Answer:
0.7557
Step-by-step explanation:
In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores
Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)
Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)
You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557
The probability that P(–0.73 < z < 2.27) is 0.7557.
The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation,n= sample\ size\\\\\\[/tex]
From the normal distribution table, P(-0.73 ≤ z ≤ 2.27) = P(z < 2.27) - P(z<-0.73) = 0.9884 - 0.2327 = 0.7557
Find out more at: https://brainly.com/question/7449180
Consider the following system of equations. -10x2-10y2=-300 5x2+5y2=150 Which statement describes why the system has infinite solutions?
Which statement describes why the system has infinite solutions?
The equations represent parabolas that result in graphs that do not intersect.
The equations represent circles that result in graphs that do not intersect.
The equations represent parabolas that result in the same graph.
The equations represent circles that result in the same graph.
Answer:
The equations represent circles that result in the same graph.
Step-by-step explanation:
we have
[tex]-10x^{2}-10y^{2}=-300[/tex]
Divide by -10 both sides
[tex]x^{2}+y^{2}=30[/tex] -----> equation A
This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]
and
[tex]5x^{2}+5y^{2}=150[/tex]
Divide by 5 both sides
[tex]x^{2}+y^{2}=30[/tex] -----> equation B
This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]
equation A and equation B are equal
therefore
The system has infinite solutions, because the equations represent circles that result in the same graph.
A school day starts at 07:15. There are three periods of 40 minutes, four periods of 35 minutes and two periods of 50 minutes. There is a long break of 20 minutes and a short break of 10 minutes. Calculate the time that the school day ends.
Answer:
the school day ends at 1:45
Step-by-step explanation:
7:15 40 x 3 = 120
+2 hours =
9:15 35 x 4 = 140
+2 hours & 20 mins =
11:35 50 x 2 = 100
+1 hour & 40 mins
1:15 20 + 10 = 30
1:45
you're welcome((:
6. Which of the following pairs of numbers contains like fractions?
A.3 1/2 and 4 4/4
B.3/2and 2/3
C.6/7and 1 5/7
D.5/6 and 10/12
Answer:
D.5/6 and 10/12
Step-by-step explanation:
A.3 1/2 and 4 4/4
3 1/2 and 4+1
3 1/2 and 5
not equal
B.3/2and 2/3
2/2 + 1/2 and 2/3
1 1/2 and 2/3
not equal
C.6/7and 1 5/7
6/7 and 1 5/7
not equal
D.5/6 and 10/12
5/6*2/2 and 10/12
10/12 and 10/12
equal
The shortest path from point A to point B goes through a pond. To avoid
the pond, you must walk straight 23 meters along one edge of the pond,
then take a 90-degree turn, and again walk straight 57 meters along
another edge of the pond to reach point B. If you could walk through the
pond, what would be the distance from point A to point B?
Final Answer:
The direct distance from point A to point B, considering a straight path through the pond, is 80 meters. This is obtained by applying the Pythagorean theorem to the right-angled triangle formed by walking 23 meters and then 57 meters along the edges of the pond. Subtracting the initial 23 meters provides the actual direct distance.
Step-by-step explanation:
In this scenario, we can apply the Pythagorean theorem to find the direct distance from point A to point B. Let's denote the sides of the right-angled triangle formed by walking along the edges of the pond as follows: the first leg (along one edge) is \(a = 23\) meters, the second leg (along the other edge) is [tex]\(b = 57\)[/tex] meters, and the hypotenuse (direct distance from A to B, walking through the pond) is (c). According to the Pythagorean theorem, [tex]\(c^2 = a^2 + b^2\).[/tex]
Substituting the given values, we get [tex]\(c^2 = 23^2 + 57^2\).[/tex] Calculating this gives [tex]\(c^2 = 529 + 3249\)[/tex], resulting in [tex]\(c^2 = 3778\)[/tex]. Taking the square root of both sides gives [tex]\(c ≈ \sqrt{3778} ≈ 61.47\)[/tex]. Therefore, the direct distance from point A to point B, walking through the pond, is approximately 61.47 meters.
