Answer:
There is not a convincing statistical evidence, at the significance level of a = 0.05, that the manager's belief is correct.
As the null hypothesis maybe false accepting it makes a type II error.
Step-by-step explanation:
Let the null and alternate hypotheses be
H0: p ≤ 0.4 vs Ha : p>0.4
q= 1-p= 1-0.4= 0.6
The significance level alpha is 0.05
The critical region for one tailed test is Z> ± 1.645
The sample proportion is p^= x/n= 38/90=0.42222
Using the z statistic
z= p^- p/ √pq
z= 0.422-0.4/ √0.4*0.6
z= 0.04536
Since the calculated value of z= 0.04536 does not lie in the critical region Z> ± 1.645 we fail to reject null hypothesis.
There is not sufficient evidence to support the manager's claim.
Type I error is when we reject the true null hypothesis .
Type II error is when we accept the false null hypothesis .
As the null hypothesis maybe false accepting it makes a type II error.
There is not enough statistical evidence that the managers' claim is true.
What is the z test statistic for one sample proportion?Suppose that we have:
n = sample size[tex]\hat{p}[/tex] = sample proportionp = population proportion (hypothesised)Then, the z test statistic for one sample proportion is:
[tex]Z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
What are type I and type II errors?The Type I error is false positive (returning the test result as positive, which means, rejecting the null hypothesis(conclusion of rejection of null hypothesis is called positive test result) when its incorrect).
The Type II error is false negative (returning the test result as negative, which means, accepting the null hypothesis(assuming negative test result, so no flaw in null hypothesis from the perspective of test) when its wrong).
For this case, we've got:
Assumption by manager = Population proportion of repurchase by customers > 0.4Sample size = n = 90Sample proportion of repurchase = 38/90 ≈ 0.422Level of significance = α = 0.05The hypotheses for test would be:
Null hypothesis: Manager is not correct(nullifies managers' assumption): [tex]H_0: p \leq 0.4[/tex] (p is population proportion of repurchasing customers)Alternate hypothesis: Managers' assumption is true: [tex]H_1: p > 0.4[/tex]It is single tailed.
At the level of significance 0.05, for single tail, the critical value of Z test statistic is found to be [tex]Z_{\alpha/2} = \pm1.645[/tex]
The z test statistic for one sample proportion is:
[tex]Z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
We test null hypothesis, according to which p is 0.4 or less, so we get:
[tex]Z \approx \dfrac{0.422- 0.4}{\sqrt{\dfrac{0.4(1-0.4)}{90}}} \approx \dfrac{0.022}{\sqrt{0.00267}} \approx 0.426 < |Z_{\alpha/2}| = 1.645[/tex]
Thus, we accept the null hypothesis (we do so when [tex]Z < |Z_{\alpha/2}|[/tex] )
Therefore, there is not enough statistical evidence that the managers' claim is true.
Thus, here, we get:
Type I error: Rejecting the fact that manager's claim is wrong(and thus accepting that manager's claim is right) when actually manager's claim is wrong.Type II error: Accepting the fact that manager's claim is wrong(and thus rejecting that manager's claim is right) when actually manager's claim is right.Learn more about type I and type II errors here:
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If you know how to solve this, Please answer it. Thank You
Please show your work and the steps.
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answer:
2 Step-by-step explanation:
in the places there is X you put -3 , -3 squared minus 7 is equal to 9 , 9-7 is equal to 2
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
We're provided : F ( x ) = x² - 7 & we're asked to evaluate F ( - 3 ).All you need to do is to assume the value of x as ( - 3 ).[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]
When x = ( - 3 ) ,[tex] \large{ \tt{⋆ \: f( - 3) = {( - 3)}^{2} - 7}}[/tex]
[tex] \large{ \tt{↦ \: f( - 3) = ( - 3) \times ( - 3) - 7}}[/tex]
Multiplying a negative integer by a negative integer gives a positive integer![tex] \large{ \tt{↦f( - 3) = 9 - 7}}[/tex]
[tex]↦ \large{ \tt{f( - 3) = \boxed{ \tt{2}}}}[/tex]
Hence , F ( - 3 ) = 2 .[tex] \tt{✺ \: COMFORT \: IS \: THE \: ENEMY \: OF \: ACHIEVEMENT\: ♪}[/tex]
♡ Hope I helped! ♕
☃Have a wonderful day / evening ! ☼
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How do you apply frequency distribution table in real life?
Answer:
As a statistical tool, a frequency distribution provides a visual representation for the distribution of observations within a particular test. Analysts often use frequency distribution to visualize or illustrate the data collected in a sample.
What is the solution to this system of equations?
There is no solution.
Step-by-step explanation:
Given:
y = 2x + 1
4x - 2y = 4
Substitute y = 2x + 1 into 4x - 2y = 4
4x - 2(2x + 1) = 4
4x - 4x - 2 = 4
0x = 4 + 2
0x = 6
Anything to the multiple of zero is zero. Hence 0x = 0, and 0 ≠ 6
So there is no solution to the equation.
If correct ill give brainly
Answer:
Hello! answer: x = 16
Step-by-step explanation:
16 × 16 = 256
12 × 12 = 144
256 + 144 = 400
√400 = 20 therefore x = 16 hope that helps!
Answer:
23
Step-by-step explanation:
Tiger Woods's agent earns $2,000 per week plus 25% commission on all of Tiger's
earnings. Last week, Tiger earned $81,718. How much money did the agent make?
a) $20,429.50
b) $22,429.50
c) $63,288.50
d) $104,147.50
3
Select the correct answer.
Cora, her sister, and four friends are going to share a bag of candy equally. There are 120 candies in the bag. How many candles will each person
get?
OA 20
OB. 24
OC. 30
Reset
Next
21 Edmentum. All rights reserved.
Cora, her sister, and four friends. So there are 6 people, 120 candies are divided equally in the bag, so each person gets 20 candies
Each person will get 20 candles.
What is division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.
Now it is given that,
Number of candles in the bag = 120
Cora, her sister, and four friends are going to share.
So, Number of person = 6
Thus, candles each person gets = Number of candles in the bag / Number of person
⇒ candles each person gets = 120 / 6
⇒ candles each person gets = 20
Thus, each person will get 20 candles.
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A membership committee for a local community group consists of twenty-two individuals. a. If a task force of eight members of this committee must be formed to investigate the membership rules, how many different task force groups might possibly be formed
Answer:
319,770 different task force groups might possibly be formed
Step-by-step explanation:
The order in which the members of the task force are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[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]
In this question:
Groups of 8 from a set of 22. So
[tex]C_{22,8} = \frac{22!}{8!(22-8)!} = 319770[/tex]
319,770 different task force groups might possibly be formed
8. Hilma invested N$20 000 on 01/01/2018 at 9.5 % interest p.a compounded semi-annually.
How much will she receive by 01/01/2022?
[5]
Answer:
A = $29,201.97
A = P + I where
P (principal) = $20,000.00
I (interest) = $9,201.97
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 9.5/100
r = 0.095 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 20,000.00(1 + 0.095/12)(12)(4)
A = 20,000.00(1 + 0.007916667)(48)
A = $29,201.97
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $20,000.00 at a rate of 9.5% per year compounded 12 times per year over 4 years is $29,201.97
On a piece of paper, graph y>-2x-2. Then determine which answer choice matches the graph you drew.
Answer:
Graph B
Step-by-step explanation:
Hope this helps
Geometry need to find the lengths of DE , EF AND DF , respectively? ASAP
Answer:
option D
because every length is one fifth of the corresponding length of the bigger triangle
Which of the following represent statistical questions? Select the two correct answers.
A How many books did each student in your school read last year?
В.
How many types of vegetables are in Mary's salad today?
C. What was the temperature in Chicago at noon yesterday?
D. How many types of bears exist today?
E. What types of movies do people like to watch?
Answer:
A and E
Step-by-step explanation:
Can someone please help me with this I'm really stuck!!!
