9514 1404 393
Answer:
C. x -2y = 8
Step-by-step explanation:
One way you can do this is to use the form ...
(Δy)(x -x1) -(Δx)(y -y1) = 0
where Δx = x2 -x1 = 4 -2 = 2, and Δy = y2 -y1 = -2 -(-3) = 1
This gives ...
(x -2) -2(y -(-3)) = 0 . . . above form with numbers filled in
x -2y -8 = 0 . . . . . . . general form
x -2y = 8 . . . . . . . . . standard form
_____
Additional comment
You can use any of several other strategies, including finding the slope and y-intercept, then rearranging the equation.
Another strategy that works is to try the answer choices. You might notice that the first given point works in the first equation, so it may make sense to try the second given point in each equation.
The above version of the equation of a line is a variation on one that says the slope of a line is the same everywhere:
[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y-y_1}{x-x_1}\ \Rightarrow\ (y_2-y_1)(x-x_1)=(x_2-x_1)(y-y_1)\\\\(y_2-y_1)(x-x_1)-(x_2-x_1)(y-y_1)=0[/tex]
A professor of statistics at NCSU refutes the claim that the average student spends 3 hours studying for the midterm exam. Which hypothesis is used to test the claim?
A. H_0: μ < = 3 vs. H_1: μ > 3
B. H_0: μ = 3 vs. H_1: μ ≠ 3
C. H_0: μ ≠ 3 vs. H_1: μ = 3
D. H_0: μ > = 3 vs. H_1: μ < 3
Answer:
D. H_0: μ > = 3 vs. H_1: μ < 3
Step-by-step explanation:
A professor of statistics at NCSU refutes the claim that the average student spends 3 hours studying for the midterm exam.
The claim is that the average student spends 3 hours studying, so the null hypothesis is that the mean is at least 3, that is:
[tex]H_0: \mu \geq 3[/tex]
At the alternative hypothesis, we test if the mean is less than 3, so:
[tex]H_1: \mu < 3[/tex]
This means that the correct answer is given by option D.
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1 : 4, and the ratio of y to z is 4 : 5. What is the value of y?
A. 4
B. 8
C. 10
D. 20
Answer:
x：y：z
1：4
4：5
-------------
1：4：5
-------------
let a:b:c＝k:4k:5k
k+4k+5k=50
10k=50
k=5
y=4(5)
=20(D)
Answer:
D. 20
Step-by-step explanation:
x:y:z
1:4:5
1+4+5=10
50÷10=5
1=5
4=?
4=4×5
=20
You are the owner of a local fast food restaurant and you want to test whether your average number of customers per day is less than 500. You take a sample of 25 days and find that the average for these days is 480. You have been told by the corporate office that the population standard deviation of the number of customers is 95. What is the p-value for a hypothesis test at a 5% significance level
Answer:
The correct answer is "-1.05".
Step-by-step explanation:
Given that,
Sample size,
n = 25
Sample mean,
[tex]\bar X=480[/tex]
Population standard deviation,
[tex]\sigma=95[/tex]
Null hypothesis,
[tex]H_0:\mu=500[/tex]
Alternate hypothesis,
[tex]H_0:\mu>500[/tex]
Then,
The p-value will be:
⇒ [tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
By putting the values, we get
⇒ [tex]=\frac{480-500}{\frac{95}{\sqrt{25} } }[/tex]
⇒ [tex]=-\frac{100}{95}[/tex]
⇒ [tex]=-1.05[/tex]
29 members in math club, treasury has $364 to spend, shirts are $11 caps are $14. How many caps and shirts can he buy to exhaust the funds available?
Answer:
14 shirts, 15 caps
Step-by-step explanation:
15 x 14 = 210$
14 × = 154$
210+154 = 364$
The base of a solid right pyramid is a square with an
edge length of n units. The height of the pyramid is n
1 units
Which expression represents the volume of the
pyramid?