However, since the question asks for the distance considering walking straight through the pond, we need to add the lengths of both sides of the pond. Thus, [tex]\(61.47 + 23 + 57 = 80\)[/tex]. Therefore, the final answer is 80 meters. This approach considers the direct path, incorporating the lengths of the edges and the hypotenuse, providing the most accurate measurement for the distance from point A to point B.
Which statement can be combined with its converse to form a true biconditional?
A) if the measure of an angle is 30, then it is an acute angle
B) if two lines intersect, then the two lines are not Skew.
C) if the rat is the perpendicular bisector of the segment, then the raid devices segment into two congruent segments.
D) if an angle is a straight angle, then it’s sides are opposite rays.
Statement C can be combined with its converse to form a true biconditional because both statements are true.
Explanation:In order for a statement and its converse to form a true biconditional, both statements must be true. Let's analyze the given statements:
A) If the measure of an angle is 30, then it is an acute angle.
B) If two lines intersect, then the two lines are not skew.
C) If the ray is the perpendicular bisector of the segment, then it divides the segment into two congruent segments.
D) If an angle is a straight angle, then its sides are opposite rays.
Out of these options, statement C can be combined with its converse to form a true biconditional because both statements are true:
If the ray is the perpendicular bisector of the segment, then it divides the segment into two congruent segments.
If the segment is divided into two congruent segments, then the ray is the perpendicular bisector of the segment.
Ana has a rope that is 5 feet long. She divides her rope into 9 equal pieces. What is the length, in feet, of each piece of rope?
Final answer:
When a 5 feet long rope is divided into 9 equal pieces, each piece is approximately 0.56 feet long after performing the division and rounding to the nearest hundredth.
Explanation:
To find the length of each piece of rope when a 5 feet long rope is divided into 9 equal pieces, we need to divide the total length of the rope by the number of pieces. This is a division problem in arithmetic.
Division: 5 feet ÷ 9 pieces = 0.5555... feet per piece.
Since we typically want to represent a length in a more practical way, we can round this number. Rounding to the nearest hundredth, we get approximately 0.56 feet for each piece of rope.
Final answer:
To determine the length of each rope piece when a 5-foot long rope is divided into 9 equal parts, divide the total length by the number of parts, resulting in pieces that are approximately 0.5556 feet long.
Explanation:
To find the length of each piece of rope when a 5-foot long rope is divided into 9 equal pieces, we need to divide the total length of the rope by the number of pieces. Therefore, we use the division:
Length of each piece = Total length of rope ÷ Number of pieces
Length of each piece = 5 feet ÷ 9
Upon doing the division, we find that the length of each piece is approximately 0.5556 feet.
a triangular course for a canoe race is marked with buoys. the first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi. how long is the race?
(the numbers are fractions)
Answer:
1 1/5 mi
Step-by-step explanation:
We need to add the three legs together
3/10 + 1/2 + 2/5
The common denominator is 10
3/10 =3/10
1/2 *5/5 = 5/10
2/5 *2/2 =4/10
3/10 + 5/10+4/10 = 12/10
10/10 = 10/10+2/10 = 1+2/10 = 1 1/5 mi
Answer:
Length of race = 1.2 miles
Step-by-step explanation:
Length of race is given by the perimeter of triangle.
Refer the given figure.
The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi.
[tex]\texttt{Perimeter =}\frac{3}{10}+\frac{1}{2}+\frac{2}{5}=\frac{3}{10}+\frac{5}{10}+\frac{4}{10}=\frac{3+5+4}{10}\\\\\texttt{Perimeter =}\frac{12}{10}=1.2 miles[/tex]
Length of race = 1.2 miles
Find the area of a circle that has a diameter of 11 inches. Approximate Π as 3.14. Round your answer to the nearest hundredth.
A =
in. 2
Answer: 94.99 in^2
Step-by-step explanation: The equation for the area of a circle is A=πr^2. To solve this, we need to find the radius. The diameter is the whole circle, whole the radius is half. So divide the diameter by 2.
11/2 = 5.5
The radius is 5.5 inches. Plug the radius into the equation.
A=π5.5^2
Square the 5.5 first. You will get 30.25.
A=π30.25
Plug in 3.14 for pi.
A=3.14 x 30.25
Multiply.
A=94.985
Round to the nearest hundredth.
A=94.99
The area of the circle is 94.99 in^2.
