Answer:
7
Step-by-step explanation:
The mathematics faculty at a college consists of 7 professors, 4 associate professors, 4 assistant professors, and 6 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.
Answer:
0.619 = 61.9% probability of choosing a professor or an instructor.
Step-by-step explanation:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
7 + 4 + 4 + 6 = 21 members
7 + 6 = 13 professors or instructors.
Find the probability of choosing a professor or an instructor.
p = 13/21 = 0.619
0.619 = 61.9% probability of choosing a professor or an instructor.
A contractor is building a fence around a square garden that has a side length of 3 inches in a scale drawing. The scale factor of the drawing is 1 1/2 inches : 4 feet. If one link of fence measures 2 2/3 feet, shade the correct number of links needed to build a fence around the entire garden
The number of fences needed to build around the entire garden is 12.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Side of the square garden = 3 inches
Scale factor.
1(1/2) inches = 4 feet
3/2 inches = 4 feet
3 inches = 8 feet
Now,
Length of one fence.
= 2(2/3) feet
= 8/3 feet
Now,
The perimeter of the square.
= 4 side
= 4 x 3 inches
= 12 inches
= 4 x 8 feet
= 32 feet
Now,
The number of fences needed to build the fence around the garden.
= 32 ÷ 8/3
= 32 x 3/8
= 12 fences
Thus,
12 fences are needed to cover the entire garden.
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GUYS HELP ME PLS. Tina is standing at the bottom of a hill. Matt is standing on the hill so that when Tina's line of sight is
perpendicular to her body, she is looking at Matt's shoes.
a. If Tina's eyes are 5 feet from the ground and 14.5 feet from Matt's shoes, what is the angle of elevation of
the hill to the nearest degree?
Answer:
71°
Step-by-step explanation:
The angle of elevation of the hill can be obtiaed using trigonometry :
Given
the opposite length = 14.5 feets
Adjacent = 5 feets
The angle of elevation vabnbe obtained using :
Tan θ = opposite / Adjacent
Where θ = angle of elevation
Tan θ = 14.5 / 5
Tan θ = 2.9
θ = tan^-1(2.9)
θ = 70.97 = 71°
Evaluate the expression. Show work.
2w + 2l when w= 4 and l=6
Answer:20
Step-by-step explanation:
2(4)+2(6)
8+12=20
Answer: 20
Step-by-step explanation:
Plug in 4 for w and 6 for I.
2(4) + 2(6) = 8 + 12 = 20
what angle is this I need help
Consider function f, where B is a real number.
f(x)=tan(Bx)
Complete the statement describing the transformations to function f as the value of B is changed.
As the value of B increases, the period of the function (remains the same, increases, decreases), and the frequency of the function (remains the same, increases, decreases).
When the value of B is negative, the graph of the function (reflects over the y-axis, remains the same, reflects over the x-axis).
Using the concept of the tangent function, it is found that:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
---------------------------------
Tangent function:
It is given by:
[tex]f(x) = \tan{Bx}[/tex]
The period is [tex]P = \frac{\pi}{|B|}[/tex].The frequency is [tex]F = \frac{1}{P} = \frac{|B|}{\pi}[/tex].---------------------------------
The period is inversely proportional to B, thus, as B increases, the period decreases.Frequency is inversely proportional to the period, thus, as the period decreases, the frequency increases.When B is negative, we get [tex]f(x) = \tan{-Bx} = f(-x)[/tex], thus, the function is reflected over the y-axis, as the graph at the end of the answer shows, with f(x) is red(B positive) and f(-x) in blue(B negative).---------------------------------
Considering the three bullet points above, the correct option is:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
A similar problem is given at https://brainly.com/question/16828446
Answer:
got it right
Step-by-step explanation:
Consider the probability that fewer than 46 out of 134 students will not pass their college placement exams. Assume the probability that a given student will not pass their college placement exam is 98%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
a. Yes
b. No
Answer:
b. No
Step-by-step explanation:
Binomial approximation to the normal:
Binomial distribution has n trials, with p probability.
If
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], it can be approximated to the normal distribution.
Assume the probability that a given student will not pass their college placement exam is 98%.
This means that [tex]p = 0.98[/tex]
134 students:
This means that [tex]n = 134[/tex]
Necessary conditions:
[tex]np = 134*0.98 = 131.32 \geq 10[/tex]
[tex]n(1-p) = 134*0.02 = 2.68 < 10[/tex]
Since the necessary condition n(1-p) < 10 is not satisfied, the answer is No, given by option b.
Pyramid A has a height of 10 feet and a volume of 120 cubic feet. The base of Pyramid B has the same dimensions as Pyramid A but is twice as tall. How is the volume affected by the change in the dimensions? (PLEASE HELP!)
