Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
PLS HELP ...... Urgently
Answer:
18+18 as point XYZ is in centroid of Q
Step-by-step explanation:
so it's equal.
36.which is option A.
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
5 (u + 1) -
7 = 3
3 (u - 1) + 2u
Correct Question:
5 (u + 1) - 7 = 3 (u - 1) + 2u.
Solve for u
Answer:
See explanation below
Step-by-step explanation:
In this given question, we are required to find u.
Given the equation:
5 (u + 1) - 7 = 3 (u - 1) + 2u
Required:
Solve for u
To find u, first simplify both sides individually.
Simply 5 (u + 1) - 7:
Expand the parenthesis:
5u + 5 - 7
Collect like terms:
5u - 2
Simplify 3 (u - 1) + 2u:
Expand the parenthesis:
3u - 3 + 2u
Collect like terms:
3u + 2u - 3
5u - 3
Bring both simplified equations together:
5u - 2 = 5u - 3
5u - 5u - 2 = -3
-2 = -3
Since -2 ≠ -3, there is no solution.
Therefore, we can say the equation is invalid.
What is the value of 3/4 increased by 2 1/6?
Answer:
2 11/12
Step-by-step explanation:
3/4 + 2 1/6
Add the fractions.
35/12
= 2 11/12
Answer:
[tex]2\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]
h(6)= ? I don't even know what the question is asking me to do
Answer:
h(6) = 8
Step-by-step explanation:
h(6) is find the value of the function when x=6
What is the y value ( the value of the blue line) when x=6
Go to x=6 and go up to the blue line
y =8
h(6) = 8
Answer:
8At X = 6 , h(X) = 8
plug the value of x
h (6) = 8
please see the attached picture..
Hope this helps...
Good luck on your assignment...
A newspaper reported that 4040% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 5050 adults. a. Identify the population of interest in this study. b. Identify the sample for the study. c. Identify the parameter of interest in the study. d. Find and interpret a 9595% confidence interval for the parameter of interest.
Answer:
a. Identify the population of interest in this study.
all the population of the countryb. Identify the sample for the study.
50 adults (the ones that were surveyed)c. Identify the parameter of interest in the study.
the parameter of interest is the people that believe that coffee shops are overpricedd. Find and interpret a 95% confidence interval for the parameter of interest.
z score for a 95% confidence level = 1.96
margin of error (E) = z score x √{[0.4(1 - 0.4)] / 50} = 1.96 x 0.069282 = 0.13579
95% confidence level interval:
0.4 - 0.13579 = 0.26421
0.4 + 0.13579 = 0.53579
95% confidence interval (0.26421 , 0.53579)
The length of human pregnancies from conception to birth varies accordingly to a distribution that is approximately normal with mean 266 days and standard deviation 16 days. a study enrolls a random sample or 16 pregnant women. what are the mean and standard deviation of the sampling distribution of Xbar? What is the probability the average pregnancy length exceed 270 days?
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.
a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:
[tex]\mu_x=\mu=266\ days[/tex]
The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]
b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x > 270 days:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]
The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%
Which of the following steps indicates the distributive property when solving –3(x + 2) = 21?
Question 4 options:
A)
–3x + 2 = 21
B)
–3x – 6 = 21
C)
D)
–3x – 6 = –63
Answer:
B) –3x – 6 = 21
Step-by-step explanation:
Well the distributive property is the multiplying of a number by more numbers in parenthesis.
For example -3(x + 2) by using the distributive property we get,
-3x - 6
Thus,
the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.
Hope this helps :)
When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.
What is distributive property?Distributive property explains us how to solve expressions in the form of a(b + c).
After apply distributive property this term convert as ab+ac.
The given expression is,
3(x + 2) = 21
To solve the expression, use distributive property,
According to distributive property,
a(b + c) changes in the form of ab+ac.
Solve for the given expression,
3x + 2×3 = 21
3x + 6 = 21
Solve for the value of x,
3x = 21 - 6
3x = 15
x = 5
Hence, option (C) is correct.
To know more about Distributive property on:
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Almost there, then everything is set! Thanks guys
Answer:
x = 50°
Step-by-step explanation:
Step 1.
180° - 80° (because there are 180 degrees in a triangle) = 100°
Step 2.
100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)
Step 3.
Answer: x = 50°
Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about the origin? A. (x,y)→(y,−x) B. (x,y)→(−y,−x) C. (x,y)→(y,x) D. (x,y)→(−x,−y)
Hey there! I'm happy to help!
If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒ (-x,-y).
Have a wonderful day! :D
Combine like terms: 10 + 6y + 2x - 3
Answer:
6y +2x +7
Step-by-step explanation:
10 + 6y + 2x - 3
The only like terms are the constant
6y+2x +10-3
6y +2x +7
Answer:
2x + 6y + 7.
Step-by-step explanation:
10 + 6y + 2x - 3
= 2x + 6y - 3 + 10
= 2x + 6y + 7.
