Answer:
The Answer would be D) 3
A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question.
Suppose a student guesses the answer to each question. Assuming the guesses are independent, find the probability
that the student will guess correctly when answering two questions.
o 1/5
1/10
01/25
Answer:
1/25
Step-by-step explanation:
The probability of guessing the first question correct is 1/5
The probability of guessing the second question correct is 1/5
Since they are independent
P(correct, correct) = P(1st correct) * P(2nd correct)
= 1/5 * 1/5
= 1/25
If carol can read 45 pages in one hour how many pages can she read in four hours
Answer:
She can read 180 pages in 4 hours
45*4=180
Carol can read 180 pages in four hours.
Simply multiply the rate (45 pages/hour) by the time (4 hours) to get 180 pages/4 hours.
What is the equation, in point-slope form, of the line that has a slope of 6 and passes through the point (–1, –8)? a. y+8 = 6 (x+1 )
Answer:
y + 8 = 6(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 6 and (a, b) = (- 1, - 8), hence
y - (- 8) = 6(x - (- 1)), that is
y + 8 = 6(x + 1)
ANSWER
[tex]y + 8=6(x + 1)[/tex]
EXPLANATION
The point-slope form of an equation is given by the formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex](x_1,y_1)[/tex]
is a point on this line and
[tex]m[/tex]
is the slope of the line.
From the question, the line has slope 6 and passes through (-1,-8).
This means that
[tex]x_1=-1[/tex]
[tex]y_1=-8[/tex]
and
[tex]m = 6[/tex]
We substitute these values into the point-slope formula to get:
[tex]y- - 8=6(x- - 1)[/tex]
We simplify to get:
[tex]y + 8=6(x + 1)[/tex]
i need help im stuxk again and thanks who help me
Answer:
b C = 25m + 75
Step-by-step explanation:
The total cost for m months is the one time fee plus the cost per month times the number of months
C = fee + cost per month * m
C = 75 + 25m
Rearranging the equation
C = 25m + 75
Use the point-slope formula (if possible) to write an equation of the line given the following
information.
The slope is - 5, and the line passes through the point (-2,0).
The equation of the line is?
Answer:
y = -5 (x+2)
Step-by-step explanation:
We can use the point slope form of a line
y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope
y-0 = -5(x--2)
y = -5 (x+2)
If f(x)=5x-1, then f^-1(x)=
Answer:
f^-1(x) = (x+1)/5
Step-by-step explanation:
f(x)=5x-1
y = 5x-1
Exchange x and y
x = 5y-1
Solve for y
Add 1 to each side
x+1 = 5y-1+1
x+1 = 5y
Divide by 5
(x+1)/5 = 5y/5
(x+1)/5 = y
The inverse is (x+1)/5
f^-1(x) = (x+1)/5
A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected.
39 31 38 40 29
32 33 39 35 32
32 27 30 31 27
30 29 34 36 25
30 32 38 35 40
29 32 31 26 26
32 26 30 40 32
39 37 25 29 34
Which sample size would you use to get the best point estimate?
A.
90
B.
70
C.
150
D.
500
E.
280
Answer:
B
Step-by-step explanation:
The recommended sample size n for point estimates is:
n = NX / (N + X - 1)
where N is the population size, and X is defined as:
X = Z² p (1 - p) / E²
where Z is the critical value, p is the sample proportion, and E is the margin of error.
Assume a confidence level of level of 95% and a margin of error of 5%.
α = 0.05, Z(α/2) = 1.96
E = 0.05
Of the 40 units tested, 2 had lifespans less than 26 days. So the proportion is:
p = 2/40 = 0.05
Therefore:
X = (1.96)² (0.05) (1 - 0.05) / (0.05)²
X = 73
Given N = 2000:
n = (2000) (73) / (2000 + 73 - 1)
n = 70.45
Rounding, the recommended sample size is 70.
Answer:
B
Step-by-step explanation:
What is the result if 3x-9 is evaluated when x = -5?
Answer:
Step-by-step explanation:
I wonder if it is the minus that is causing the problem?
Let x = - 5
3*(-5) - 9
-15 - 9
This is a money question. If you are 15 dollars in debt and you spend another 9, where are you? (In the company of the American government. They do this all the time).
