Answer:
90 km/hr
Step-by-step explanation:
If x is the speed of the slower car, and x+20 is the speed of the faster car, then:
5x + 5(x+20) = 1000
x + x + 20 = 200
2x + 20 = 200
x + 10 = 100
x = 90
In the NFL, a football field is 200 feet longer than it is wide, and the area of the field is 57,600ft^2
What is the width of the field?
(Before you mess this up, the field is not 100 yards long. You must include the lengths of the end Zones.) (And hey wait a second! Before you mess it up now, notice the problem is in
FEET.)
Answer
160ft
Step-by-step explanation:
Let the width be x.
Then the length is (x+200)
The area of the field=57600
Area=length*width
x(x+200)=57600
x^2+200x-57600=0
x=-360 or x=160
The width and length of the football field are 160 feet and 360 feet respectively.
Suppose the width of the field = x
So, the length of the field =x+200
What is the area of a rectangle?The area of a rectangle with length l and width b is lb.
So, the area of the football field =x(x+200)
Given that x(x+200)=57600
[tex]x^{2} +200x=57600[/tex]
[tex]x^{2} +200x-57600=0[/tex]
[tex]x=\frac{-200+\sqrt{200^2-4*1*(-57600)} }{2}[/tex]
x=160
So, the width of the field is 160 feet.
Hence, the width and length of the football field are 160 feet and 360 feet respectively.
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Qualification exams for becoming a state-certified welding inspector are based on multiple-choice tests. As in any multiple-choice test, there is a possibility that someone who is simply guessing the answers to each question might pass the test. Let x denote the number of correct answers given by a person who is guessing each answer on a 25-question exam, with each question having five possible answers (for each question, assume only one of the five choices is correct).(a) What type of probability distribution does x have?(b) For the 25-question test, what are the mean and standard deviation of x?(c) The exam administrators want to make sure that there is a very small chance, say, 1%, that a person who is guessing will pass the test. What minimum passing score should they allow on the exam to meet this requirement?
Answer:
(a) The probability distribution of the random variable X is Binomial.
(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c) The value of x is 0.34.
Step-by-step explanation:
The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.
There are five possible answer for every question.
This implies that the probability of getting a correct answer is:
P (X) = 0.20.
There are a total of n = 25 questions.
Every answer is independent of the others.
(a)
The random variable X has finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).
Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.
(b)
Compute the mean of the random variable X as follows:
[tex]E(X)=np\\=25\times 0.20\\=5[/tex]
Compute the standard deviation of the random variable X as follows:
[tex]SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2[/tex]
Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c)
The sample is large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 5
2. n(1 - p) ≥ 5
Check the conditions as follows:
[tex]np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(5, 2^{2})[/tex]
It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.
That is P (X < x) = 0.01.
⇒ P (Z < z) = 0.01
The value of z is -2.33.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34[/tex]
Thus, the value of x is 0.34.
What’s the amplitude,period,equation of axis, and range for y=3sin[2(x+90)]?
Answer:
amplitude: 3period: πaxis: y = 0range: [-3, +3]Step-by-step explanation:
The amplitude is the multiplier of the sine function: 3.
The period is 2π divided by the coefficient of x: 2π/2 = π.
The equation of the axis is any added constant: y = 0.
The range is the axis value ± the amplitude value: from -3 to +3.
Suppose that in a random sample of 200 New York City residents 55% can name a player on the Knicks. In a random sample of 120 Toronto residents, 70% can name a player on the Raptors. At the 5% level of significance, determine if we can conclude that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors. C.
a. State the null and alternative hypotheses.
b. Are all criteria for the hypothesis test satisfied?
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
b) Yes.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.
As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The conditions to met for this test are:
- The sampling method for each population is simple random sampling.
- The samples are independent.
- Each sample includes at least 10 successes and 10 failures.
[tex]\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}[/tex]
- Each population is at least 20 times as big as its sample.
This conditions are met, so all criteria for the hypothesis test is satisfied.
What is the volume of the cylinder below?
Answer:
The volume of the cylinder is [tex]112\ \text{units}^3[/tex].