Hope this helps!
evaluate 4! +!3 /2 8 10 or 15
Answer:
15
Step-by-step explanation:
4! +3! /2
4!=4*3*2*1=24
3!=3*2*1=6
24+6/2=30/2=15
Please answer this correctly without making mistakes
Answer:
2 km
Step-by-step explanation:
Since we know that the TOTAL distance from Kensington to Greenville is 4.3 km, and we also that the distance from Kensington to Springfield is 2.3 km, we can subtract these values to find the distance from Springfield to Greenville.
[tex]4.3-2.3=2[/tex]
I hope this helped!
Answer:
Simple math, different numbers.
Step-by-step explanation:
Take the total distance, 4.3
And subtract it from the given segment of the road.
4.3 - 2.3 = 2.0
So the distance between Springfield and Greenville is 2 kilometers.
find the lowest common denominator of 3/x^3y and 7/xy^4
[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]
It's xy.
The result of a biology test was collected, and the grades and gender are summarized below A B C Total Male 5 4 17 26 Female 6 2 15 23 Total 11 6 32 49 Let p p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents).
Answer:
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Step-by-step explanation:
| A | B | C | Total
Male | 5 | 4 | 17 | 26
Female | 6 | 2 | 15 | 23
Total | 11 | 6 | 32 | 49
If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
All female students = 23
Female students that score an A = 6
p = (6/23) = 0.2608695652 = 0.261
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (6/23) = 0.261
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.
we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 23 - 1 = 22.
Significance level for 99.5% confidence interval
(100% - 99.5%)/2 = 0.25% = 0.0025
t (0.0025, 22) = 3.119 (from the t-tables)
Standard error of the mean = σₓ = √[p(1-p)/N]
p = 0.261
N = sample size = 23
σₓ = √(0.261×0.739/23) = 0.091575
99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.261 ± (3.119 × 0.091575)
CI = 0.261 ± 0.2856
99.5% CI = (-0.0246, 0.5466)
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Hope this Helps!!!
SAT Scores Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of these high school seniors, those who are in the National Honor Society, is selected, would you expect the distribution of scores to have the same mean and standard deviation? Explain your answer.
Answer:
The distribution of scores would not have the same mean and standard deviation
Step-by-step explanation:
According to the given data we have the following:
mean=456
Standard deviation=100
mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed
Therefore, we can conclude that a subgroup of these high school seniors would not to be a perfect representation, hence, the distribution of scores would not have the same mean and standard deviation.
The measure of < A is 45 degree
We are given [tex]\triangle ABC \cong \triangle EFG[/tex]
The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure
angle A = angle E
3x+20 = 5x-80
3x-5x = -80-20
-2x = -100
x = -100/(-2)
x = 50
Use this x value to find the measure of angle A
angle A = 3x+20
angle A = 3(50)+20
angle A = 150+20
angle A = 170 degrees
Therefore, the statement "the measure of angle A is 45 degrees" is false.
Find the distance between the points X and Y shown in the figure.
Answer:
XY ≈ 14.87 units
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)
d = [tex]\sqrt{(8+6)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{14^2+(-5)^2}[/tex]
= [tex]\sqrt{196+25}[/tex]
= [tex]\sqrt{221}[/tex]
≈ 14.87 ( to 2 dec. places )
Jack is doing a test launch of his hovercraft for the upcoming STEM competition.
Answer:
The answer is missing.
I think there is something wrong with the equation on its own
Step-by-step explanation:
Equation for the hovercraft
F(x)= X²+6x+2
Olivia catapult equation
F(x)= √2x
Differential of the both equation will give the velocity at x time
F(x)= X²+6x+2
DF(x)/Dx= 2x +6
F(x)= √2x
F(x)= (2x)^½
DF(x)/Dx= (2x)^-½
So the differential is the velocity of the both equation.
Let's equate both equation to find the value of x at which they have same velocity.
(2x)^-½=- 2x+6
(2x)^-1= (-2x+6)²
(2x)^-1= 4x² -24x +36
0= 8x³ - 48x² +72x -1
The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
t the end of the past month the cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500. What was the balance in the Cash account at the beginning of last month?
Answer:
In this question it is given that:
The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.
And we have to use the formula
Substituting the values , we will get
Therefore beginning cash balance is
Find the reciprocal of 5/6, b≠0
Answer:
6/5
Step-by-step explanation:
The reciprocal of 5/6 means flip it
6/5
Answer:
6/5
Step-by-step explanation:
The reciprocal of a fraction is switching the numerator with denominator.
5/6 ⇒ 6/5
i give you a tricky one Express 108 ×125as a product of prime factors in exponential form
Answer:
[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]
Step-by-step explanation:
To express the given product (108 X 125) as a product of prime factors
Step 1: Express each of the numbers as a product of its prime factors.
[tex]108=2^2 \times 3^3\\125=5^3[/tex]
Step 2: Write the product together, and combine any like terms if any
Therefore,
[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]
Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.)
sinh(0.4) ≈ 1 − (0.4)^2 / 2! + (0.4)^2 / 4!
R4 ≤
R4 =
Specifically what does R4 equal.