- 15 - 9 = - 24
31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,
then value of CD =
B.213
A. 2 12
C.4
D. 275
Answer:
The value of CD is 2√5
Step-by-step explanation:
* Lets describe the figure to know its name
- ABCD is a quadrilateral
∵ BC parallel to AD
∵ BC = 6 units and AD = 8 units
- The quadrilateral which has two parallel sides not equal in length is a
trapezoid
∴ ABCD is a trapezoid, where BC and AD are its bases
∵ BA perpendicular to AD
∴ BA is the height of the trapezoid
- The area of the trapezoid = 1/2 (base 1 + base 2) × its height
∵ The bases of the trapezoid are BC and AD
∵ BC = 6 and AD = 8
∵ Its area = 28 units²
∴ 1/2 (6 + 8) × height = 28
∴ 1/2 (14) × height = 28
∴ 7 × height = 28 ⇒ divide both sides by 7
∴ height = 4
∵ The height is BA
∴ BA = 4 unit
- To find the length of CD draw a perpendicular line from C to AD and
meet it at E
∵ BA and CE are perpendicular to AD
∴ BA // CE
∵ BC // AD
- Perpendicular lines between parallel lines are equal in lengths
∴ BA = CE and BC = AE
∵ BA = 4 and BC = 6
∴ CE = 4 and AE = 6
∵ AD = 8 units
∵ AD = AE + ED
∴ 8 = 6 + ED ⇒ subtract 6 from both sides
∴ ED = 2 units
- In ΔCED
∵ m∠CED = 90°
∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem
∵ CE = 4 and ED = 2
∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5
* The value of CD is 2√5
Final answer:
The value of the unknown side CD in quadrilateral ABCD can be found using the area of a trapezoid formula and the Pythagorean theorem. Given the area, and the lengths of BC and AD, we calculated that CD equals 8 units.
Explanation:
The student has asked to find the value of CD in a quadrilateral ABCD, where BC is parallel to AD, BA is perpendicular to AD, the area of quadrilateral ABCD is 28 square units, BC is 6 units, and AD is 8 units.
Since BA is perpendicular to AD and BC is parallel to AD, we can determine that ABCD is a trapezoid with AB and CD as the non-parallel sides. The area of a trapezoid is given by the formula Area = ½ × (sum of parallel sides) × height. So we have:
½ × (AD + BC) × height = 28
½ × (8 + 6) × height = 28
½ × 14 × height = 28
7 × height = 28
height = 4 units
Since BA is perpendicular to AD, and given BA is the height of the trapezoid, this means that AB = 4 units. Now, because ABCD has right angles at A and B, triangles ABD and ABC are right triangles and we can use the Pythagorean theorem to calculate CD.
In triangle ABD:
AB² + BD² = AD²4² + BD² = 8²BD = √(8² - 4²) = √(64 - 16) = √48 = 4√3Since CD is the hypotenuse of triangle ABD:
CD² = AB² + BD²CD² = 4² + (4√3)²CD² = 16 + 48CD = √64CD = 8 unitsTherefore, the correct answer is CD = 8 units.
or what value of x does 4x=(1/8)^x+5?
–15
–3
3
15
Answer:
x = -3Step-by-step explanation:
[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3[/tex]
Answer:
B, -3
Step-by-step explanation:
Typically, a point in a three-dimensional Cartesian coordinate system is represented by which of the following
A) (x,y,v)
B) (w,x,y)
C) x,y,z
D) (x,y,z)
Answer:
option D) (x,y,z)
Step-by-step explanation:
we know that
The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space.
The three axes are labeled x ,y and z.
The x-axis is called abscissa
The y-axis is called ordinate
The z-axis is called applicate
therefore
A point in a three-dimensional Cartesian coordinate is represented by (x,y,z)
What is the value of the product (3-2i)(3+2i)?
Answer:
13
Step-by-step explanation:
(3-2i)(3+2i) = 9 + 6i - 6i - 4i^2
9 - 4i^2
9 + 4 = 13
The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.
{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}
The best measure of center for this data set is the
, and its value expressed up to one decimal place is
Answer:
Step-by-step explanation:
Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.
We can determine the skewness, if we know at least the median and the mean.
The array of the above data set is,
16,18,28,29,35,36,37,38,40,41,44,66,68,72
The Median of the above array is
\frac{37 + 38}{2} = \frac{75}{2} = 37.5
The mean is
\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38
Since the mean and the median are not the same, the distribution is skewed.
<b>For a skewed distribution, the best measure of central tendency is the median.</b>
To one decimal place, the median is;
37.5
NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.
Step-by-step explanation:
The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
Answer:
y=68(1.5)^(x-1)
Step-by-step explanation:
Answer:
The function is:
[tex]y = 68 (1.5) ^ x[/tex]
Step-by-step explanation:
Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.
