Find area of a circle having a radius 10.5cm and a diameter 17.5cm
Answer:
110.5π
Step-by-step explanation:
The formula for the area of a circle is π r ²
R stands for radius. So, the radius is 10.5, you have to square it meaning 10.5 * 10.5.
110.5 and now you multiply by π so the answer is 110.5π
Hope this helps !!
-Ketifa
suppose two soccer teams consist of players with a combined average height of 66 inches. if team a has an average height of 68 inches and has twice as many members as team b, what is the average height of team b
Answer:
The average height of team b is 62 inches.
Step-by-step explanation:
Mean:
The mean of a data-set is the sum of all values in the data-set divided by the number of values, that is:
[tex]M = \frac{s}{n}[/tex]
Sum:
Team a: Mean of 68 inches, 2x members.
Team b: Mean of y inches, x members.
So
[tex]s = 68*2x + yx = x(136 + y)[/tex]
Number of athletes:
[tex]n = 2x + x = 3x[/tex]
What is the average height of team b?
[tex]66 = \frac{x(136+y)}{3x}[/tex]
[tex]66 = \frac{136 + y}{3}[/tex]
[tex]136 + y = 198[/tex]
[tex]y = 198 - 136 = 62[/tex]
The average height of team b is 62 inches.
Two minor league baseball players got a total of 390 hits. Washington had 2 more hits than Sanchez. Find the number of hits for each player.
Washington had
hits. Sanchez had
hits
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Answer:
Washington had 196 hitsSanchez had 194 hitsStep-by-step explanation:
Let s represent the number of hits Sanchez had. Then Washington had (s+2) hits, and their hit total was ...
s +(s+2) = 390
2s = 388 . . . . . . subtract 2
s = 194 . . . . . . . . divide by 2
Sanchez had 194 hits; Washington had 196.
the angle between two lines is 60 degree. if the slope of one of them is 1. find the slope of other line
Answer:
-3.73
Step-by-step explanation:
solution:
Given:
Angle between two lines=60⁰
slope of first line=1
Or, tanA=1
Or, A= tan inverse (1)
so, A=45⁰
so, angle of inclination of first line=45⁰
Now,
angle of inclination of second line= A+ 60⁰
= 45⁰+60⁰
=105⁰
so, slope of second line = tan105.
= -3.73
Complete the input-output table:
x 3x + 7
0
4
8
14
Step-by-step explanation:
When x = 0,
3x + 7
= 3 ( 0 ) + 7
= 0 + 7
= 7
When x = 4,
3x + 7
= 3 ( 4 ) + 7
= 12 + 7
= 19
When x = 8,
3x + 7
= 3 ( 8 ) + 7
= 24 + 7
= 31
When x = 14,
3x + 14
= 3 ( 14 ) + 14
= 14 ( 3 + 1 )
= 14 ( 4 )
= 56
a plane can fly 450 miles in the same time it takes a car to go 150 miles. if the car travels 100 mph slower than the plane, find the speed (in mph) of the plane
Answer:
The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Step-by-step explanation:
Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:
450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.
Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Russell is doing some research before buying his first house. He is looking at two different areas of the city, and he wants to know if there is a significant difference between the mean prices of homes in the two areas. For the 33 homes he samples in the first area, the mean home price is $168,300. Public records indicate that home prices in the first area have a population standard deviation of $37,825. For the 32 homes he samples in the second area, the mean home price is $181,900. Again, public records show that home prices in the second area have a population standard deviation of $25,070. Let Population 1 be homes in the first area and Population 2 be homes in the second area. Construct a 95% confidence interval for the true difference between the mean home prices in the two areas.
Answer:
The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
First area:
33 homes, mean of $168,300, standard deviation of $37,825. Thus:
[tex]\mu_1 = 168300[/tex]
[tex]s_1 = \frac{37825}{\sqrt{33}} = 6584.5[/tex]
Second area:
33 homes, mean of $181,900, standard deviation of $25,070. Thus:
[tex]\mu_2 = 1819000[/tex]
[tex]s_2 = \frac{25070}{\sqrt{32}} = 4431.8[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 168300 - 181900 = -13600[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqt{6584.5^2 + 4431.8^2} = 7937[/tex]
Confidence interval:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]\mu - zs = -13600 - 1.96*7937 = -29156.52 [/tex]
The upper bound of the interval is:
[tex]\mu + zs = -13600 + 1.96*7937 = 1956.52[/tex]
The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).
At Joe's Restaurant, 80 percent of the diners are new customers (N), while 20 percent are returning customers (R). Fifty percent of the new customers pay by credit card, compared with 70 percent of the regular customers. If a customer pays by credit card, what is the probability that the customer is a new customer?
Answer:
0.7407 = 74.07% probability that the customer is a new customer.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Pays by credit card
Event B: New customer.
Probability of a customer paying by credit card:
50% of 80%(new customers).