Answer:
R4 ≤ 0.00008
R4 = 0.00001
Step-by-step explanation:
Given: sinh( 0.4 ) ≈ [tex]1 - \frac{(0.4)^2}{2!} + \frac{(0.4)^2}{4!}[/tex]
using Taylor's Theorem
R4 ≤ 0.00008
R4 = 0.00001
attached is the detailed solution
2.CommerceThe weight distribution of parcels sent in a certain manner is normal with meanvalue 12 pounds and standard deviation 3.5 pounds. The parcel service wishes to establish aweight valuecbeyond which there will be a surcharge. What value ofcis such that 99% ofall parcels are under the surcharge weight
Answer:
the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Step-by-step explanation:
Given that :
The mean value [tex]\mu[/tex] = 12
The standard deviation [tex]\sigma[/tex] = 3.5
Let Consider Q to be the weight of the parcel that is normally distributed .
Then;
Q [tex]\sim[/tex] Norm(12,3.5)
The objective is to determine thewight value of c under which there is a surcharge
Also, let's not that 99% of all the parcels are below the surcharge
However ;
From the Percentiles table of Standard Normal Distribution;
At 99th percentile; the value for Z = 2.33
The formula for the Z-score is:
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]
2.33 × 3.5 = X - 12
8.155 = X - 12
- X = - 12 - 8.155
- X = -20.155
X = 20.155
the weight value of c under which there is a surcharge = X + 1 (0) since all the pounds are below the surcharge
c = 20.155 + 1(0)
c = 20.155
Thus ; the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Chapter: Simple linear equations (Answer in steps)
Step-by-step explanation:
5) a. x/2 = 7-5
x/2 = 2
x = 2×2
x=4
b.4x - 2 = 3x +7
4x - 3x = 7 + 2
x = 9
c. x+2 = 42 × 3
x+2 = 126
x = 124
d. 13x + 260 = 39
13x = 39 - 260
13x = -221
x = -17
6) a. 6x / 7 = 4 +2
6x = 6 × 7
6x = 42
x = 7
b. -49 = 7x + 7
-49 - 7 = 7x
7x = - 56
x = -8
c. -7 + 7x - 21 = 0
7x - 28 = 0
7x = 28
x = 4
d. 8x - 32 + 2 = 42
8x - 30 = 42
8x = 42 + 30
8x = 72
x = 9
e. 5x + 7 = 18
5x = 11
x = 2.5
Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is the largest data value. D. The mean does not represent the center because it is not a data value. E. There is no mean age.
Answer:
A. The mean represents the center.
A. The median represents the center.
B. The mode does not represent the center because it is the smallest data value.
Step-by-step explanation:
Mean
(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2
The mean 9.2 and it represents the center of data.
Median
By arranging the set of data, the median, the median is the center number
8,8,8,8,8,8,(9),9,9,10,11,12,12
The median is 9 and it represents the center of data.
Mode
The mode is the number that appears most in the set of data.
The number that appears most in the set of data is 8 and does not represent the set of data.
Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Given the following data set:
9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11
Let's find the mean, median, and mode.
Mean of the data set:
Mean = sum of all values / number of values
Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]
Mean = [tex]\frac{120}{13} = 9.2[/tex]
Median of the data set:
Order the data from the least to the greatest then find the middle value.
Thus:8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12
The middle value is 9.
The median = 9Mode of the data set:
The mode = the data value that appears most
8 appeared the most, therefore, the mode = 8
If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.
In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Learn more here:
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The sample consisted of 55 night students, with a sample mean GPA of 2.3 and a standard deviation of 0.02, and 50 day students, with a sample mean GPA of 2.35 and a standard deviation of 0.08. The test statistic is: (to 2 decimals)
Answer:
-4.30
Step-by-step explanation:
The computation of the test statistic is shown below:
Data are given in the question
Sample = 55 night students
Sample mean = 2.3
Standard deviation = 0.02
Sample = 50 day students
Sample mean = 2.35
Standard deviation = 0.08
Based on the above information, the test statistic is
[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma _1^2}{n_1} + {\sqrt{\frac{\sigma _2^2}{n_2}}}}}[/tex]
[tex]z = \frac{2.3 - 2.35}{\sqrt{\frac{(0.02)^2}{55} + {\sqrt{\frac{(0.08)^2}{50}}}}}[/tex]
= -4.30
Hence, the test statistic is -4.30
Find the value of x. Give reasons to justify your solution. D ∈ AC
Answer:
x = 25°
Step-by-step explanation:
From the picture attached,
Since AE║BC and AC is a transverse,
Therefore, ∠EAC ≅ ∠BCA [Alternate interior angles]
m∠EAC = m∠BCA = x°
∠BCD = ∠DCB + ∠DBC [Since ∠BCD is an exterior angle of ΔBDC]
m∠BCD = m∠DCB + m∠DBC
50° = x° + x°
2x = 50
x = 25°
Therefore, value of x is 25°.
Answer: 25 degrees
Step-by-step explanation: