Answer:
B and DStep-by-step explanation:
This equation is true in either case, because the expression [tex]\sqrt{2x} +3[/tex] is equivalent to itself, that means the equation is true for all positive real numbers including the zero.
Therefore, the right answers are B and D, both numbers are true solutions of the expression.
Answer:
A: x=1/2 is an extraneous solution.
Step-by-step explanation:
Elif is arranging 28 chairs in rows in a room. Each row must be the same
length. The room is wide enough to make a row of 9 chairs, but no more
The room is deep enough to make 8 rows, but no more. What are the
possible numbers of rows and chairs in each row that Elif can make?
Answer:
Hey there!
Elif can only arrange the chairs like: 4 by 7, and 7 by 4.
Hope this helps :)
You can retry this question below
A6 inch personal pizza has 610 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices.
Estimate the number of calories in one slice of a 12 inch pizza.
Answer:
305 calories, 120 from fat
Step-by-step explanation:
The ratio of the area of the larger pizza to that of the smaller pizza is the square of the ratio of the diameters. So, the larger pizza has an area that is ...
(12/6)² = 4
times that of the smaller pizza. When that area is divided into 8 parts, each part has an area that is 4/8 = 1/2 the area of the smaller pizza.
We expect a slice of the larger pizza to have 1/2 the calories of a smaller pizza, so 305 calories, 120 from fat.
__
610/2 = 305; 240/2 = 120.
Solve 56000(1+1.8%)^5
Answer:
The solution to this expression is 61,224.74
Step-by-step explanation:
To solve we initially have to convert the percentage to a decimal:
[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]
So
56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74
The solution to this expression is 61,224.74
A right triangle has two shorter sides that differ in length by 7cm. The length of the
hypotenuse is 8 cm longer than the shortest side. Find the lengths of the three sides.
Show all of your steps.
Pls help!!! 75 points
Answer:
a = 5
b = 12
c = 13
Step-by-step explanation:
a^2+b^2=c^2
b-a=7(b=a+7)
c=a+8
Then, substitute
a^2+((a+7)*(a+7))=c^2
a^2+a^2+7a+7a+49=c^2
2a^2+14a+49=c^2
Because c = a+8
2a^2+14a+49=(a+8)(a+8)
2a^2+14a+49=a^2+16a+64
a^2-2a=15
a^2-2a-15=0
(a-5)(a+3)=0
a = 5,-3
a = 5(a side cannot be negative)
Plug in a=5 to the other equations to get
a = 5, b = 12, c = 13
Hope it helps <3
Answer:
The lengths of the sides are 5, 12, 13.
Step-by-step explanation:
In a right triangle, the two shorter sides are the legs. The longest side is the hypotenuse.
Let the shorter leg = x.
The longer leg is 7 cm longer, so its length is x + 7.
The length of the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8.
The lengths are:
x, x + 7, x + 8
Since the triangle is a right triangle, we can use the Pythagorean theorem.
a^2 + b^2 = c^2
x^2 + (x + 7)^2 = (x + 8)^2
Square the trinomials.
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
Combine like terms and place them all on the left side equaling zero.
x^2 - 2x - 15 = 0
Factor the left side.
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Since the length of a side of a triangle cannot be negative, we discard the solution x = -3.
x = 5
x + 7 = 5 + 7 = 12
x + 8 = 5 + 8 = 13
Answer: The lengths of the sides are 5, 12, 13.
Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation to enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution.
Answer:
x=½
y=5
Step-by-step explanation:
(8x+7y=39)2
16x+14y=78
4x-14y=-68 add the two equations
20x=10.
divide both sides by 20
x=½
8x+7y=39
4+7y=39
7y=39-4
7y=35
y=5
The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.
8x + 7y = 39
4x – 14y = –68
Multiply the first equation to enable the elimination of the y-term:Multiply by 2
16x + 14y = 78
Add the equations to eliminate the y-terms:-14y + 14y = 0
4x + 16x = 20x
-68 + 78 = 10
Solve the new equation for the x-value20x = 10
x = 1 / 2
Substitute the x-value back into either original equation to find the y-value8(1 / 2) + 7y = 39
4 + 7y = 39
7y = 35
y = 35 / 7
y = 5
learn more on system of equation here: https://brainly.com/question/3861421?referrer=searchResults
Find the measure of each angle: Supplementary angles with measures (2x+3)° and (3x+2)°.
