 3t - 4yNext, divide both sides of the equation by m to solve for x:x = (3t - 4y) / mYou can now plug in the known values for y, t, and m to find the value of x.
Ahmed is taking orders for lunch. A slice of pizza cost $2 and a chicken sandwich costs $3. He collects $24 for the group of 10 people.How many people ordered a chicken sandwich?
1.5x+2.5y=21.50
x+y=9
8 people ordered chicken sandwich
A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.
Height of water in hexagonal prism vase = 384 inches, given equal volume of water and wet portion.
Let's denote the height of the water in the vase as [tex]\( h \)[/tex] inches.
The volume of a hexagonal prism can be calculated using the formula:
[tex]\[ V = \frac{3\sqrt{3}}{2}a^2h \][/tex]
where [tex]\( a \)[/tex] is the length of one side of the hexagon (which represents the base of the prism), and [tex]\( h \)[/tex] is the height of the prism.
Since the base of the vase is a hexagon, we need to find the side length of this hexagon.
The area of a regular hexagon can be calculated using the formula:
[tex]\[ A = \frac{3\sqrt{3}}{2}a^2 \][/tex]
Given that the volume of water in the vase is 512 cubic inches, and the wet portion's volume and its height are equal, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2h \][/tex]
We are also given that the wet portion's volume is numerically equal to its height, so:
[tex]\[ h = 512 \][/tex]
Substituting this value of [tex]\( h \)[/tex] into the volume equation, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2(512) \][/tex]
Now, we can solve for [tex]\( a \).[/tex]
[tex]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{2}{3\sqrt{3}} \]\[ a^2 = \frac{2\sqrt{3}}{9} \]\[ a = \sqrt{\frac{2\sqrt{3}}{9}} \]\[ a = \frac{\sqrt{2\sqrt{3}}}{3} \][/tex]
Now, let's find the height of the water by substituting the value of [tex]\( a \)[/tex]into the volume equation:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{\sqrt{2\sqrt{3}}}{3}\right)^2h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{4}{3}h \]\[ h = \frac{512 \times 3}{4} \]\[ h = 384 \][/tex]
So, the height of the water in the vase is 384 inches.
Jarek buys jerseys for his team online. He pays a constant shipping price plus a special rate for each jersey. During the spring season, Jarek paid $151 for 24 jerseys. In the summer season, he paid $79 for 12 jerseys. What is the special rate Jarek pays for each jersey and how much does he pay for shipping?
Thanks to anyone who can help!
Suppose you deposited $10 into your savings account each month, as indicated in the table. Your account pays 4%, compounded monthly. How much will you have in your account at the end of 15 years? a. $2,908 c. $3,668 b. $2,461 d. $1,800 Please select the best answer from the choices provided
What is the resulting ordered pair if the value of the independent variable is x=-3?f(x) = –2x-3
Find the measure of
Jeremiah has a batting average of 0.312 this baseball season. Express his average as a fraction in lowest terms.
Am I able to evaluate sin(cos^1(7/11)) without a calculator? If yes, how? ...?
Yes, you can evaluate sin(cos^-1(7/11)) without a calculator. The result can be simplified to √(72/121).
Explanation:Yes, you can evaluate sin(cos-1(7/11)) without a calculator. Let's break it down step by step:
cos-1(7/11) represents the inverse cosine of 7/11. Inverse cosine is the angle whose cosine is equal to the given value. So, cos-1(7/11) is the angle whose cosine is 7/11.To evaluate sin(cos-1(7/11)), we need to find the sine of the angle we found in the previous step.Since we know that sin2(θ) + cos2(θ) = 1, we can use this relationship to find sin(θ) when we know cos(θ).Let's assume the angle we found in step 1 is θ. We know that cos(θ) = 7/11, so we can substitute this value into the equation sin2(θ) + (7/11)2 = 1 and solve for sin(θ).By solving the equation, we find that sin(θ) = √(1 - (7/11)2).Finally, we can simplify the expression sin(θ) = √(1 - (49/121)) or sin(θ) = √(72/121).Therefore, sin(cos-1(7/11)) can be evaluated as √(72/121).
-2i over 1+i ... help :(
What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?