Step-by-step explanation:
We have,
Radius of the cylinder is 4 units
Height of the cylinder is 7 units
It is required to find the volume of the cylinder. The formula of the volume of the cylinder is given by :
[tex]V=\pi r^2 h[/tex]
Plugging all the values, we get :
[tex]V=\pi \times (4)^2\times 7\\\\V=112\ \text{units}^3[/tex]
So, the volume of the cylinder is [tex]112\ \text{units}^3[/tex]. The correct option is (b).
When Mustafa threw a beach ball to his friend, its horizontal velocity changed as it traveled through the air. The relationship between the elapsed time, tttt, in seconds, since Mustafa threw the ball, and its horizontal velocity, V(t)V(t)V(t)V, left parenthesis, t, right parenthesis, in cm/s\text{cm/s}cm/sstart text, c, m, slash, s, end text, is modeled by the following function: V(t)=4⋅(0.81)t Complete the following sentence about the percent change of the horizontal velocity of the ball. Every second, %\%%percent of horizontal velocity is the total horizontal velocity of the ball.
Answer:
The rate at which the horizontal velocity of the ball changes every second is, 19%.
Step-by-step explanation:
The exponential decay function is given by:
[tex]y=a(1-r)^{t}[/tex]
Here,
y = final value
a = initial value
r = decay rate
t = time
The relationship between the elapsed time, t, in seconds, since Mustafa threw the ball, and its horizontal velocity, V (t) is:
[tex]V(t)=4\cdot (0.81)^{t}[/tex]
The expression for the horizontal velocity of the ball represents the exponential decay function.
On comparing the two equations we get:
[tex]1-r=0.81\\r=1-0.81\\r=0.19[/tex]
Thus, the rate at which the horizontal velocity of the ball changes every second is, 19%.
A round cake has a diameter of 30 cm. Angela places the cake on a circular cake board with a diameter 5 cm
longer than that of the cake.
What is the circumference of the cake board?
Give your answer in terms of T.
cm
Stuck? Watch a video or use a hint.
Report a problem
Doble
Answer: Circumference of cake board is 35π cm.
Step-by-step explanation:Since we have given that
Diameter of a round cake = 30 cm
Diameter of a cake board is 5 cm longer than the diameter of a round cake.
So, Diameter of a cake board = 30+5=35 cm
So, radius of a cake board will be
As we know the formula for " Circumference of Circle ":
So, According to question, we get,
Hence, Circumference of cake board is 35π cm.
Answer: 35π cm
Step-by-step explanation:
A population of insects can double in 30 days. After
80 days, how many times greater will the population be than
after 30 days?
Answer:
about 2.666 times
Step-by-step explanation:
you know that 80 days have past and it only takes 30 days for the population to double. if you do 80/30 you get 2.666 meaning that the population would of been 2.666 times greater.
The population be than after 30 days about 2.666 times greater.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given; A population of insects can double in 30 days.
After 80 days, We need to find that how many times greater will the population be than after 30 days
We know that 80 days have past and it only takes 30 days for the population to double.
if we do 80/30 = 2.666 meaning that the population would of been 2.666 times greater.
Therefore, The population be than after 30 days about 2.666 times greater.
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the base of a expoential function can be a negative number true or false
Answer:
This would be false
Step-by-step explanation:
Exponents can't be negative
Answer:
An exponential function can not be either 1, 0, or any negative number.
Change 460g into kg
Answer:
0.46 kg is your answer
Step-by-step explanation:
We know (by definition) that: 1 g = 0.001 kg.
We can set up a proportion to solve for the number of kilograms.
1 g / 460 g = 0.001 kg / x kg
Now, we cross multiply to solve for our unknown x:
x kg = (460 g / 1 g) * 0.001 kg → x kg = 0.46 kg
Conclusion:
460 g = 0.46 kg
Answer:
460g = 0.46 kg
Step-by-step explanation:
just divide 460/1000 since 1 kg = 1000 grams
simplify the numerical expression
12-2³
Answer:
12-2³ = 12 - 8 = 4
Hope this helps!
:)
There are six space shuttles
visiting your planet. Each
shuttle contains 8 people.
How many people visit
your planet
There are six space shuttles with 8 people inside. Meaning, for every space shuttle, there are 8 people so multiply that by six to get the overall people who visited your planet (48)
I have 25 pound bags of cat food . Each serving is 1.8 from the bag. How many servings can you get?
Answer:
10 servings
Step-by-step explanation:
try your best
Answer:
13.8 servings
Step-by-step explanation:
25 divided by 1.8
What is the value of | 3 | (PLEASE HELPP!!)