70% of 20%(regular customers). So
[tex]P(A) = 0.5*0.8 + 0.7*0.2 = 0.54[/tex]
Probability of a customer paying by credit card and being a new customer:
50% of 80%, so:
[tex]P(A \cap B) = 0.5*0.8 = 0.4[/tex]
What is the probability that the customer is a new customer?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.54} = 0.7407[/tex]
0.7407 = 74.07% probability that the customer is a new customer.
If f(x) = x
2−3x+1
x−1
find f(-1) and f(-3)
Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
Determine if the sequence below is arithmetic or
geometric and determine the common difference / ratio in
simplest form.
3, 8, 13, ..
(PLEASE HELPP)
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Answer:
arithmetic; common difference of 5
Step-by-step explanation:
It usually works well to check differences first. Here, they are ...
8 -3 = 5
13 -8 = 5
These are the same value, so the sequence is arithmetic with a common difference of 5.
Domain and range problem Help
Answer:
Range y≤-1
Domain all reals
Step-by-step explanation:
The range is the output values (y)
Y is less than or equal to -1
y≤-1
The domain is the values that the input can take
the arrows on the ends of the graph tells us x can take all real numbers
The range is the span of y-values. What is the smallest possible y-value and what is the largest possible y-value?
For this problem, the y-values start at -1 and decrease infinitely. Therefore, the range is y <= -1.
The domain is the span of x-values. What is the smallest possible x-value and what is the largest possible x-value?
For this problem, the parabola will keep expanding horizontally (or to the left and right). Therefore, the range is all real numbers.
Hope this helps!
SOMEONE HELP PLEASE ASAP PLES DONT LEAVE UR ANSWER AS AN IMAGE SOMETIMES I CANT SEE IMAGES. THANK YOU VERY MUCH! WILL MARK BRAINLIEST :)))
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Answer:
x = -2/5 or -1
Step-by-step explanation:
The last two terms of the expression on the left can be factored also.
(5x+2)² +3(5x+2) = 0
And the common factor can be factored out:
(5x+2)(5x +2+3) = 0
5(5x +2)(x +1) = 0
Solutions to the equation make the factors zero:
5x +2 = 0 ⇒ x = -2/5
x +1 = 0 ⇒ x = -1
The values of x that are solutions to the equation are x = -2/5 and x = -1.
_____
Once you realize that (5x+2) is a factor, you know one solution is x = -2/5. The rest is just fluff to find the second solution. It is not required in order to answer the question.
Select the correct answer.
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in by all, how many more games must it win to
finish the season with a 90% winning percentage?
A.12
B.14
C.15
D.27
Find the value of the variable y, where the sum of the fraction 2/y-3 and 6/y+3 is equal to the quotient.
PLEASE HELPPPPPPP NEED ASAPPPPPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRRRR
Answer:
Here we need to solve:
[tex]\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} }[/tex]
The sum of the fractions is equal to the quotient between the fractions.
Notice that the two values:
y = 3
y = -3
make the denominator equal to zero, so those values are restricted.
We can simplify the right side to get:
[tex]\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} } = \frac{2*(y + 3)}{6*(y - 3)} = 3*\frac{y + 3}{y - 3}[/tex]
Now we can multiply both sides by (y - 3)
[tex](y - 3)*(\frac{2}{y - 3} + \frac{6}{y + 3 }) = 3*(y + 3)\\2 + 6*\frac{y -3}{y + 3} = 3*(y + 3)[/tex]
Now we can multiply both sides by (y + 3)
[tex](2 + 6*\frac{y -3}{y + 3})*(y + 3) = 3*(y + 3)*(y + 3)[/tex]
[tex]2*(y + 3) + 6*(y - 3) = 3*(y + 3)*(y + 3)\\\\2*y + 6 + 6*y - 18 = 3*(y^2 + 2*y*3 + 9)\\\\8*y - 12 = 3*y^2 + 6*y + 33\\\\0 = 3*y^2 + 6*y + 33 - 8*y + 12\\\\0 = 3*y^2 - 2*y + 45[/tex]
First, let's see the determinant of that quadratic equation:
[tex]D = (-2)^2 - 4*3*45 = -536[/tex]
We can see that it is negative, thus, there are no real solutions of the equation.
Thus, there is no value of y such that the origina equation is true,
Answer:
y=15
Step-by-step explanation:
URGENT!!!!!! 15 POINTDS
Answer:
Option C
Step-by-step explanation:
thankful that there are graphing tools. see screenshot
A certain manufacturing process yields electrical fuses of which, in the long run
15% are defective. Find the probability that in a random sample of size n=10, fuses
selected from this process, there will be
(i) No defective fuse
(ii) At least one defective fuse
(iii) Exactly two defective fuses
(iv) At most one defective fuse
Answer:
i) 0.1969 = 19.69% probability that there will be no defective fuse.
ii) 0.8031 = 80.31% probability that there will be at least one defective fuse.
iii) 0.2759 = 27.59% probability that there will be exactly two defective fuses.
iv) 0.5443 = 54.43% probability that there will be at most one defective fuse.
Step-by-step explanation:
For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
15% are defective.