Answer:
we use side of triangle to find area and divide by 2 so first one is 15*15+ 8*15/2 225+60=285
Hello guys can somebody please help me solve this equation
Answer:
a) cosA=5/13 b) sinA=12/13
Step-by-step explanation:
Look at the needed angle, then use SOHCAHTOA!
Answer:
cos A = 5/13, sin A = 12/13
Step-by-step explanation:
Watch the picture for help.
sin A = a/c (According to the picture)
cos A = b/c (According to the picture)
Factor using sum and product
Answer:
Step-by-step explanation:
y=x^2+x-30
y=x^2-(6-5)x-30
y=x^2-6x+5x-30
y=x(x-6)-5(x-6)
y=(x-5)(x-6)
Answer:
(x+6)(x-5)
Step-by-step explanation:
The product is -30 and the sum is 1.
Factors of -30 are
-1 and 30
-2 and 15
-3 and 10
-5 and 6
-5 + 6 = 1
The volume of a right circular cylinder with radius r and height h is Vrh. Is the volume an increasing or decreasing function of the radius at a fixed height%E2%80%8B (assume r0 and h%E2%80%8B0)?
Answer:
The rate of change of volume of the cone with respect to radius is [tex]\frac{2}{3}\pi\times rh\\[/tex].
Step-by-step explanation:
radius of come = r
height of cone = h
Volume of cone
[tex]V = \frac{1}{3}\pi\times r^2 h[/tex]
As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.
[tex]\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh\\\\[/tex]
7*4/2*9/4+1/3*17
Jojocyosmith
Answer:
37.1666666667
Step-by-step explanation:
brainiest please
NEED ASAP! What is m
Answer:
B = 31.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan B = opp / adj
tan B = 28.2 / 45.8
taking the inverse tan of each side
tan ^ -1 ( tan B) = tan ^-1 (28.2/45.8)
B =31.62145
Rounding to the nearest tenth
B = 31.6
please solve right now
Answer:
45 mph
251 ft
Step-by-step explanation:
[tex] s = \sqrt{30fl} [/tex]
a.)
[tex] s = \sqrt{30(0.85)(80)} [/tex]
[tex] s = \sqrt{2040} [/tex]
[tex] s = 45 [/tex]
Answer: 45 mph
b.)
[tex] 80 = \sqrt{30(0.85)l} [/tex]
[tex] 80^2 = (\sqrt{25.5l})^2 [/tex]
[tex] 25.5l = 6400 [/tex]
[tex] l = 251 [/tex]
Answer: 251 ft
A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence interval for the population mean. Round your answers to one decimal place. ( , ) b. Assume that the same sample mean was obtained from a sample of items. Provide a confidence interval for the population mean. Round your answers to two decimal places. ( , ) c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a - Select your answer - margin of error.
Answer:
(a): The 95% confidence interval is (46.4, 53.6)
(b): The 95% confidence interval is (47.9, 52.1)
(c): Larger sample gives a smaller margin of error.
Step-by-step explanation:
Given
[tex]n = 30[/tex] -- sample size
[tex]\bar x = 50[/tex] -- sample mean
[tex]\sigma = 10[/tex] --- sample standard deviation
Solving (a): The confidence interval of the population mean
Calculate the standard error
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{10}{\sqrt {30}}[/tex]
[tex]\sigma_x = \frac{10}{5.478}[/tex]
[tex]\sigma_x = 1.825[/tex]
The 95% confidence interval for the z value is:
[tex]z = 1.960[/tex]
Calculate margin of error (E)
[tex]E = z * \sigma_x[/tex]
[tex]E = 1.960 * 1.825[/tex]
[tex]E = 3.577[/tex]
The confidence bound is:
[tex]Lower = \bar x - E[/tex]
[tex]Lower = 50 - 3.577[/tex]
[tex]Lower = 46.423[/tex]
[tex]Lower = 46.4[/tex] --- approximated
[tex]Upper = \bar x + E[/tex]
[tex]Upper = 50 + 3.577[/tex]
[tex]Upper = 53.577[/tex]
[tex]Upper = 53.6[/tex] --- approximated
So, the 95% confidence interval is (46.4, 53.6)
Solving (b): The confidence interval of the population mean if mean = 90
First, calculate the standard error of the mean
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{10}{\sqrt {90}}[/tex]
[tex]\sigma_x = \frac{10}{9.49}[/tex]
[tex]\sigma_x = 1.054[/tex]
The 95% confidence interval for the z value is:
[tex]z = 1.960[/tex]
Calculate margin of error (E)
[tex]E = z * \sigma_x[/tex]