Answer: 73 degrees and 107 degrees.
Step-by-step explanation:
The total of supplementary angles are 180 degrees. So you add 2x+3 and 3x+2. Then you get 5x+5=180.
Subtract 5 from both sides. Now the equation is 5x=175.
Divide 5 on each side. x=35
Replace x with 35 in the equations. The angles are 73 and 107.
They both add up to 180 degrees so it is correct.
The public radio show "A Prairie Home Companion," features news from the fictional town of Lake Wobegon, MN, home to many Norwegian bachelor farmers, and where "all the women are strong, all the men are good looking, and all the children are above average." Suppose average means average for the town. Such a town could not possibly exist, because (select all that apply)
a. not all women are strong
b. not all the children can be above average
c. not all Norwegian bachelor farmers are good looking
d. half the children must be below average
Answer:
b. not all the children can be above average
d. half the children must be below average
Step-by-step explanation:
In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.
Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.
Therefore, the correct answers are:
b. not all the children can be above average
d. half the children must be below average
Answer:
Second and last options are correct choices.
Step-by-step explanation:
If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.
Best Regards!
rounded to the nearest whole, what is the radius length if minor arcYZ = 12 and angleYXZ is one-third of a full circle? (i guessed it idk if it’s right)
Answer:
Option (1)
Step-by-step explanation:
Since the length of arc YZ = 12 units
m∠YXZ = one third of the full circle = [tex]\frac{360}{3}[/tex] = 120°
From the formula of arc length,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = Central angle subtended by the arc
r = radius of the circle
By substituting these values in the formula,
12 = [tex]\frac{120}{360}(2\pi r)[/tex]
12 = [tex]\frac{2}{3}\pi r[/tex]
[tex]18=\pi r[/tex]
r = [tex]\frac{18}{\pi }[/tex]
r = 5.73
r ≈ 6 units
Therefore, Option (1) will be the answer.
What is the equation of the line ( -4,8 ) ( 0,0 )
Answer:
Step-by-step explanation:
First you need to find the slope of the line that contains those 2 points.
[tex]m=\frac{0-8}{0-(-4)}=\frac{-8}{4}=-2[/tex]
So the slope is -2. Now we can pick one of those points and sub it into the point-slope formula to find the equation:
y - 0 = -2(x - 0) gives us an equation of
y = -2x
The relative frequency distribution of the number of phobias reported by a hypothetical sample of 500 college students is given as follows.
0–2 0.48
3–5 0.26
6–8 0.12
9–11 0.09
12–14 0.05
Required:
a. What is the probability that a college student expresses fewer than three phobias?
b. What is the probability that a college student expresses more than eight phobias?
c. What is the probability that a college student has between 3 and 11 phobias?
Answer:
a. 0.48
b. 0.14
c. 0.47
Step-by-step explanation:
Data provided in the question
0 - 2 0.48
3 - 5 0.26
6 - 8 0.12
9- 11 0.09
12- 14 0.05
Based on the above information
a. The probability for fewer than three phobias is
= P( x < 3)
= 0.48
b. The probability for more than eight phobias is
= P( x >8)
= 0.09 + 0.05
= 0.14
c. Probability between 3 and 11 phobias is
= P(3 < x < 11)
= 0.26 + 0.12 + 0.09
= 0.47
Select all numbers that are in the range.
-3
-2
-1
0
1
2
-2
0
2
Answered on edge
Answer:
-2, 0, 2
Step-by-step explanation:
edge 2020
The Nielsen Company reported that U.S. residents aged 18 to 24 years spend an average of 32.5 hours per month using the Internet on a computer.13 You wonder if this it true for students at your large university because so many students use their smartphones to access the Internet. You collect an SRS of n=75 students and obtain ¯x=28.5 hours with s=23.1 hours.
Required:
a. Report the 95% confidence interval for μ, the average number of hours per month that students at your university use the Internet on a computer.
b. Use this interval to test whether the average time for students at your university is different from the average reported by Nielsen. Use the 5% significance level. Summarize your results.