So:
After an hour the number of people is:
[tex]y = 68 (1.5)[/tex]
After two hours the number of people is:
[tex]y = 68 (1.5) (1.5) = 68 (1.5) ^ 2[/tex]
After x hours the number of people is:
[tex]y = 68 (1.5) ^ x[/tex]
Therefore, the exponential growth function that models the number of people y at the fair after x hours is:
[tex]y = 68 (1.5) ^ x[/tex]
Miguel is making smoothies out of yogurt and juice to serve to his friends, and he needs to make 12 cups. The ratio of yogurt to juice is 2 cups to 1 cup.
How much yogurt will he use?
A.
3 cups
B.
4 cups
C.
8 cups
D.
9 cups
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answer:
2/3
Step-by-step explanation:
Y varies directly as x
Y =kx
Y=6 when x = 72
First find the relationship between y and x.
i.e find the value of k
Substitute the value of x and y
6 = k *72
Make k the subject of the formula
K = 6/72
K= 1/12
:. The rlationship between x and y is
Y = 1/12x
When x is 8
Y = 1/12 * 8
Y = 8/12
Y = 2/3 and that is the answer
Hope it helped you
Answer:
The answer is : 2/3
Step-by-step explanation:
Given is that y varies directly as x.
Means as y increases or decreases, x also increases or decreases.
When y is 6 when x is 72,
So, when x = 8, we have to find y.
We can write the relation as follows:
[tex]\frac{6}{y}= \frac{72}{8}[/tex]
[tex]72y=48[/tex]
[tex]y=\frac{48}{72}[/tex] = [tex]\frac{2}{3}[/tex]
Which is equivalent
Answer:
4x^4
Hope this helps
For this case we must find an expression equivalent to:
[tex](256x^{16}) ^ {\frac {1} {4}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Then, rewriting the expression:
[tex](256 ^ {\frac {1} {4}} * x ^ {\frac {16} {4}}) =[/tex]
We have by definition:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt [4] {256} * x ^ 4 =\\\sqrt [4] {4 ^ 4} * x ^ 4 =\\4x ^ 4[/tex]
ANswer:
Option B
Please someone help me out
Answer: 60/2
Step-by-step explanation:
When you multiply 60 and 1/2 you get 30 which is the same as 60/2
ANSWER
[tex] \sqrt{60} [/tex]
EXPLANATION
The given exponentiial expression is
[tex] {60}^{ \frac{1}{2} } [/tex]
Recall that
[tex] {a}^{ \frac{1}{n} } = \sqrt[n]{a} [/tex]
A special case of this rule is when n=2.
Then,
[tex] {a}^{ \frac{1}{n} } = \sqrt{a} [/tex]
This implies that
[tex]{60}^{ \frac{1}{2} } = \sqrt{60} [/tex]
The correct answer is B.
What is the slope of a line that is parallel to y=3x+5
Answer: Slope = 3
Step-by-step explanation:
On a 2D-Plane, any two lines with the same slope and a different y-intercept will be parallel
Knowing this, any line with the same slope as our given line and a different y-intercept will be parallel to it
Therefore, any line with a slope of 3 and a y-intercept other than 5 will be parallel to y = 3x + 5
The answer you are looking for is a slope of 3.
Parallel lines have the same slope (M value in Y = MX + B), but different y-intercepts (B value in Y = MX + B) For example, y = 3x + 7 would be parallel to the line given above, since they slope is the same, but the y-intercept is different.
I hope this helps!
How much money will you have if you started with $20 and put it in an account that earned 12% every year for 3 years?
Answer:
34,560
Step-by-step explanation:
Started of with 20 and earned 12% each year.
12% is just 12 as a whole number
so from that 20 12x12x12=1,728
1,728x20=
34.560
Identify the opposite number of -22.7. Then, explain why the two numbers are opposites.
22.7
Explanation:They are opposites because they are both the same distance from 0 and are on different sides of 0 on a number line.
They are also opposites because when either of them is multiplied by -1, you get the other one.
[tex]22.7*-1=-22.7[/tex]
[tex]-22.7*-1=22.7[/tex]
Answer:
22.7 because it's the same number but different
3. Which number is closest to zero on
the number line?
A -3/8
B 3/4
C 0.3
D 0.50
Final answer:
The number closest to zero on the number line from the given options is 0.3, making the correct answer C) 0.3.
Explanation:
The question asks which number is closest to zero on the number line from the given options: A) -3/8, B) 3/4, C) 0.3, D) 0.50. To find out which is closest to zero, compare the absolute values of these numbers (since we are interested in the distance from zero, not the direction).
Absolute value of A) -3/8 is 0.375
Absolute value of B) 3/4 is 0.75
Absolute value of C) 0.3 is 0.3
Absolute value of D) 0.50 is 0.5
Comparing these values, 0.3 is the smallest absolute value, which means it is the closest to zero. Therefore, the correct answer is C) 0.3.