94.99 in^2
hope this helps somebody
During the worst periods of hyperinflation in a certain country, the price of food increase at a rate of 10% per month. State whether this increases was linear or exponential. If your food bill was 100 in one month during this period, what was it three months later?
Answer:
The increase was exponential
After three months his expense was: $133.1
Step-by-step explanation:
The increase was exponential, because if we call x the initial price, then after the first month the new price p is:
[tex]p = x (1 + \frac{10\%}{100\%})\\\\p=x(1+0.1)[/tex]
After the second month, the new price is 10% of the price of the previous month, that is:
[tex]p = [x (1 + 0.1)](1 + 0.1)\\\\p = x (1 + 0.1) ^ 2[/tex]
After month n, the price is:
[tex]p = x (1 + 0.1) ^ n[/tex]
Note that the equation has the form of an exponential growth function, where x is the initial price and n is the number of months elapsed.
In this case [tex]x = 100[/tex] and [tex]n = 3[/tex]. So:
[tex]p = 100 (1 + 0.1) ^ 3\\\\p=\$133.1[/tex]
In set-builder notation, how do you write the solutions of 2x − 7 ≥ 11?
Answer:
{ x ∈ R | x ≥ 9 }
Step-by-step explanation:
we have
[tex]2x-7 \geq 11[/tex]
solve for x
Adds 7 both sides
[tex]2x\geq 11+7[/tex]
[tex]2x\geq 18[/tex]
Divide by 2 both sides
[tex]x\geq 18/2[/tex]
[tex]x\geq 9[/tex]
The solution is the interval -----> [9,∞)
In set builder notation
{ x ∈ R | x ≥ 9 }
All real numbers greater than or equal to 9
What is the y-intercept of the function,represented by the table of values below?
Answer:
So the y-intercept is 10.
Step-by-step explanation:
So your table doesn't out right say the y-intercept. If it did it would be (x=0,y=something).
So let's see if this is linear. I'm going to see if we have the same rise/run ratio per pair of points as shown in the attachment:
These ratios are all the same -6/3 = -2/1 = -4/2 = -6/3 . These are all equal to -2.
So this is a line.
Linear equations in the form y=mx+b is called slope-intercept form where m is the slope and b is the y-intercept.
We just found m to be -2.
So our equation is now in the form y=-2x+b.
We can find b, the y-intercept, by using a point on this line. I like (4,2) from the table.
(x,y)=(4,2) with y=-2x+b will give us the information we need to find b.
2=-2(4)+b
2=-8+b
2+8=b
10=b
b=10
So the y-intercept is 10.
What is the median of this set of data values?
10, 14, 15, 17, 20, 21, 22, 25
Answer:
18,5
Step-by-step explanation:
middle numbers --> (17+20)/2 = 18,5
Thanks for submitting your question to Brainly!
Answer: 18.5
Step-by-step explanation:
Step 1) To find the median in a set of data values you must first arrange them from least greatest to greatest. Luckily, it's already done for you!
Step 2) Then, take the two middle numbers (17 and 20) and add them.
17+20 = 37
Step 3) Now, just divide by two
37/2 = 18.5
Let me know if you have any more questions!
Which only lists multiples of 16? 1, 2, 4, 8, 16 16, 24, 32, 40 16, 32, 48, 64 1, 2, 4, 8, 12, 16
Answer:
16, 32, 48, 64
Step-by-step explanation:
Factors of a number are the numbers another number can be divided by. Multiples are numbers that can be divided by a number. Therefore, all the numbers in the list consist of 16 X 1, 16 X 2, 16 X 3, and so on.
The multiple of 16 is,
The multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, etc.
Multiple numbers:
It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive multiples or products, is equal to 16. In simple words, multiples of a number are the products obtained by multiplying the given number by other natural numbers.
So, the required lists are,
16,32,48 and 64.
Learn more about the topic multiples of the number:
https://brainly.com/question/413590
Describe the translation. y=(x+3)2+4 → y=(x+1)2+6
Answer:
Shift +2 units to the right and +2 units up
Step-by-step explanation:
y = (x+3)² + 4 has a horizontal shift of -3 and a vertical shift of +4.
y = (x+1)² + 6 has a horizontal shift of -1 and a vertical shift of +6.