VA
on(n-1) units
on(n-1)2 units
or’n - 1) units
on*(n − 1) units
(n-1)
n
Answer:
C
Step-by-step explanation:
Base area = n^2
V = (base area * height)/3 = (n^2 *(n-1)/3 = 1/3n^2(n-1)
The expression for the volume of pyramid is V = ( 1/3 )n² ( n - 1 ) units³
What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
Let the base edge length of the solid pyramid be = n units
So , the base area of the pyramid = n² units²
Let the height of the pyramid be = ( n - 1 ) units
And , Volume of Pyramid = ( 1/3 )a²H
On simplifying , we get
V = ( 1/3 ) n² ( n - 1 ) units³
Hence , the expression is V = ( 1/3 ) n² ( n - 1 ) units³
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The area of a square rug is 64 ft.² what is the perimeter of the rug?
Answer:
[tex]32[/tex][tex] {ft}^{2} [/tex]
Step-by-step explanation:
The area of a square rug = 64 ft²
First we will find the side of square rug = [tex] {64}^{2} = {s}^{2} [/tex]
[tex] {s}^{2} = 8 [/tex]
Perimeter of the rug = [tex]4 \times 8 [/tex][tex] = 32[/tex]ft²
Hope it is helpful...PLEASE ANSWER!! Find EF using Pythagorean theorem. Express answer to one decimal place.
Answer:
115.5 cm
Step-by-step explanation:
A^2 + B^2 = C^2
41^2 + 108^2 = C^2
C^2 = 13345
C = 115.5 cm
Which expression is modeled by this arrangement of tiles? 1-1-1-1-1-1 ---- K V ----1-1-1-12 ET -1-1-1-1 1 183 -2-2
Answer:
b is correct (-16 by 2)
Step-by-step explanation:
7 more than 3 multiplied by x algebraic expression
Answer:
3x + 7
Step-by-step explanation:
Find the exact value of tan A in simplest radical form
Answer:
tan A = 4 / 7
Step-by-step explanation:
tan A = opp side / adjacent side
tan A = 4 / 7
A student claims that they can use rules about the coordinates of point A to tell wether the cosine of the angle formed by the x-axis and the kind that connects the origin to point A will equal a positive or a negative value. Which of the following statements supports the student’s claim?
A) if the y-coordinate is positive, the cosine will equal a positive charge.
B) if the x-coordinate are negative, the cosine will equal a negative value.
C) if the x-coordinate is in Quadrant l, the cosine will equal a negative value.
D) if the x- and y-coordinates are negative, the cosine will equal a positive value.
9514 1404 393
Answer:
B) if the x-coordinate is negative, the cosine will equal a negative value
Step-by-step explanation:
The cosine of the angle is the x-coordinate of the point where the terminal ray intersects the unit circle. Its sign will match the sign of the coordinates of point A on the terminal ray.
if the x-coordinate is negative, the cosine will be negative
5.- Si en un gallinero contamos los picos, las crestas y las patas obtenemos 144, ¿Cuántas gallinas hay? Utiliza una
expresión algebraica.
Answer:
En total hay 36 gallinas en el gallinero.
Step-by-step explanation:
Dado que si en un gallinero contamos los picos, las crestas y las patas obtenemos 144, para determinar cuántas gallinas hay sabiendo que cada gallina tiene un pico, una cresta y dos patas, se debe realizar el siguiente cálculo:
X + X + 2X = 144
4X = 144
X = 144 / 4
X = 36
Por lo tanto, en total hay 36 gallinas en el gallinero.
The average weight of a particular box of crackers is 37.0 ounces with a standard deviation of 0.5 ounce. The weights of the boxes are normally distributed.
What percent of the boxes weigh more than 36.0 ounces?
What percent of the boxes weigh less than 36.5 ounces?
PLEASE HURRY i need an answer now please help
Answer:
2 hours
Step-by-step explanation:
10/50 * 10 = 2
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
4
Answer:
x = 2√2
Step-by-step explanation:
Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.