Write the sentence as an equation.
b increased by 281 is d
Answer:
B + 281d
Step-by-step explanation:
I think that's the answer the "is" is throwing me off "is" is either = or (x)
Hope my answer has helped you and if not i'm sorry.
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume?
The (blank) has the greater volume because the (blank) fits within the (blank) with extra space between the two figures.
Please fill in the blanks
Answer:
Filling in the blanks: (rectangular prism) (cylinder) (rectangular prism)
The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.
A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
We can see this by comparing the formulas for the volumes of the two shapes.
The volume V of a rectangular prism with length L, width W, and height H is given by:
V = L x W x H
The volume V of a cylinder with radius r and height H is given by:
V = πr²H
Now,
We are told that the length of each side of the prism base is equal to the diameter of the cylinder.
Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.
So we can write:
L = 2r
W = 2r
Substituting these values into the formula for the volume of the rectangular prism, we get:
V prism = L x W x H
V prism = 2r x 2r x H
V prism = 4r²H
Substituting the radius and height of the cylinder into the formula for its volume, we get:
V cylinder = πr^2H
To compare the volumes,
We can divide the volume of the cylinder by the volume of the prism:
V cylinder / V prism = (πr²H) / (4r²H)
V cylinder / V prism = π/4
π/4 is greater than 1/1,
Thus,
The cylinder has a greater volume.
The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ3
What is the solution to this system of equations?
x+2y=4
2x-2y=5
a. (3, -5.5)
b. (3, 0.5)
c. no solution
d. indefinitely many solutions
Answer:
b. (3, 0.5).
Step-by-step explanation:
x + 2y = 4
2x - 2y = 5
Adding the 2 equations eliminates the y:
3x = 9
x = 3
Substitute fro x in the first equation:
3 + 2y = 4
2y = 1
y = 0.5.
Option B is correct, (3, 0.5) is the solution of the system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
x+2y=4...(1)
2x-2y=5...(2)
Add equation 1 and 2
x+2y+2x-2y=4+5
3x=9
Divide both sides by 3
x=3
3+2y=4
Subtract 3 from both sides
2y=1
y=1/2
y=0.5
Hence, option B is correct, (3, 0.5) is the solution of the system of equations.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Sara needs to take a taxi to get to the movies the taxi charges $4.00 for the first mile and then $2.75 for each mile after that if the total charge is $20.50 then how far was Sara’s taxi ride to the movie
Answer:
6 miles
Step-by-step explanation:
4+2.75m=20.50
-4 -4
2.75m=16.50/2.75
m=6
Answer:
6 miles
Step-by-step explanation:
So the total charge is $20.50, what I personally did was
Subtract $4 from $20.50
You get $16.50
Now divide $16.50 by $2.75
There's your miles
Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A.
A. x + 3y = 11 → x + 3y = 11
5x − y = 17 → 15x − 3y = 51
15x = 62
B. x + 3y = 11
15x = 62
What is the solution to both systems A and B?
Answer:
The answer is [4,3] Hope this helps.
Step-by-step explanation:
The solution to the both system of equations A and B are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Consider system A.
x + 3y = 11
15x − 3y = 51
Adding both equations,
16x = 62
x = 3.875
3y = 7.125
y = 2.375
Consider system B.
x + 3y = 11
15x = 62 ⇒ x = 4.133
3y = 6.867
y = 2.289
Hence the solutions are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
Learn more about System of Equations here :
https://brainly.com/question/24065247
#SPJ7
In one U.S. city, the taxi cost is $5 plus $0.90 per mile. If you are traveling from the airport, there is an additional charge of $5.00 for tolls. How far can you travel from the airport by taxi for $59.50?
How many states are there
Answer:
50
Step-by-step explanation:
Hello There!
There are 50 states in the United States
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
George and his dad are planning to attend the state fair. An adult tickets is $19.00. The price of an adult tickets is 1/3 the price of a student ticket plus $15.00. Write an equation to determine how much George will pay for a student ticket
Answer:
$12
Step-by-step explanation:
If x is the price that George pays for a student ticket, then:
19 = ⅓ x + 15
To solve for x, first subtract 15 from both sides:
19 - 15 = ⅓ x
4 = ⅓ x
Then multiply both sides by 3:
4 × 3 = x
12 = x
Answer:
1/3x + 15 = 19
Step-by-step explanation:
Well this is a simple equation where you write it out EXCACTLY like the question says, the 1/3 is the 1/3 the price of a student ticket and add the x to represent the unknown amount (student ticket), the 15 represents the plus $15.00 which equals 19
Hope this helps,
(btw dont >EVER TRUST< the -->"TRUSTED ANSWERS"<-- because all it means is that they are expirienced NOT that the answer is right)