Answer:
a) [tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
b) For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
Step-by-step explanation:
Information given
[tex]\bar X=28.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=23.1 represent the sample standard deviation
n=75 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=75-1=74[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] and the critical value would be [tex]t_{\alpha/2}=1.993[/tex]
Now we have everything in order to replace into formula (1):
[tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
Part b
For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
Use x=1 to identify the value of each expression.
Answer:
[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]
Phoenix hiked the Rocky Path Trail last week. It took four days to complete the trip. The first two days she hiked a total of 26 miles. The second and third days she averaged 12 miles per day. The last two days she hiked a total of 28 miles. The total hike for the first and third days was 22 miles. How many miles long was the trail?
Answer:
50 miles
Step-by-step explanation:
let he hiked a,b,c and d miles on each of the four days respectively.
then, according to the question.
a+b=26...i
b+c= 24...ii
c+d=28...iii
a+c=22...iv
now, adding i,ii,iii,iv we get
2(a+b+c+d) = 100
a+b+c+d= 50 miles.
Hence, he traveled in all 50 miles.
Teresa is investigating if grade level has any effect on time spent studying. What is the response variable?
Answer:
The time spent studying is the response variable.
Step-by-step explanation:
The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable. In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.
The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.
PLEASE HELP!!!!!! Find common difference
Answer:
d = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference , thus
a₇ = a₁ + 6d
a₄ = a₁ + 3d
Given a₇ - 2a₄ = 1 , then
a₁ + 6d - 2(a₁ + 3d) = 1, that is
a₁ + 6d - 2a₁ - 6d = 1
- a₁ = 1 ( multiply both sides by - 1 )
a₁ = - 1
Given a₃ = 0 , then
a₁ + 2d = 0 , thus
- 1 + 2d = 0 ( add 1 to both sides )
2d = 1 ( divide both sides by 2 )
d = [tex]\frac{1}{2}[/tex]
what is the length of ac? a)96 b)132 c)72 d)136
Answer:
show a picture
Step-by-step explanation:
You and 3 of your friends decide to sell lemonade around town, and then split the money you make evenly. You decide to sell each cup of lemonade for 50 cents. In total, you all sell 120 cups of lemonade. How much money will each of you earn? Write an expression for the problem too.
Expression:
Answer:
$15
Step-by-step explanation:
Each cup is 50 cents which is basically $0.50
Multiply $0.50 by 120= $60
Because you and your three friends equal 4 total people,
divide 60 by 4 to get your own profit:
60/4=15
what is the solution set of y= x^2+2x+7 and y= x+7 ?
Answer:
(-1, 6)
(0, 7)
Step-by-step explanation:
Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.
Pleaseeeeeee helppppppp
Answer:
[tex]\boxed{Option \ D}[/tex]
Step-by-step explanation:
The combination of a rational number (3) and an irrational no. ([tex]4i[/tex]) is called a complex number.
So,
[tex]3+4i[/tex] is a complex no.
Answer:
D. Complex number.
Step-by-step explanation:
This number is not irrational, since 3 is rational.
The number is not entirely rational, since 4i is irrational.
The number is not real because i is not real.
So, the number is a Complex number, since it includes both real and nonreal numbers.
Hope this helps!
What is the measure of C?
Answer:
C.) 60°
Step-by-step explanation:
The triangle is an equilateral triangle. So that means that all the angles measure the same. And we have to remember that a triangle always equals 180°
So, to find out the measure of an angle. We must divide 180 by 3. Which is 60
=60°
Hope this helps you out! : )
38â% of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball. Complete partsâ (a) throughâ (d) below.(a) Find the mean of the binomial distribution.
μequals= ( ) (Round to the nearest tenth asâ needed.) â
(b) Find the variance of the binomial distribution.
sigmasquared= ( ) â(Round to the nearest tenth asâ needed.)
â(c) Find the standard deviation of the binomial distribution.
sigma = ( ) (Round to the nearest tenth asâ needed.) â
(d) Interpret the results in the context of theâ real-life situation.
Onâ average ( ) out of 6 women would consider themselves baseball fans. The standard deviation is ( ) âwomen, so in most samples of 6â women, the number of women who consider themselves baseball fans would differ from the mean by no more than ( ).â(Type integers or decimals rounded to the nearest tenth asâneeded.)
Answer:
a) 2.3
b) 1.4
c) 1.2
d) On average, 2.3 out of 6 women would consider themselves baseball fans. The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.