[tex]E = 1.960 * 1.054[/tex]
[tex]E = 2.06584[/tex]
The confidence bound is:
[tex]Lower = \bar x - E[/tex]
[tex]Lower = 50 - 2.06584[/tex]
[tex]Lower = 47.93416[/tex]
[tex]Lower = 47.9[/tex] --- approximated
[tex]Upper = \bar x + E[/tex]
[tex]Upper = 50 + 2.06584[/tex]
[tex]Upper = 52.06584[/tex]
[tex]Upper = 52.1[/tex] --- approximated
So, the 95% confidence interval is (47.9, 52.1)
Solving (c): Effect of larger sample size on margin of error
In (a), we have:
[tex]n = 30[/tex] [tex]E = 3.577[/tex]
In (b), we have:
[tex]n = 90[/tex] [tex]E = 2.06584[/tex]
Notice that the margin of error decreases when the sample size increases.
Someone please help me
Answer:
David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?
Step-by-step explanation:
Answer:
X= 20
Step-by-step explanation:
Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.
how many days are there in xweeks and x days
Answer:
7 DAYS IN A WEEK
Step-by-step explanation:
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDA
7 DAYS
Answer:
it depends... What is X in this situation?
Step-by-step explanation:
A week has seven days.
A day has one day..?
I dont know how to help you, Sorry
he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 5 weekdays and finds an average of 259.23 gallons of milk sold on those days with a standard deviation of 34.713. 10 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 365.12 with a standard deviation of 48.297. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays - average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.
Answer:
90% confidence interval is ( -149.114, -62.666 )
Step-by-step explanation:
Given the data in the question;
Sample 1 Sample 2
x"₁ = 259.23 x"₂ = 365.12
s₁ = 34.713 s₂ = 48.297
n₁ = 5 n₂ = 10
With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }
significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1
Since we are to assume that variance are equal and they are know, we will use pooled variance;
Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13
Now, pooled estimate of variance will be;
[tex]S_p^2[/tex] = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]
we substitute
[tex]S_p^2[/tex] = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]
[tex]S_p^2[/tex] = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]
[tex]S_p^2[/tex] = [ 4819.9692 + 20993.4 ] / [ 13 ]
[tex]S_p^2[/tex] = 25813.3692 / 13
[tex]S_p^2[/tex] = 1985.64378
Now the Standard Error will be;
[tex]S_{x1-x2[/tex] = √[ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]
we substitute
[tex]S_{x1-x2[/tex] = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]
[tex]S_{x1-x2[/tex] = √[ 397.128756 + 198.564378 ]
[tex]S_{x1-x2[/tex] = √595.693134
[tex]S_{x1-x2[/tex] = 24.4068
Critical Value = [tex]t_{\frac{\alpha }{2}, df[/tex] = [tex]t_{0.05, df=13[/tex] = 1.771 { t-table }
So,
Margin of Error E = [tex]t_{\frac{\alpha }{2}, df[/tex] × [ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]
we substitute
Margin of Error E = 1.771 × 24.4068
Margin of Error E = 43.224
Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89
So, Limits of 90% CI will be; x₁ - x₂ ± E
Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114
Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666
Therefore, 90% confidence interval is ( -149.114, -62.666 )
substitution method y= 3x-2 and 2x-3y=16
solution (__), (__)
thanks
Answer:
i got (-10/7, -44/7)
This question has two parts.
Many artists incorporate geometric shapes into their art. An artist wants to make a sculpture shaped like a cone with a height of 4.2 inches and a radius of 2.5 inches. The artist needs to know the volume of the sculpture to purchase the correct amount of materials.
Part A. Which equation should the artist use to calculate the volume of the cone with the given measurements?