This means that [tex]p = 0.15[/tex]
We also have:
[tex]n = 10[/tex]
(i) No defective fuse
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
0.1969 = 19.69% probability that there will be no defective fuse.
(ii) At least one defective fuse
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We already have P(X = 0) = 0.1969, so:
[tex]P(X \geq 1) = 1 - 0.1969 = 0.8031[/tex]
0.8031 = 80.31% probability that there will be at least one defective fuse.
(iii) Exactly two defective fuses
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{10,2}.(0.15)^{2}.(0.85)^{8} = 0.2759[/tex]
0.2759 = 27.59% probability that there will be exactly two defective fuses.
(iv) At most one defective fuse
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
[tex]P(X = 1) = C_{10,1}.(0.15)^{1}.(0.85)^{9} = 0.3474[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1969 + 0.3474 = 0.5443[/tex]
0.5443 = 54.43% probability that there will be at most one defective fuse.
The diameter of the circle is 2”. What is the area of the circle
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
1. 2/2 =1 1 is the radius
2. [tex]A = \pi r^2[/tex]
3. [tex]A=\pi 1^2[/tex]
4. [tex]A=\pi[/tex]
The gross domestic product (GDP) of the United States is defined as
Answer:
the market value of all final goods and services produced within the United States in a given period of time.
3. line has undefined slope and passes through (1,8)
Answer: x = 1
Step-by-step explanation:
(any line with an undefined slope is a vertical line)
x = 1 has an undefined slope and passes through (1,8)
a.
What is 46.7% of
4/5?
Answer:
0.3736
Step-by-step explanation:
46.7 percent of [tex]\frac{4}{5}[/tex] is 0.3736.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.What is a fraction?A number is stated as a quotient in mathematics when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.Solution -To find 46.7% of [tex]\frac{4}{5}[/tex].
So,
[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]
[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]0.3736[/tex]
Therefore, 46.7% of [tex]\frac{4}{5}[/tex] is 0.3736.
Know more about percentages here:
https://brainly.com/question/24304697
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Use the figure to find y.
Tanθ =sin /cos
tan θ = 5/2 / y
tan (30°) = 5/2 /y
[tex]y = \frac{5 \sqrt{3} }{2} [/tex]
y=4.33
Help me! Thanks! Show work too! Please!
Answer:
(2, 79) (12, 24)
24-79/12-2=-55/10
m=-0.55
24=-6,6+b
30.6=b
y=-0.55x+30.6
Step-by-step explanation:
you multiply
using the equation to represent your answer
find two factors of the first number such that their product is the first number and their sum is the second number.
70,17
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Answer:
7, 10
Step-by-step explanation:
It often works well to look at the factor pairs that form the product.
70 = 1×70 = 2×35 = 5×14 = 7×10
The sums of these are 71, 37, 19, 17. The last pair of factors is the one of interest:
7 and 10.
HELP PLEASE BE CORRECT
Answer:
12
Step-by-step explanation:
Scale factor of 4
CD = 3
3 · 4 = 12
Length of C'D' is 12 units
Answer:
12 units
Step-by-step explanation:
The original segment CD = 3 units
Scale factor is 4.
3 x 4 = 12
PLEASE HELP
Identify the 15th term of the arithmetic sequence in which a. = 10 and ao = 20.
Answer:
The 15th term is 160
Step-by-step explanation:
The details are not clear. So, I will make the following assumptions
[tex]d = 10[/tex] ---- common difference
[tex]a_1 = 20[/tex] ---- first term
Required
The 15th term
This is calculated as:
[tex]a_{n} = a + (n - 1) * d[/tex]
Substitute 15 for n
[tex]a_{15} = a + (15 - 1) * d[/tex]
[tex]a_{15} = a + 14 * d[/tex]
Substitute values for d and a
[tex]a_{15} = 20 + 14 * 10[/tex]
[tex]a_{15} = 20 + 140[/tex]
[tex]a_{15} = 160[/tex]
Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
What is the other dimension of the rectangular cross section that is perpendicular to the base (the face that is shaded) and passes through the midpoints of the 10 cm edges?
________ centimeters by 18 centimeters
PLZ PLZ HELP
A rectangular prism with length of 10 centimeters, width of 8 centimeters, and height of 18 centimeters.
A. 2
B. 8
C. 10
D. 18
what's a divisor a dividend and a quotient
QUESTION 20
The patient's weight is 245 lbs. If the patient loses 1 kg every week for 5 weeks:
a. How much will the patient weight in pounds?
b. How much will the patient weight in kilograms?
.Answer:
The answer is below
Step-by-step explanation:
The patient loses 1 kg every week for 5 weeks.
1 kg = 2.2 lbs
Therefore the patient loses 2.2 lbs every week for 5 weeks.
a) The weight of the patient after 5 weeks = 245 lbs. - (5 weeks)(2.2 lbs per week)
The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.
b) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.
1 kg = 2.2 lbs.
234 lbs. = 234 lbs. * 1 kg per 2.2 lbs. = 106.36 kg
Why lines e and f must be parallel