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21
Complete question is;
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x² + 2x + 7 = 21 The number of positive solutions to this equation is . The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answer:
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is 2.87.
Step-by-step explanation:
We are given the quadratic equation as;
x² + 2x + 7 = 21
Subtract 21 from both sides to give ;
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
Using quadratic formula, we cam find the roots of the equation.
x = [-b ± √b² - 4ac]/2a
Plugging in the values;
x = [-2 ± √(2² - 4(1*-14))]/2(1)
x = [-2 ± √(4 + 56)]/2
x = [-2 ± √60]/2
x = - 4.87 or 2.87
Thus, this equation has only one positive solution which is the greatest.
Thus, greatest solution is 2.87
The diagram shows 2 different shapes ...................................................................................................................
Thanks in advance
Answer:
A) ?
B) Rhombus
Step-by-step explanation:
For A count the squares inside the shape. I am sorry I had to answer this quickly and did not have time time to count them, but that should be fairly straight forward.
B is Rhombus.
Answer:
P = 12
The height = 6
Base = 4
24*0.5 = 12
B = rhombus
Each of the following statements is true or false. Which statements are true?
A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.
Type your answer as an list, separated by commas. For example, if you believe statements A, C, and D are true, type A, C, D.
Answer:
B,D
Step-by-step explanation:
The true statements are given below.
The sum of the interior angles of a concave pentagon is $540^{\circ}.$The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.Why does the Pentagon have 5 sides?The land the Pentagon become first planned to head on become bordered on 5 aspects through roads, so the architects designed a five-sided building.
What is the Pentagon shape?A pentagon is a geometrical form, which has 5 facets and five angles. here, “Penta” denotes five, and “gon” denotes attitude. The pentagon is one of the forms of polygons. The sum of all the indoor angles for a normal pentagon is 540 ranges.
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evaluate 9+(-8)÷4+5(-2)-(-3)
Answer:
hi there
0
Step-by-step explanation
9+[(-8)÷4]+[5(-2)]-(-3)
9+[-2]+-10+3
7+-7
0
Answer:
-57
hope this helped correct me if i'm wrong
What is the midline equation of y = 8 cos (5pix+3pi/2)-9
Answer:
[tex]y = -9[/tex]
Step-by-step explanation:
The curve intersects the midline when effect of amplitude is annulled. The midline equation is of the form:
[tex]y = y_{o}[/tex]
The midline equation is:
[tex]y = -9[/tex]
If MH = 18cm and HA = 29cm, what is MA?
Answer:
The leg MA measures 22.7 centimeters.Step-by-step explanation:
Assuming that's about a right triangle, the image attached shows a representation of this problem.
We use the Pythagorean Theorem to find the missing leg, which we are gonna call [tex]y[/tex]
[tex]29^{2} =18^{2}+y^{2}\\y^{2}=29^{2}-18^{2}\\y=\sqrt{841 - 324} \approx 22.7 \ cm[/tex]
Therefore, the leg MA measures 22.7 centimeters.
describe the domain and range of y=2(3)^x-2+5
Answer:
Step-by-step explanation:
Answer:
the domain is "the set of all real numbers."
the range of the given function is (5, infinity)
Step-by-step explanation:
This is an exponential function. For the sake of clarity you must enclose "x - 2" inside parentheses: f(x) = 2(3)^(x-2). This function is defined for all real x-values, so the domain is "the set of all real numbers."
Focusing on (3)^x: This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0. The functions y = e^x and that of y = 3^x are always positive. Likewise in the case of f(x) = 2(3)^(x-2): the function is always positive. If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity). But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.
Thus, the range of the given function is (5, infinity).
In ΔIJK, the measure of ∠K=90°, KI = 3.8 feet, and JK = 6.7 feet. Find the measure of ∠I to the nearest degree.
Answer:
60
Step-by-step explanation:tanI=
adjacent
opposite
=
3.8
6.7
\tan I = \frac{6.7}{3.8}
tanI=
3.8
6.7
I=\tan^{-1}(\frac{6.7}{3.8})
I=tan
−1
(
3.8
6.7
)
I=60.44\approx 60^{\circ}
I=60.44≈60
∘
In a board game, each player must roll a number cube and spin a spinner. The number cube is labeled with the numbers 1 through 6 and the spinner consists of eight equal parts shown below. What is the probability you will roll a 5 and land on blue?