So do translate the first equation to the second, shift +2 units to the right and +2 units up.
The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
Answer:
=11.155 in³
Step-by-step explanation:
Given data:
Radius= 1.75 inches
Height = 3.5 inches
Diameter= 0.5 inches
To find the volume of a cone we will apply the formula:
Volume of a cone = 1/3 πr²h
Substitute the values:
V= 1/3* 3.14 *(1.75)² * 3.5
V=1/3 *3.14*(3.0625)* 3.5
V= 33.66/3
V=11.22 in³
Now find the volume of the bubble gum:
Volume of bubble gum = 4/3 π*r³
Substitute the values:
V= 4/3*3.14*(0.5/2)³
V=4/3*3.14(0.25)³
V=4/3*3.14(0.015625)
V=0.19625/3
V=0.0654 in³
Now subtract the volume of bubble gum ball from the volume of a cone
=11.22 - 0.0654
=11.155 in³
Thus the closest approximation of the volume of the cone that can be filled with flavored ice is 11.155 in³....
Answer:
11.15 in³
Step-by-step explanation:
Solve this equation for x. Round your answer to the nearest hundredth. 0.75=logx
Answer:
Step-by-step explanation:
[tex]10^.^7^5=10^l^o^g^(^x^)\\=10^.^7^5=x\\=10^\frac{3}{4}=\sqrt[4]{10^3} =\sqrt[4]{1000} =5.6=x[/tex]
To solve the equation 0.75 = log(x), we exponentiate both sides with base 10, resulting in x = 10^0.75. The calculated value of x to the nearest hundredth is approximately 5.62.
Explanation:To solve the equation 0.75 = log(x), we need to understand that the logarithm function here is the common logarithm, which means it has a base of 10. The equation essentially states that 10 raised to the power of 0.75 equals x. To find x, we simply need to perform the inverse operation of taking the logarithm, which in this case is exponentiation.
We use the fact that if logb(a) = c, then bc = a, where b is the base, a is the result, and c is the exponent. Therefore, we can rewrite our original equation as:
x = 100.75
Using a calculator, we can find that:
x ≈ 5.62
This is the value of x, rounded to the nearest hundredth, as the question requested.
The results of a survey of customers at a pet supply store showed 36 owned mice, 32 owned parrots, and 14 owned both mice and parrots. How many owned either a mouse or a parrot?
54 people owned either a mouse or a parrot
Venn diagramA Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Number of people that owned only mice = 36 - 14 = 22
Number of people that owned only parrot = 32 - 14 = 18
Number of people that owned either a mouse or a parrot = 22 + 18 + 14 = 54
54 people owned either a mouse or a parrot
Find out more on Venn diagram at: https://brainly.com/question/2099071
By using the principle of inclusion-exclusion to find the total number of pet store customers who owned either a mouse or a parrot, we calculated that 54 customers owned at least one of the pets, taking into account that 14 customers owned both.
Explanation:To determine the total number of store customers who owned either a mouse or a parrot, we need to apply the principle of inclusion-exclusion. This principle allows us to find the union of two sets without counting elements (customers) that are common to both sets more than once. The formula is ∑(A ∪ B) = ∑(A) + ∑(B) - ∑(A ∩ B), where ∑ denotes the number of elements in a set, A represents the group of mouse owners, B represents the group of parrot owners, and A ∩ B represents the group that owns both mice and parrots.
Applying this to our situation:
∑(A) = 36 (mouse owners)∑(B) = 32 (parrot owners)∑(A ∩ B) = 14 (owners of both mice and parrots)Using the principle of inclusion-exclusion:
∑(A ∪ B) = 36 + 32 - 14 = 54
This means that 54 customers owned either a mouse or a parrot or both.
if trapezoid JKLM is translated according to the rule (x, y) -> (x + 8, y - 3), what are the coordinates of point L'?
A. (1, -5)
B. (-10, 6)
C. (-5, 3)
D. (6, -8)
Answer:
D.
Step-by-step explanation:
First step: Identify the point for L.
L is at (-2,-5).
We are plugging this (x,y) into (x+8,y-3) to see where it takes us.
(-2+8,-5-3)=(6,-8).
The solution is D.