A volume of a pyramid=base area×height/3
both the bases have same dimensions
pyramid B is twice the height of A
therefore the volume is doubled
Answer:
Pyramid B = 240 cubic feet, the volume doubled
Step-by-step explanation:
Pyramid A: 120/10 =12, 12 x 3 = 36 ft² base
Pyramid B: 36 ft² base x 20 ft tall x 1/3 = 240 cubic feet
what 1 + 2 i have know idea of what it is
Answer:
3
Step-by-step explanation:
Answer:
1+ 2 = 3
Step-by-step explanation:
find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0
Answer:
Radius: [tex]r =\frac{\sqrt {21}}{6}[/tex]
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
Step-by-step explanation:
Given
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Solving (a): The radius of the circle
First, we express the equation as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
So, we have:
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Divide through by 9
[tex]x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0[/tex]
Rewrite as:
[tex]x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}[/tex]
Group the expression into 2
[tex][x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
Next, we complete the square on each group.
For [tex][x^2 + 3x][/tex]
1: Divide the [tex]coefficient\ of\ x\ by\ 2[/tex]
2: Take the [tex]square\ of\ the\ division[/tex]
3: Add this [tex]square\ to\ both\ sides\ of\ the\ equation.[/tex]
So, we have:
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Factorize
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Apply the same to y
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}[/tex]
Add the fractions
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
By comparison:
[tex]r^2 =\frac{7}{12}[/tex]
Take square roots of both sides
[tex]r =\sqrt{\frac{7}{12}}[/tex]
Split
[tex]r =\frac{\sqrt 7}{\sqrt 12}[/tex]
Rationalize
[tex]r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}[/tex]
[tex]r =\frac{\sqrt {84}}{12}[/tex]
[tex]r =\frac{\sqrt {4*21}}{12}[/tex]
[tex]r =\frac{2\sqrt {21}}{12}[/tex]
[tex]r =\frac{\sqrt {21}}{6}[/tex]
Solving (b): The center
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
From:
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
[tex]-h = \frac{3}{2}[/tex] and [tex]-k = \frac{2}{3}[/tex]
Solve for h and k
[tex]h = -\frac{3}{2}[/tex] and [tex]k = -\frac{2}{3}[/tex]
Hence, the center is:
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
hi can I send a screenshot?
Answer:
Yeah
Step-by-step explanation:
☁️ Answer ☁️
Yes! Send a screenshot and ask ur question
Question 9 of 10 What is one strategy that can help a person avoid spending too much money on interest when borrowing money? O A. Choosing a credit card with a low minimum monthly payment O B. Choosing a loan with a simple rather than compound interest rate O C. Choosing a credit card with a high minimum monthly payment O D. Choosing a loan with a compound rather than simple interest rate
Answer:
Hello There!!
Step-by-step explanation:
The answer is B. Choosing a loan with a simple rather than compound interest rate.
hope this helps,have a great day!!
~Pinky~
A racing car driver is investigating whether the type of fuel he uses in his car affects his overall speed. He uses three different types of fuel. The driver runs an experiment where he fills his car with each type of fuel 20 times, and each time records the time taken to drive one lap of a track. A one-way ANOVA test is conducted to test the null hypothesis that type of fuel is not a significant factor in determining speed. The result of the test is that the null hypothesis is not rejected.
The conclusion that follows from this test is that: __________
a. it has been proven that the type of fuel is a significant factor in determining speed
b. it cannot be ruled out that the type of fuel is an insignificant factor in determining speed
c. it has been proven that the type of fuel is an insignificant factor in determining speed
d. it has been proven that the type of fuel can sometimes be a significant factor in determining speed
Answer:
b. it cannot be ruled out that the type of fuel is an insignificant factor in determining speed.
Step-by-step explanation:
From the question :
Let the speed of each fuel be represented as ;
u1, u2, u3
The null hypothesis, H0 ;
H0 : u1 = u2 = u3
H0 is of the notion that fuel type is not a significant factor in determining speed
The alternative hypothesis, H1;
H1 : u1 ≠ u2 ≠ u3
The alternative is the opposite of the null, fuel type is a significant factor in determining speed
If after conducting the statistical test, the null hypothesis cannot be rejected ;
Then the conclusion will be ;
There is no significant evidence to conclude that the fuel type is a significant factor in determining speed ;
Hence, fuel fuel type remains an insignificant factor in determining speed.
please help me asap!!
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
x^2 + 5^2 = 13^2
x^2 + 25 = 169
x^2 = 144
---> x = 12
LOOK AT THE IMAGE!!!
DO NOT JUST ANSWER FOR POINTS
Answer:
C) (-3,-1)
Step-by-step explanation:
C) (-3,-1)
An unbiased estimator is one for which: Group of answer choices its value always equals the value of the parameter it estimates. its standard deviation always decreases as the sample size increases. its sampling distribution is Normal. its average value is equal to the parameter it estimates.
Answer:
its sampling distribution is centered exactly at the parameter it estimates.
Step-by-step explanation:
An unbiased estimator is an estimator that shows the correct statistic applied for the parameter of the population
Here correct represents that it should not be overestimated or underestimated. In the case when there is an underestimate or overestimate this means that there is a bias
So as per the given options the above option is correct
The height of a ball dropped from a 160 foot building after 1 seconds is represented by h(t) = 160 - 1612
How high will the ball be after 3 seconds?