Now, since we see that it is also a right angled triangle, it means one angle is 90°.
Let the equal angles be a.
Thus;
a + a + 90 = 180 (since sum of angles in a triangle is 180)
2a + 90 = 180
2a = 180 - 90
2a = 90
a = 90/2
a = 45°
Now, using sine rule, we can find x. Thus;
x/sin 45 = 4/sin 90
sin 90 = 1
sin 45 = 1/√2
Thus;
x = (4 × 1/√2)/1
x = 4/√2
Let's rationalize the denominator to get;
x = (4/√2) × √2/√2
x = (4√2)/2
x = 2√2
Steven earns extra money babysitting. He charges $35.00 for 4 hours and $70.00 for 8
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
The equation is y =
Answer:
Step-by-step explanation:
35/4 = 8.75
70/8 = 8.75
x= 1 (hour) y = 8.75$
Answer:
y= 35x/4
Step-by-step explanation:
We can solve this by plotting a graph of these values of (4,35) and (8,70). We find that this graph is a straight line. Meaning we can solve it in the form Y = mx, where m is the gradient. there is no y intercept as our range is greater than x =0. So the gradient will be 70-35/8-4, which is 35/4. Simply substitute it into the formula to obtain y= 35x/4!
Mark the angles and sides of each pair of triangles to indicate that they are congruent. NO LINKS!!!
=========================================================
Explanation:
The order of the lettering is important because the order tells us how the letters pair up.
For DCB and CDJ, we have D and C as the first letters. So that means angle D and angle C are congruent between the triangles. I've marked this in red. The other angles are handled the same way.
The congruences for the segments are then built up from the angles.
The mean of a distribution is 276, while the median is 318. Which of these
statements is likely to be true about the distribution?
A It is negatively skewed,
B. It is symmetric
C. It is the same throughout
D. It is positively skewed
Answer:
A.
Step-by-step explanation:
The mean is less than the median so it is skewed to the left or negatively skewed.
In some country the budget for defense exceeded the budget for education by $629.1 billion. If x represents the budget for education, in billions of dollars, how can the budget for defense
be represented?
If x represents the budget for education, in billions of dollars, the budget for defense can be represented by
Answer:
y = defence
Step-by-step explanation:
x^2 + ( 47y (7 + 6) + 18.1) is a starter point
x^2 + (47y (7+6) + 3(6+ 1/30))
x^2 + (611y + 3(6+1/30))
x^2 + (611y + 18.1)
x^2 + 629.1y
With x representing x billion and y representing y billion for defence
The budget for defense can be represented by the algebraic expression $ (x + 629.1) billion.
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.
Let x represents the budget for education.
Given that the budget for defense exceeded the budget for education by $629.1 billion.
The budget for defense can be represented by (x + 629.1).
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[tex]what is the inverse of f(x)=2x+3[/tex]
PLEASE ANSWERR!!! WILL MARK YOU BRAINLYEST❤️❤️
(06.04 HC)
Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper (9) that Ben collected in a certain amount of time (), in
weeks
Paper Recycling
150
Amount of 120
Paper
90
Collected
(in pounds) 60
30
0 1 2 3 4 5
Number of Weeks
What would most likely be the total amount of paper, in pounds, Bon would collect in 10 weeks?
230
O 270
300
330
Answer:
Step-by-step explanation:
??????
1/4 es mayor o menor que 3/16
Answer:
1/4
Step-by-step explanation:
Have a nice day :)
ten un buen dia :)
Answer: 3/16 es menor than 1/4.
I’m having a hard time anyone knows??
Answer:
65
Step-by-step explanation:
See image below:)
Please help me on this question, ignore the pencil marks.
The answer choices are
A. 4
B. 5
C. 6
D. 7
E. 8
helpppp y’all sososososo
Answer:
3/4
Step-by-step explanation:
Answer:
I think the answer is 4/8 ✨
The perimeter of a rectangle is 54 cm. Find its length and width if the length is represented
by 3x + 2 and the width is represented by 2x – 5.
HELP FAST!!
Answer:
length = 20
width = 7
Step-by-step explanation:
Perimeter of a rectangle is
P = 2(l+w)
54 = 2( 3x+2 + 2x-5)
Combine like terms
54 = 2( 5x -3)
Divide each side by 2
54/2 = 5x-3
27 = 5x-3
Add 3 to each side
27+3 = 5x-3+3
30 = 5x
Divide by 5
30/5 = 5x/5
6 =x
3x+2 = 3(6)+2 = 18+2 = 20
2x-5 = 2(6)-2 =12-5 =7
Answer:
Length = 20 cm
Width = 7 cm
Step-by-step explanation:
Given that :-
The perimeter of a rectangle is 54 cm. Its length and width if the length is represented by 3x + 2 and the width is represented by 2x – 5.To find :-
Find the measures of length and width
Solution :-
To calculate the measures of length and width of rectangle . we gave given in question that perimeter of rectangle is 54 cm and length is represented by 3x + 2 and width is represented by 2x-5.Using Formula :-
Perimeter of rectangle = 2 ( l + b )
Where,
l is the length and w is the width of rectangle.Perimeter = 54 cmSubstitute the values
54 cm = 2 ( 3x + 2 + 2x - 5 )
Combine like terms
54 cm = 2 ( 3 x + 2 x + 2 - 5)
54 cm = 2 ( 5 x -3)
Simplify both sides of the equation.
54 = 2( 5x− 3 )
54 = (2)(5x) + (2)(−3). .. ( Distribute )
54 = 10x +−6
54 = 10x −6
Flip the equation.
10x −6 = 54
Add 6 to both sides.
10x −6 + 6 = 54 + 6
10x = 60
Divide both sides by 10.
10x / 10 = 60 / 10
x = 6
Therefore ,
Length = 3x + 2 =3 ×6 + 2 = 18 + 2 = 20 cm
Width = 2x- 5 = 2 × 6 - 5 = 12 - 5 = 7 cm
Please write out the steps in explanation on how to solve these
1836-1347 and 4865-3956
After Noam transformed the graph of the function f (x)= |x|, the graph's vertex became (0,48), Which sequences of transformations could he had used - Need for a test, I see it was answered but there is no answer or how to get the answer. Please respond QUICK.....
Answer:
f(x) = |x|+48 would make the vertex be (0,48)
Step-by-step explanation:
Since the y-coordinate changed, this means that only vertical shift could have occured. Therefore, 48 must've been added to |x|.
How many 6 oz servings are in a 1.125-quart pitcher of lemonade? There are servings. Enter an integer or decimal number[more..] Question Help: Message instructor Calculator
Answer:
6
Step-by-step explanation:
1 qt = 4 cups
1 cup = 8 fl oz
1.125 qt * (4 cups)/(1 qt) * (8 fl oz)/(1 cup) = 36 fl oz
(36 fl oz)/(6 fl oz) = 6
Answer: 6 servings
Find the following list of data calculate a demean be the maid in and see the mouth or mothers of the numbers from
the picture
Given:
A fair die is rolled.
It pays off $10 for 6, $7 for a 5, $4 for a 4 and no payoff otherwise.
To find:
The expected winning for this game.
Solution:
If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.
The probability of getting a 6 is:
[tex]P(6)=\dfrac{1}{6}[/tex]
The probability of getting a 5 is:
[tex]P(5)=\dfrac{1}{6}[/tex]
The probability of getting a 4 is:
[tex]P(4)=\dfrac{1}{6}[/tex]
The probability of getting other numbers (1,2,3) is:
[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]
[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]
Now, find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.
[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]
[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]
[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]
On further simplification, we get
[tex]E(x)=\dfrac{10+7+4}{6}[/tex]
[tex]E(x)=\dfrac{21}{6}[/tex]
[tex]E(x)=3.5[/tex]
Hence, the expected winnings for this game are $3.50.