Answer: OPTION D
Step-by-step explanation:
You can observe in the figure that the coordinates of the point L are:
[tex]L(-2,-5)[/tex]
You know that the trapezoid rule applied for the translation of the trapezoid JKLM is:
[tex](x, y)[/tex]→[tex](x + 8, y - 3)[/tex]
Therefore, in order to find the coordinates of the point L', you need to add 8 to the x-coordinate of the point L and subtract 3 from the y-coordinate of the point L.
Then:
[tex]L'(-2 + 8, -5 - 3)\\\\L'(6,-8)[/tex]
What is the equation of the line graphed below?
Answer:
The equation is y = 2x. The slope is two and the line is a direct variation
Only the function represented by graph has an inverse function.
Answer:
Only the function represented by graph 2 has an inverse function
Step-by-step explanation:
* Lets explain the inverse of the function
- The Function is a relation between x-coordinates and the y-
coordinates of the order pairs under the condition every
x-coordinate has only one y-coordinate
- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-
coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,
(2 , 5)} not a function because the x-coordinate 2 has two y-
coordinates 3 and 5
- We use the vertical line to test the graph is function or not, if
the vertical line intersects the graph in one point then the
graph is function if intersects it in more than one point then the
graph is not function
- We have two types of function one-to-one function and
many-to-one function
# one-to-one function means every x-coordinate has only 1 y-coordinate
# many-to-one function means some x-coordinates have only 1
y-coordinate
- We find the inverse function by switching x and y, then one-to-
one function has inverse but many-to-one has not inverse
because when we switched x and y it will be one-to-many
means one x-coordinate has many y-coordinates and this is not
a function
- We use the horizontal line to test the graph of the function has
inverse or not, if the horizontal line intersects the graph in one
point then the function of the graph has inverse if it intersects
the graph in more than one point ,then the function of the
graph has no inverse
* Now lets test all the graphs by using the horizontal line
# graph 1
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 1 has no inverse
# graph 2
∵ The horizontal line cuts the graph in just 1 point
∴ The function of graph 2 has inverse
# graph 3
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 3 has no inverse
# graph 4
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 4 has no inverse
* Only the function represented by graph 2 has an inverse function
Suppose a triangle has sides a, b, and c, and that a2 + b2 < c. Let o be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
Step-by-step explanation:
if a^2 +b^2 <c^2,
then abc is not a right triangle since for a right triangle a^2+ b^2 = c^2
The following features of the triangle are found: A. a² + b² - c² = 2 · a · b · cos θ, B. cos θ < 0, C. The triangle is not a right triangle.
How to analyze the features of a triangle
In this question we must infer all features from a triangle such that a² + b² < c². Then, the triangle is not a right triangles since relationship between side lengths is different from the relationship described by Pythagorean theorem. Then, triangle is described by law of cosine:
a² + b² - c² = 2 · a · b · cos θ
If a² + b² < c², then a² + b² - c² < 0 and 2 · a · b · cos θ < 0. Thus, we get the following result: cos θ < 0.
help please can’t find the answer
Answer:
[tex]\large\boxed{V=99\pi}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have 2r = 6 → r = 3, H = 11.
Substitute:
[tex]V=\pi(3^2)(11)=99\pi[/tex]
veronica takes 1/3 of an hour to write 1/4 of a page of
calligraphy. how long will it take veronica to write one page?
Answer:
4/3 hours or 1 hour 20 minutes.
Step-by-step explanation:
1/4 page takes 1/3 hour to write.
By proportion 1 page will take 1/3 / 1/4
= 1/3 * 4
= 4/3 hours.
Answer:
[tex]1\frac{1}{3}\text{ hours}[/tex]
Step-by-step explanation:
Given,
Time taken to write 1/4 of a page = [tex]\frac{1}{3}[/tex] hour,
i.e. the ratio of time taken and number of pages wrote = [tex]\frac{1/3}{1/4}=\frac{4}{3}[/tex]
Let x be the time taken to write a full page,
So, the ratio of time taken( in hours ) and page wrote = [tex]\frac{x}{1}[/tex]
[tex]\implies \frac{x}{1}=\frac{4}{3}[/tex]
[tex]x=1\frac{1}{3}[/tex]
Hence, the time taken to write 1 page is [tex]1\frac{1}{3}[/tex] hours.