A. O feet
B. 9 feet
C. 16 feet
D. 112 feet
E. 151 feet
Answer:
C. 16 feet.
Step-by-step explanation:
How to find the maximum height of a projectile
if α = 90°, then the formula simplifies to: hmax = h + V₀² / (2 * g) and the time of flight is the longest.
if α = 45°, then the equation may be written as:
if α = 0°, then vertical velocity is equal to 0 (Vy = 0), and that's the case of horizontal projectile motion.
38 POINTS FOR THIS
pls answer some of these questions or even all ty
Answer:
there are no questions
Step-by-step explanation:
but may i still please have a brainliest
if not then it is ok
write the questions in the comments
Answer:
What questions?
I don't see anything
HELPPPP ME PLEASEEE
Answer:
your answer will be 588in²
Step-by-step explanation:
Area=πr²
=π(14)²
=3×(14)²
Area=588in²
hope it helps..
have a great day!!!
Ms. Vasquez's daughter lives 1,650 miles away. Ms. Vasquez won a gift card for 100 gallons of gas. If her car can travel 35 miles on each gallon, can she travel roundtrip to see her daughter on free gas? Explain how you know.
Answer:
yes, since it takes 48 gallons of gas to go one direction to go back it is 96
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
If her daughter lives 1,650 miles away, and her gift card is for q00 miles of gas, and her car can travel 35 miles on each gallon, it would take about 47 gallons to make the 1,650 mile trip to her daughter. Leaving 53 gallons on her car.
To make the 1,650 mile trip back to her own home, it would take another 47 gallons. Since she still has 53 gallons left from her trip there, she will be able to make the trip back with still 6 gallons in her tank.
The function g is given in three equivalent forms.
Which form most quickly reveals the y-intercept?
Choose 1 answer:
g(x) = 3x² + 6x - 9
g(x) = 3(x + 1)² – 12
-
g(x) = 3(x+3)(x - 1)
What is the y-intercept?
y-intercept = (0,
▸
The form of the function that most quickly reveals the y-intercept is the second form:
[tex]g(x)=[/tex] [tex]3(x+1)^{2} - 12[/tex]
To find the y-intercept, we need to determine the value of g(x) when x is equal to 0. By substituting x = 0 into the function, we have:
[tex]g(0)=3(0+1)^{2} -12[/tex]
[tex]=3(1)^{2} -12[/tex]
[tex]=3-12[/tex]
[tex]=-9.[/tex]
Therefore, the y-intercept is -9. This means that the graph of the function intersects the y-axis at the point (0, -9), where the x-coordinate is 0 and the y-coordinate represents the y-intercept value.
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true or false
There are four quartiles altogether,
Factor out the common terms: 24a + 12b - 40c
I'll give brainliest
Answer:
4(6a+3b-10c)
Step-by-step explanation:
Answer and Step-by-step explanation:
All of the terms have a common factor of 4.
4(6a + 3b - 10c)
#teamtrees #PAW (Plant And Water)
please help.
grocery store workers restock cans of soup and bags of rice at constant rates. which item was restocked at a faster rate and what is the rate? let x represent the number of minutes and y represent the total number of bags or cans
Answer:
Cans of soup are restocked at a faster rate
Step-by-step explanation:
With an equation y=mx+b, m = slope
m of rice = 12
The slope of the graph for the cans of soup is 30/2 = 15
m of soup = 15
15 is greater than 12
What is the slope of the line?
Answer:
-2
Step-by-step explanation:
This is an easy way to do it with points
(0,2)
+1 -2
(1,0)
rise/run -2/1= -2
Find the area of the polygon.
log (5x) (x)= 7/2
Answer:
[tex]x = \frac{\sqrt{70} }{10}, - \frac{\sqrt{70} }{10}[/tex]
What is the value of x?
These are the options!
1- x= 15
2- x= 12
3- x= 24
4- x= 17
Answer:
since they are alternate angles(equal)
4x-10=58
4x=68
x=17
Answer:
option 4
Step-by-step explanation:
(4x - 10) and 58 are alternate angles and are congruent, then
4x - 10 = 58 ( add 10 to both sides )
4x = 68 ( divide both sides by 4 )
x = 17
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of
25. By what factor were the dimensions of the pentagon multiplied?
a) 12.5
b) 625
c) 5
d) 50
Since the area of the figure changed by a factor of 25, a factor by which the dimensions of the pentagon were multiplied include the following: C. 5.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
(Scale factor of dimensions)² = Scale factor of area
(Scale factor of dimensions)² = 25
Scale factor of dimensions = √25 = 5
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Answer:
c.5
Step-by-step explanation:
The Candy Store is selling packs of gummies. A pack has 2 and 1/3 pound
of pineapple gummies and 1 and 5/6 pound of strawberry gummies. How
may pounds of gummies is in a pack?
Answer:
4 pounds
Step-by-step explanation: