Answer:
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Step-by-step explanation:
Represent the bus average speed with x and the motorcycle average speed with y
Given
[tex]x = y + 2[/tex]
Distance covered by bus = 165 miles
Distance covered by motorcycle in same time = 155 miles
Required
Determine the speed of each
Average Speed is calculated as;
[tex]Average\ Speed = \frac{Distance}{Time}[/tex]
Since the two are measured with the same time, represent time with T
For the bus
[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes
[tex]x = \frac{165}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{165}{x}[/tex]
For the motorcycle
[tex]y = \frac{155}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{155}{y}[/tex]
Since, T = T; we have that
[tex]\frac{165}{x} = \frac{155}{y}[/tex]
Cross Multiply
[tex]165y = 155x[/tex]
Substitute [tex]x = y + 2[/tex]
[tex]165y = 155(y+2)[/tex]
Open Bracket
[tex]165y = 155y - 310[/tex]
Collect Like Terms
[tex]165y - 155y = 310[/tex]
[tex]10y = 310[/tex]
Divide both sides by 10
[tex]y = 31[/tex]
Recall that [tex]x = y + 2[/tex]
[tex]x = 31 +2[/tex]
[tex]x = 33[/tex]
Hence;
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Find the area of the shaded regions:
area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$
so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$
$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$
abd there are 2 such arcs, so double the area.
[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]
Given:-Radius of the circle = 10 inchesAngle of each sector = 72°Number of sectors = 2To FinD:-Find the area of the shaded regions....?How to solve?For solving this question, Let's know how to find the area of a sector in a circle?
[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]
Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.
Solution:-We have,
No. of sectors = 2Angle of sector = 72°By using formula,
⇛ Area of shaded region = 2 × Area of each sector
⇛ Area of shaded region = 2 × Θ/360° × πr²
⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²
⇛ Area of shaded region = 2/5 × 100 × 22/7
⇛ Area of shaded region = 40 × 22/7
⇛ Area of shaded region = 880/7 inch. sq.
⇛ Area of shaded region = 125.71 inch. sq.
☄ Your Required answer is 125.71 inch. sq(approx.)
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60feet to meters plaese with work
Answer:
60 Feet = 18.288 Meters
Step-by-step explanation:
foot = 12 inch = 0.3048 m
0.3047 × 60
18.288 meters
is -54 rational number whole number or integersis
Answer:
-54 is a integer and rational number
Step-by-step explanation:
All human blood can be "ABO-typed" as O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here are the distributions of blood types for a randomly chosen person in China and in the United States:The probability O A B ABChinese 0.35 0.27 0.26 0.12American 0.45 0.4 0.11 0.04Suppose we randomly select an American and a Chinese, independently of each other, apply multiplication and addition probability rules, compute:a. Pr(They both have type O)b. Pr( they both have the same blood type)c. Pr( at least one person has type O)
Answer:
a. Pr(They both have type O)
= Pr(They both have type O)
= 0.35 x 0.45
= 0.1575 = 15.75%
b. Pr( they both have the same blood type)
= Pr( they both have the same blood type)
= 2/8
= 0.25 = 25%
c. Pr( at least one person has type O)
= Pr (at least one person has type O)
= 1 - 0.3575
= 0.6425 = 64.25%
Step-by-step explanation:
a) Data:
O A B AB
Chinese 0.35 0.27 0.26 0.12
American 0.45 0.4 0.11 0.04
b) Calculations:
i. Pr(They both have type O)
= Probability of Chinese with O multiplied by Probability of American with O
= 0.35 * 0.45
= 0.1575 = 15.75%
ii. Pr( they both have the same blood type)
= Probability of two out of 8 outcomes
= 2/8
= 0.25 = 25%
iii. Pr( at least one person has type O)
= Probability of (1 – p(none) )
The probability of none = p(none O blood type)
= p(none)
for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)
= 0.65 * 0.55 = 0.3575
Pr (at least one person has type O) = 1 - 0.3575
= 0.6425
What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24
Answer:
D question,somewhat confusing, itsit's like simultaneous equation,but values are different
Answer:
x = 4 + 2y/3
Step-by-step explanation:
An online polling site posed this question: "How much stock do you put in long-range weather forecasts?" Among its Web site users, 38, 528 chose to respond Complete parts (a) through (c) below.
a. Among the responses received, 3% answered with "a lot". What is the actual number of responses consisting of "a lot"?
b. Among the responses received, 18, 566 consisted of "very little or none". What percentage of responses consisted of "very little or none"?
c. Because the sample size of 38, 528 is so large, can we conclude that about 3% of the general population puts "a lot" of stock in long-range weather forecasts? Why or why not?
A. No, because the sample is a voluntary response sample, so the sample is not likely to be representative of the population.
B. Yes, because the sample is so large, the margin of error is negligible.
C. No, because even though the sample size is so large, there is still a margin of error.
D. Yes, because the sample size is large enough so that the sample is representative of the population.
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, N = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]
[tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).
Which of the following is an arithmetic sequence? A.-2, 4, -6, 8, ... B.2, 4, 8, 16, ... C.-8, -6, -4, -2, ...
Answer:
C. -8, -6, -4, -2, ...
Step-by-step explanation:
An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.
A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.
B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.
C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.
Hope this helps!
22. f(x) is stretched horizontally by a factor of 2 and reflected across the x-axis. Which choice shows the correct representation of f(x) after these transformations?
Options:
A. –f(1/2x)
B. f(–2x)
C. –f(2x)
D. f(–1/2x)
Answer:
A. -f(1/2 x)
Step-by-step explanation:
Reflextion about the x-axis is
f(x) -> -f(x)
and horizontal dilation is
f(x) -> f(-x/b) where b is the factor of dilation.
so the proper answwer is
A. -f(1/2 x)
A rectangle has an area of 81 square centimeters. Which of the following would be the rectangle's length and width? (Area = equals length×times width)
Answer:
length: 9cm
width: 9cm
Step-by-step explanation:
9×9=81
What does "C" represent and how do you evaluate this?
[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?
Answer:
We conclude that no more than 10% of its microwaves need repair during the first five years of use.
Step-by-step explanation:
We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.
In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.
Let p = population proportion of microwaves who need repair during the first five years of use.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that no more than 10% of its microwaves need repair during the first five years of use}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of microwaves who need repair during the first 5 years of use = 12%
n = sample of microwaves = 50
So, the test statistics = [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]
= 0.471
The value of z-test statistics is 0.471.
Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.
So, to answer the first question, [tex]6^2[/tex] is a perfect square.
(a,b,c) is a Pythagorean triple means the following
[tex]a^2+b^2=c^2[/tex]
Here, it means that
[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]
Thank you.
Answer:
Its B
Step-by-step explanation:
Help me and I will for real give u brainleist
should be 2 3 andd 5
think of the - (- as a plus sign (this is what i was always taught) to add them so it would in turn be (-5) + 12 which equals 7 and choice 3 and 5 also equal this
Shawna finds a study of American men that has an equation to predict weight (in pounds) from
height (in inches): y = -210 + 5.6x. Shawna's dad's height is 72 inches and he weighs 182 pounds.
What is the residual of weight and height for Shawna's dad?
a. 11.2 pounds
b. -11.2 pounds
c. 193.2 pounds
d. 809.2 pounds
Answer:
-11.2 pounds
Step-by-step explanation:
It is given that,
Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches):
y = -210 + 5.6x
Height of Shawna's dad is 72 inches
Weight is 182 pounds
We need to find the residual of weight and height for Shawna's dad.
Predicted weight of 72 inches men,
y' = -210 + 5.6(72)
y' = 193.2 pounds
So, residual is :
Y = 182 - 193.2
Y = -11.2 pounds
So, the residual of weight and height for Shawna's dad is -11.2 pounds.
Answer:
-11.2 pounds
Step-by-step explanation:
Got it right on the test.
F(x)=2x+6,g(x)=4x^2 find (f+g)(x)
Work Shown:
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 2x+6 + 4x^2
(f+g)(x) = 4x^2+2x+6
Find the rectangular coordinates of the point with the given polar coordinates.
Answer:
[tex]( - \sqrt{3} \: an d \: 1)[/tex]
Reduce the following fraction to lowest terms: 8/14
Answer:
4/7
Step-by-step explanation:
divide both by two for its simplest form
Answer:4/7
Step-by-step explanation
Divide both the numerator and denominator by 2
The result for the numerator is 8/2=4
that of the denominator is 14/2=7
Therefore the resultant answer is 4/7
A market survey shows that 50% of the population used Brand Z computers last year, 4% of the population quit their jobs last year, and 2% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting your job independent
Answer:
the events of using Brand Z computers and quitting your job are independent.
Step-by-step explanation:
Let A be the event that the population used Brand Z computers and let B be the event that the population quit their jobs.
We are told that 50% of the population used Brand Z computers last year. Thus, the probability of event A is;
P(A) = 50% = 0.5
Also, we are told that 4% of the population quit their jobs last year. Thus the probability of event B is;
P(B) = 4% = 0.04
Since 2% of the population used Brand Z computers and then quit their jobs. Then the probability of the population used Brand Z computers and then quit their jobs is;
P(A ∩ B) = 2% = 0.02
From the law of independent events, if A and B are to be independent events, then;
P(A ∩ B) = P(A) × P(B)
Thus;
P(A ∩ B) = 0.5 × 0.04 = 0.02
This is same value as what was given in the question, thus the events of using Brand Z computers and quitting your job are independent.
Consider the following. x = t2 − 2t, y = t5, 1 ≤ t ≤ 4 Set up an integral that represents the length of the curve. 4 1 dt Use your calculator to find the length correct to four decimal places.