A: 1 over 12
B: 1 over 10
C: 5 over 12
D: 2 over 3
Answer:
i think it is 5/12???
I hope i am right :C, if not you can delete this answer
The function g(x) = x^3 has the point (-3, -27) on its graph. The function g(x) is:
even
odd
Answer:
Odd.
Step-by-step explanation:
You don't need the point, its pretty much useless.
If its even, when you plug -x into the equation, it will stay the same
If its odd, when you plug -x into the equation, the signs will change
g(x) = [tex]x^{3}[/tex]
Lets plug in -x.
g(x) = (-x)³
g(x) = -x³
The equation is different! That means the equation is odd!
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day. The table shows the amount of fiber Jodi has eaten today. How many more grams of fiber does she need to get the recommended daily amount of fiber?
The amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day.
The total amount of fiber Jodi took = 19 + 4 + 2(1) = 25 grams
1 gram = 1000 milligrams
25 grams = 25000 milligrams
The amount of fiber she needs to eat
= 31000 - 25000
= 6000 milligrams
or
= 6 grams
Thus, the amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
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PLEASE HELP
Which of the following lists is ordered from least to greatest?
Answer:
the selected list is correct
Step-by-step explanation:
Negative numbers with larger magnitudes are smaller in value, so -2 is less than -1.5.
A fraction is smaller in value if it has a smaller numerator and the same denominator. It is also smaller in value if it has the same numerator and a larger denominator.
2/5 is smaller than 3/4 because it has both a smaller numerator and a larger denominator. So the ordering of the positive numbers is 2/5, 3/4.
The ordering you want is the one checked.
In a classic prisoner's dilemma game with money for prizes, players who cooperate with each other both earn good prizes. If, however, your opposing player cooperates but you do not (the term used is defect), you receive an even bigger payout and your opponent receives nothing. If you cooperate but your opposing player defects, he or she receives that bigger payout and you receive nothing. If you both defect, you each get a small prize. Because of this, most players of such games choose to defect, knowing that if they cooperate but their partners don't, they won't win anything. The strategies of U.S. and Chinese students were compared. The researchers hypothesized that those from the market economy (United States) would cooperate less (i.e., would defect more often) than would those from the nonmarket economy (China). Defect Cooperate China 31 36 United States 41 14 What is/are the variable(s) in this study and, if appropriate, what are the levels of any variables you identified?
Answer:
Check the explanation
Step-by-step explanation:
a. there are two categorical variables here:
region with two level : China and US
and cooperation with two level : Defect and cooperate.
b. Chi-square test for association can be used here since the variables are categorical in nature.
Chi-Square Test for Association: C6, Worksheet columns
Rows: C6 Columns: Worksheet columns
defect cooperate All
China 31 36 67
39.54 27.46
US 41 14 55
32.46 22.54
All 72 50 122
Cell Contents: Count
Expected count
Pearson Chi-Square = 9.985, DF = 1, P-Value = 0.002
Likelihood Ratio Chi-Square = 10.231, DF = 1, P-Value = 0.001
The jogging track is 5/9 of a mile long. If Ashley jogged around it four times how far did she run
Answer:
20/9 mile
Step-by-step explanation:
idk pretty self-explanatory
A lending institution supplied the following data on loan approvals by four loan officers. Use α = .05 and test to determine whether the loan approval decision is associated with the loan officer reviewing the loan application.
Loan Approval Decision
Loan Officer Approved Rejected
Miller 24 16
McMahon 17 13
Lee 35 15
Sanchez 11 9
Answer:
As chi^2 < 7.815, and P > 0.05, we do not reject null hypothesis.
Thus, there is no significant evidence that the loan approval decision is not independent of the loan officer reviewing the loan application.
Step-by-step explanation:
Find the given attachment
Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the water level when the water is 6 m deep. (1 L = 1000cm^3)
Answer:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
Step-by-step explanation:
For a tank similar to a cylinder the volume is given by:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:
[tex] \frac{dV}{dt}= \pi r^2 \frac{dh}{dt}[/tex]
And solving for [tex]\frac{dh}{dt}[/tex] we got:
[tex] \frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}[/tex]
We need to convert the rate given into m^3/min and we got:
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]