Answer:
D. $7.00
Step-by-step explanation:
I just did it.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers 1. x^2-2x-15=(ax+b)(cx+d) 2. 2x^-6x-36x=2x(ax+b)(cx+d) 3. 4x^2+10x+4=(ax+b)(cx+d) . Fill in the table with the missing values of a, b, c, and d.
Answer:
(1, -5, 1, 3)(2, -12, 1, 3)(4, 2, 1, 2)Step-by-step explanation:
Obviously, factors can be written in any order. So, there are multiple answers to this question.
1. x^2 -2x -15 = (x -5)(x +3) . . . . (a, b, c, d) = (1, -5, 1, 3)
__
2. 2x^2 -6x -36 = 2(x^2 -3x -18) = 2(x -6)(x +3) . . . . (a, b, c, d) = (2, -12, 1, 3)
__
3. 4x^2 +10x +4 = 2(2x^2 +5x +2) = 2(2x +1)(x +2) . . . . (a, b, c, d) = (4, 2, 1, 2)
Verify that (AUB)’=A’n B’
Assuming [tex]A'[/tex] denotes the complement of the set [tex]A[/tex], i.e. all elements in the universal set that do not belong to [tex]A[/tex], then we can prove this in general.
To establish equality between two sets, you need to show that they are both subsets of one another.
Prove [tex](A\cup B)'\subseteq A'\cap B'[/tex]:Let [tex]x\in(A\cup B)'[/tex].
By definition of set complement, this means [tex]x\not\in A\cup B[/tex].
By definition of set union, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].
By definition of complement, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].
By definition of set intersection, [tex]x\in A'\cap B'[/tex].
Therefore [tex](A\cup B)'[/tex] is a subset of [tex]A'\cap B'[/tex], because membership of some arbitrary element in the first set directly implies membership in the second set.
Prove [tex]A'\cap B'\subseteq(A\cup B)'[/tex]:Let [tex]x\in A'\cap B'[/tex]. The proof follows similarly as above.
By definition of intersection, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].
By definition of complement, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].
By definition of union, [tex]x\not\in(A\cup B)[/tex].
By definition of complement, [tex]x\in(A\cup B)'[/tex].
Therefore [tex]A'\cap B'[/tex] is a subset of [tex](A\cup B)'[/tex].
And hence both sets are equal, regardless of what the sets may be.
What are the values of a and b? Select one: a. a equals 18 comma space b equals 4 square root of 5 b. a equals 64 comma space b equals 80 c. a equals 8 comma space b equals 4 square root of 5 d. a equals 8 comma space b equals 8 square root of 5
Answer:
a is a value of 5 and b is is equal to 9
Step-by-step explanation:
all you have to do is get 16 and 4 by them self and take them out, and find the remaining numbers
Answer: a = 8, b = [tex]4\sqrt{5}[/tex]
Find the slope of a line perpendicular to the line whose equation is 2y − 6x = 4.
Answer:
- 1/3
Step-by-step explanation:
2y - 6x = 4
y - 3x = 2
y = 3x + 2
Slope of the given line = 3.
Slope of the perpendicular line is negative reciprocal = - 1/3.
lee and maya are collecting leaves for an art project. lee collects 24-100 of the total leaves needed. maya collects 4-10 of the total leaves needed. What fraction of the total number leaves did they collect altogether
Answer:
16/25
Step-by-step explanation:
4/10=40/100
24/100=24/100
40+24=64
64/100
16/25
Answer:
16/25
Step-by-step explanation:
what divided by 2 equals 6.5
Answer:
hope this helps, take care and stay safe
Step-by-step explanation:
you can do this by timing 6.5 by 2 which = 13. if you get stuck on questions like this, do the rewind effect, that is when you do the opposite of the question, which is what i did above, you can check this in 2 ways, on a calculator (if of course you are allow) or do the question again by using what you have work out, so 13 divide by 2 = 6.5.
The number 13 is divided by 2 to give the number 6.5.
Used the concept of divide which states that,
The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.
To find the number that is divided by 2 to give the number 6.5
Let us assume that the number = x
Hence, it can be written as,
x ÷ 2 = 6.5
x/2 = 6.5
Multiply both sides 2;
x = 2 × 6.5
x = 13
Therefore, the number of the given condition is 13.
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a bucket that holds 5 1/4 gallons of water is being used to fill a tub that can hold 34 1/8 gallons. How many buckets will be needed to fill the tub?
The answer is 6 1/2 buckets.
What is did was turn the fractions into decimals to make it easier.
So the ratio is 5.25 gallons per bucket. I divided 34 1/8 by 5 1/4 in decimal form (34.125/5.25) and got 6.5
So therefore, the answer is 6 1/2 buckets of water is needed ti fill up the tub.
Hand sanitizer containing 70% ethanol (HL+) is recommended to prevent the transmission of the rhinovirus (RV) that causes the common cold. A study with 212 subjects was conducted. Subjects were assigned at random to either the HL+ group, which used hand sanitizer after hand washing, or a control group, which did not use hand sanitizer after hand washing. The number of subjects with and without RV infection in the two groups over the ten week study are below. RV Infection Yes No HL+ Group 49 67 Control Group 49 47 (a) (2 points) Is this an experiment or observational study? Why? (b) (2 points) What is the response variable? Is it qualitative or quantitative? (c) (5 points) Does the data suggest that the RV infection rate of subjects using hand sanitizer is significantly (a = 0.05) lower? Perform the appropriate procedure and include all the steps. (d) (2 points) Construct and interpret a 95% confidence interval to estimate the difference between the two proportions.
Answer:
a) Experiment
b) Proportion of subjects infected. Quantitative
c) Null hypothesis failed to be rejected. P-value=0.101.
There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.
d) The 95% confidence interval for the difference between proportions is (-0.223, 0.047).
As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.
Step-by-step explanation:
a) This is an experiment, as the groups are designed by the researcher. The individuals are then asigned randomly to one of both groups.
b) The response variable is the proportion of subjects infected. This variable is quantitative, as is a sum of positive cases divided by the total amount of subjects in the group.
c) This is a hypothesis test for the difference between proportions.
The claim is that the RV infection rate of subjects using hand sanitizer is significantly lower.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is 0.05.
The sample 1 (HL+ group), of size n1=116 has a proportion of p1=0.4224.
[tex]p_1=X_1/n_1=49/116=0.4224[/tex]
The sample 2 (Control group), of size n2=96 has a proportion of p2=0.5104.
[tex]p_2=X_2/n_2=49/96=0.5104[/tex]
The difference between proportions is (p1-p2)=-0.088.
[tex]p_d=p_1-p_2=0.4224-0.5104=-0.088[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{49+49}{116+96}=\dfrac{98}{212}=0.4623[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.088-0}{0.0688}=\dfrac{-0.088}{0.0688}=-1.28[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z<-1.28)=0.101[/tex]
As the P-value (0.101) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.
d) We want to calculate the bounds of a 95% confidence interval.
For a 95% CI, the critical value for z is z=1.96.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0688=0.1348[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.088-0.1348=-0.223\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.088+0.1348=0.047[/tex]
The 95% confidence interval for the difference between proportions is (-0.223, 0.047).
As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.
A rancher has a roll of fencing to enclose a rectangular area. The table shows how the area that the rancher can enclose with the fencing depends on the width of the rectangle. Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet? ✔ A(w) = -w² + 100w The rancher decides to make the width of the rectangle 40 ft. What is the area of the rectangle? PLEASE HURRY
Answer:
A(w) = -w^2 + 100w
Step-by-step explanation:
just took the assignment
Finding the numeric value of the function, it is found that the area of the rectangle is of 2400 square feet.
---------------------------
The area of a rectangle of width w is given by:
[tex]A(w) = -w^2 + 100w[/tex]
In this question, we have a width of 40 ft, thus [tex]w = 40[/tex], and the area is of:
[tex]A(40) = -40^2 + 100(40) = -1600 + 4000 = 2400[/tex]
The area is of 2400 square feet.