1. V=4/5π (2.5)³
2.V=π(2.5)²(4.2)
3.V=1/3 (2.5)² (4.2)
4.V=1/3π (2.5)²(4.2)
B.What is the Volume Of The Cone?
Answer:
D
Step-by-step explanation:
shaped like a cone
Cone = 1/3
v = 1/3 x 3.14 x 2.5^2 x 4.2
v =27.475
The equation should the artist use to calculate the volume of the
cone is, 4. V=1/3π (2.5)²(4.2)
What is a cone?A cone is a three-dimensional geometric object with a smooth, curved top and a flat base. As a cone's height increases, its radius gradually decreases until it reaches a particular point.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, An artist is making a sculpture shaped like a cone having a radius of 2.5 inches and a height of 4.2 inches.
We know The volume of a cone is (1/3)πr²h.
Therefore, The volume of the cone would be,
= (1/3)π(2.5)²×4.2 cubic inches.
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What is the coordinate of the midpoint of segment AC
Answer:
-5.5
Step-by-step explanation:
[tex]\frac{-7+-4}{2}\\\\\frac{-11}{2}\\\\-5.5[/tex]
In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws. In a random sample of 588 men, 307 favored stricter gun control laws. Can it be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
Answer:
The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
Step-by-step explanation:
Before solving the question, 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
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.
Test if a lower proportion of men favor stricter gun control than women:
At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So
[tex]H_0: p_M - p_W = 0[/tex]
At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So
[tex]H_1: p_M - p_W < 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.
This means that:
[tex]p_W = \frac{313}{564} = 0.555[/tex]
[tex]s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209[/tex]
In a random sample of 588 men, 307 favored stricter gun control laws.
This means that:
[tex]p_M = \frac{307}{588} = 0.522[/tex]
[tex]s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206[/tex]
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_M - p_W = 0.522 - 0.555 = -0.033[/tex]
[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.033 - 0}{0.029}[/tex]
[tex]z = -1.12[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.
Looking at the z-table, z = -1.12 has a p-value of 0.1314.
The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
How many square feet does the paint need to cover?
Answer:
62 square feet
Step-by-step explanation:
9 x 8 = 72
5 x 2 = 10
72 - 10 = 62
Please show how you did it so I can learn :)
Answer:
[tex] x_{1} = 3 + \sqrt {6} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
Step-by-step explanation:
Given the quadratic equation;
x² - 6x + 3 = 0
To find the roots of the quadratic equation, we would use the quadratic formula;
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 1, b = -6 and c = 3
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the formula, we have;
[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]
[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = 3 + \sqrt {6} [/tex]
Or
[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
please help need to solve this fastt
Answer:
1979
91%
Step-by-step explanation:
Given the relation :
P = (318t + 6792) / (1.19t + 107.36)
P = % of household with PC
t = years since 2000
1.) We need to find t, when P = 85%
P = 0.85
0.85 = (318t + 6792) / (1.19t + 107.36)
0.85(1.19t + 107.36) = (318t + 6792)
1.0115t + 91.256 = 318t + 6792
Collect like terms :
1.0115t - 318t = 6792 - 91.256
−316.9885t = 6700.744
t = 6700.744 / - 316.9885
t = - 21.138760
t = - 21 years
2000 - 21 years = 1979
Percentage who had computer in 2014
t = 2014 - 2000 = 14
P = (318(14) + 6792) / (1.19(14)+ 107.36)
P = (4452 + 6792) / (16.66 + 107.36)
P = 11244 / 124.02
P = 90.6627
P = approximately 91%
Please show you're work! Thanks! Will give brainy
y = x²-8x+ 15
a. If x = -2, what does y equal?
b. If x = 1, what does y equal? (You can check your answer in Desmos Graphing)
c. Using Desmos, find the (x, y) coordinates of the vertex of the parabola.
Answer:
see below
Step-by-step explanation:
y = x²-8x+ 15
Let x = -2
y = (-2)²-8(-2)+ 15
= 4 +16 +15
= 35
Let x = 1
y = (1)²-8(1)+ 15
1 -8+15
=8
The vertex is (4,-1)