Step-by-step explanation:
For each woman, there are only two possible outcoes. Either they are a fan of professional baseball, or they are not. The prbability of a woman being a fan of professional baseball is independent of other woman. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
38% of women consider themselves fans of professional baseball.
This means that [tex]p = 0.38[/tex]
Six women are sampled:
This means that [tex]n = 6[/tex]
(a) Find the mean of the binomial distribution.
[tex]E(X) = np = 6*0.38 = 2.3[/tex]
(b) Find the variance of the binomial distribution
[tex]V(X) = np(1-p) = 6*0.38*0.62 = 1.4[/tex]
(c) Find the standard deviation of the binomial distribution.
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6*0.38*0.62} = 1.2[/tex]
(d) Interpret the results in the context of theâ real-life situation.
On average, 2.3 out of 6 women would consider themselves baseball fans. The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.
a box is filled with chocolates and its mass is 480g. The same box is now filled with mints and its mass is 350g. The chocolates weigh twice as much as the mints. what is the mass of the box
Answer:
The box weighs 220 grams.
Step-by-step explanation:
Since the box full of chocolates weighs 480 grams, and the same box full of mints weighs 350, the weight difference between them is 130 grams. According to the statement, the quantity of chocolate weighs twice that of mint, while the weight of the box does not vary.
Therefore, since chocolate weighs twice as much as mints, and the weight is reduced by 130 grams, that is the difference in weight between the two, with which chocolate weighs 260 grams and mints 130 grams.
Therefore, the box weighs 220 grams: 220 + 130 = 350, and 220 + 260 = 480.
What is the slope of the line between (−4, 4) and (−1, −2)?
Answer:
-2
Step-by-step explanation:
The slope of a line is
m = (y2-y1)/(x2-x1)
= (-2 -4)/(-1 - -4)
= -6/ ( -1 +4)
= -6 /3
=-2
Answer:
[tex]= - 2 \\ [/tex]
Step-by-step explanation:
[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]
Now let's find the slope
[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]
hope this helps you.
brainliest appreciated
good luck! have a nice day!
If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 40
Answer:
1.79% probability that the number of times that the coin lands tails will be less than 40
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
100 times
[tex]n = 100[/tex]
Then
[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]
What is the probability that the number of times that the coin lands tails will be less than 40
Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39.5 - 50}{5}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
1.79% probability that the number of times that the coin lands tails will be less than 40
Draw a graph of f(x) =3^-x+3
Answer:
Use a graphing calc or desmos
Step-by-step explanation:
What is the solution to the system of equations below? HELP!!!! y = negative one-fourth x + 2 and 3 y = negative three-fourths x minus 6 no solution infinitely many solutions (–16, 6) (–16, –2)
Answer:
No solution
Step-by-step explanation:
Step 1: Write out equations
y = -1/4x + 2
3y = -3/4x - 6
Step 2: Substitution
3(-1/4x + 2) = -3/4x - 6
Step 3: Distribute
-3/4x + 6 = -3/4x - 6
From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.
Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.
Answer:
No solution
Step-by-step explanation:
y = -1/4x + 2
3y = -3/4x - 6
Plug y as -1/4x + 2 in the second equation.
3(-1/4x + 2) = -3/4x - 6
-3/4x + 6 = -3/4x - 6
-3/4x + 3/4x = -6 -6
0 = -12
No solution.
In a 2-card hand, what is the probability of holding only face cards?
Answer:
12
Step-by-step explanation:
( J , Q, K 4 each)
so prob that for 2 cards, both cards are face
= C(12,2)/C(52,2) = 66/1326 = 11/221
3. What is the explicit formula for the arithmetic sequence 2, 7, 12, 17, ...?
Step-by-step explanation:
The given sequences are;
2,7,12,17......
difference =5
by using formula,
we get,
tn=a+(n-1)d
tn= 2+(n-1)5
Therefore, tn is 5n-3 is required formula for this arithmetic sequences.
Hope it helps....
Find the radius of the cylinder when volume is 304 cm^3 and height is 10 cm
Answer:
3.11 cmsolution,
Volume of cylinder=304 cm^3
height=10 cm
Radius=?
Now,
[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]
Hope this helps..
Good luck on your assignment..