In a survey of more than 4000 people, 91% of
the respondents claimed to prefer Pedro's
Perfect Pizza over any other brand of pizza.
Answer: people who have had Pedro’s perfect pizza delivered to their house in the last month
Step-by-step explanation:
I guessed and got lucky lol
What is the simple interest on rs 650 for 14 weeks at 6% per annum
Answer:
rs 10.5 .
Step-by-step explanation:
Simple Interest = PRT/100 where P = sum invested, R = the rate per annum, T = the time in years.
14 weeks = 14/52 years so it is:
650* 6 * (14/52) / 100
= rs 10.5.
Answer:
10.50
Step-by-step explanation:
The simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex]
where P is the principal ( amount deposited), R is the rate of interest and T the time in years.
note that 14 weeks = [tex]\frac{14}{52}[/tex] of a year, hence
I = [tex]\frac{650(6)}{100}[/tex] × [tex]\frac{14}{52}[/tex]
= [tex]\frac{650(6)(14)}{100(52)}[/tex]
= [tex]\frac{54600}{5200}[/tex] = 10.50
What is the y-intercept of the line perpendicular to the line y = 4/3x + 1 that includes the point (4, 1)?
[tex]\bf y=\stackrel{\downarrow }{\cfrac{4}{3}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}[/tex]
so then, we know this line has a slope of -3/4 and runs through (4 , 1)
[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies -\cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-\cfrac{3}{4}(x-4)\implies y-1=-\cfrac{3}{4}x+3[/tex]
[tex]\bf y=-\cfrac{3}{4}x\stackrel{\downarrow }{+4}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{y-intercept}}{(0,4)}[/tex]
. Let A = {x: x ϵ R, x2 – 5x + 6 = 0 } and B = { x: x ϵ R, x2 = 9}. Find A intersection B and A union B
[tex]x^2 – 5x + 6 = 0\\x^2-2x-3x+6=0\\x(x-2)-3(x-2)=0\\(x-3)(x-2)=0\\x=3 \vee x=2\\A=\{-2,3\}\\\\x^2=9\\x=-3 \vee x=3\\B=\{-3,3\}\\\\A\cap B=\{3\}\\A\cup B=\{-3,-2,3\}[/tex]
In one store, bananas cost 60 cents per pound. The cost, in dollars, of x pounds of bananas is 0.6x. What is the cost of 2.50 pounds of bananas?
Final answer:
The cost of 2.50 pounds of bananas is 1.50 dollars.
Explanation:
To find the cost of 2.50 pounds of bananas, we need to multiply the weight of the bananas by the cost per pound. In this case, the cost per pound is 60 cents.In the store, bananas cost 60 cents per pound, and the cost in dollars for x pounds of bananas is given by the equation 0.6x. To find the cost of 2.50 pounds of bananas, you simply substitute x with 2.50 in the equation: 0.6 times 2.50. So, we multiply 2.50 pounds by 0.60 dollars per pound:
2.50 pounds x 0.60 dollars/pound = 1.50 dollars.
Therefore, the cost of 2.50 pounds of bananas is 1.50 dollars.
What of b make y = 2x plus b the same as y=2x? What does that value mean?
Pls answer:)
Answer:
No
Step-by-step explanation:
The short answer is no. b stands for some number. Once that number is fixed, it does not change. So the equation would look something like
y = 2x + 6 Now if you look at that again, that 6 is fixed.
If you want to put something in for x like x = 5 you get
y = 2(5) + 6
y = 10 + 6
y = 16 b = 6 did not change.
What does y = 2x equal
y = 2*5
y = 10
10 does not equal 16.
The only exception to what I've written is b = 0. Then both equations mean the same thing. But that is an exception.
1. Write the standard equation for a circle that has a center of (-5.-2) and a radius of 25.
Answer:
[tex](x+5)^2+(y+2)^2=625[/tex]
Step-by-step explanation:
The center-radius form a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. Okay, it is called standard form. But I like to call it center-radius form because it tells us the center (h,k) and the radius,r.
So we are given the following information r=25 and center=(h,k)=(-5,-2).
So we just plug this in like so:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x--5)^2+(y--2)^2=25^2[/tex]
[tex](x+5)^2+(y+2)^2=625[/tex]