Answer:
L ≈ 1023.0562
Step-by-step explanation:
We are given;
x = t² - 2t
dx/dt = 2t - 2
Also, y = t^(5)
dy/dt = 5t⁴
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt
L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt
L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt
Using online integral calculator, we have;
L ≈ 1023.0562
The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.
Given :
[tex]\rm x = t^2-2t[/tex][tex]\rm y=t^5[/tex][tex]\rm 1\leq t\leq 4[/tex]First, differentiate x and y with respect to 't'.
[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]
[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]
Now, determine the length of the curve using the below formula:
[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]
Now, substitute the value of the known terms in the above formula and then integrate it.
[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]
[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]
Now, simplify the above integration using the calculator.
L = 1023.0562
For more information, refer to the link given below:
https://brainly.com/question/18651211
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.
Answer:
60/220
Step-by-step explanation:
we use combination,
[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]
[tex]5 \times 4 \times 3 = 60[/tex]
then, all divided by,
[tex] (\frac{12}{3}) = 220 [/tex]
[tex]60 \div 220[/tex]
The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{5}{12}[/tex]
Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is
[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{11}[/tex]
Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{10}[/tex]
Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is
[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]
Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
Learn more about Probability:
https://brainly.com/question/795909
Find the interquartile range of the data in the dot plot below. players blob:mo-extension://5f64da0e-f444-4fa8-b754-95
Answer:
[tex]IQR=Q_{3}-Q_{1}[/tex]
Step-by-step explanation:
The inter-quartile range is a measure of dispersion of a data set.
It is the difference between the third and the first quartile.
[tex]IQR=Q_{3}-Q_{1}[/tex]
The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.
A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48 What is the length, x, of the garden?
Answer:
[tex]x {}^{2} - 2x = 48[/tex]
[tex]x { }^{2} - 2x - 48 = 0[/tex]
using quadratic formula,
[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]
[tex]2 + \sqrt{196} \div 2[/tex]
[tex]2 + 14 \div 2[/tex]
[tex]x = 8[/tex]
or
[tex]x = - 6[/tex]
If In (x) = 3.53, what is the value of x ?
Which point is located at (5, –2)?
Explanation:
The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).
Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.
Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.
You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.
Answer:
Point D is located at (5, -2)
Step-by-step explanation:
The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2
The length of a rectangle is a inches. Its width is 5 inches less than the length. Find the area and the perimeter of the rectangle.
Answer:
[tex]Area = 5a - a^2[/tex] [tex]inches\²[/tex]
[tex]Perimeter = 10\ inches[/tex]
Step-by-step explanation:
Given
Length = a
Width = 5 - a
Required
Determine the Area and Perimeter;
Calculating Area
Area is calculated as thus;
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = a * 5 - a[/tex]
[tex]Area = a * (5 - a)[/tex]
Open Bracket
[tex]Area = 5a - a^2[/tex]
Calculating Perimeter
Perimeter is calculated as thus;
[tex]Perimeter = 2 (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 (a + 5 - a)[/tex]
Collect Like Terms
[tex]Perimeter = 2 (5 + a- a)[/tex]
[tex]Perimeter = 2 (5)[/tex]
Open Bracket
[tex]Perimeter = 10\ inches[/tex]
On a class trip with 40 students, 14 are male. What percentage of the class is female?
66%
60%
65%
58%
Answer:
65%
Step-by-step explanation:
If 14 are male, then 26 are female.
To find the percent female, divide the number of females by the total.
26/40 = 0.65
So, the percentage of the class that is female is 65%
Answer:
C. 65%
Step-by-step explanation:
We know that of the 40 total students, 14 are male, which means the remaining students are female.
To find how many are female, we subtract 14 from 40:
40 - 14 = 26 females
Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:
(26 / 40) * 100 = 65
The answer is thus C, 65%.
~ an aesthetics lover
I need help ASAP THANK YOU
Answer:
174 cm²
Step-by-step explanation:
The figure given is a prism with isosceles trapezoid as base.
Its surface area can be calculating the area of each face that makes up the prism, and summing all together.
There are 6 faces. Their dimensions and areas can be calculated as follows:
2 isosceles trapezium:
It has 2 parallel bases, (a and b), of 4cm and 6cm,
Height (h) = 2.8cm
Area = ½(a+b)*h
Area = ½(4+6)*2.8
Area = ½(10)*2.8 = 5*2.8 = 14 cm²
4 rectangles of different dimensions:
Rectangle 1 (down face): l = 10cm, b = 4cm
Area = 10*4 = 40 cm²
Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm
Area = 2(l*b) = 2(10*3) = 60cm²
Rectangle 4 (top face) = l = 10cm, b = 6cm
Area = 10*6 = 60cm²
Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²
1.Write 32 1/2 in radical form
Answer:
√32
Step-by-step explanation:
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8