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5-3+78 divided by 3=
Answer:
26 remainder 2
Step-by-step explanation:
5 - 3 =2
2 + 78 = 80
80 ÷ 3
3 can go into 8 twice remaining with 2
2 goes across to 0
3 can go into 20 6 times because 3×6= 18
so 3 into 20 is 6 remainder of 2
answer= 26 remainder of 2
Answer:
[tex]= 26 \frac{3}{2} \\ [/tex]
Step-by-step explanation:
[tex]5 - 3 + 78 \div 3 \\ 2 + 78 \div 3 \\ 80 \div 3 \\ = 26 \frac{3}{2} [/tex]
hope this helps you
What is the slope of this line?
Answer:
1
Step-by-step explanation:
We need to points
(-1,0) and (0,1)
The slope is found by
m= (y2-y1)/(x2-x1)
m = (1-0)/(0- -1)
= (1-0)/(0+1)
= 1/1
The slope is 1
Answer:
1
Step-by-step explanation:
The slope is rise/run and can be found by counting how many units up and over you must go from one point on the line to another.
Therefore the answer is
1
Square A"B"C"D" is the final image after the rule
was applied to square ABCD.
On a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5).
What are the coordinates of vertex A of square ABCD?
(–1, –6)
(–1, –2)
(–1, 6)
(–2, 1)
Answer:
The Answer is D on Edge
Step-by-step explanation:
Answer:
D is the answer
Step-by-step explanation:
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.a) The average baggage-related revenue per passenger is: $(please round to the nearest cent)b) The standard deviation of baggage-related revenue is: $(please round to the nearest cent)c) About how much revenue should the airline expect for a flight of 120 passengers?(please round to the nearest dollar)
Answer:
(a) The average baggage-related revenue per passenger is $15.70.
(b) The standard deviation of baggage-related revenue is $19.95.
(c) The expected revenue for 120 passengers is $1,884.
Step-by-step explanation:
Let the random variable X represent the baggage-related revenue per passenger.
It is provided that the baggage fees is $25 for the first bag and $35 for the second.
The probability model is:
X : 0 25 60
P (X) : 0.54 0.34 0.12
(a)
Compute the average baggage-related revenue per passenger as follows:
[tex]E(X)=\sum {X\times P (X)}[/tex]
[tex]=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70[/tex]
Thus, the average baggage-related revenue per passenger is $15.70.
(b)
Compute the standard deviation of baggage-related revenue as follows:
[tex]E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\[/tex]
[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]
[tex]=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95[/tex]
Thus, the standard deviation of baggage-related revenue is $19.95.
(c)
Compute the expected revenue for 120 passengers as follows:
[tex]E(R)=n\times E(X)[/tex]
[tex]=120\times 15.7\\\\=1884[/tex]
Thus, the expected revenue for 120 passengers is $1,884.
The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product. yequalsS(x)equals300plus40x yequalsD(x)equals4300minus40x
Answer:
The equilibrium point for the product (x,y) = (50,2300)
Step-by-step explanation:
The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.
From the question, we can identify the following;
S(x) = 300 + 40x
D(x) = 4300 - 40x
Now, at the equilibrium point, S(x) = D(x)
This means that;
300 + 40x = 4300 -40x
80x = 4300-300
80x = 4000
x = 4000/80 = 50
Now, we input the value of x into any of the equation of the demand and supply to get the quantity.
Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300
The equilibrium point for the product (x,y) = (50,2300)
Please answer this correctly
Answer:
6.3 ft
Step-by-step explanation:
The perimeter of a parallelogram is given by
P = 2(l+w)
49.6 = 2 (18.5 +t)
Divide by 2
49.6/2 = 2/2 (18.5 +t)
24.8 = 18.5+t
Subtract 18.5
24.8-18.5 = t
6.3 = t
Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school. What is the mean of the sampling distribution of the proportion of the students who prefer later start times for school
Answer:
The mean of sampling distribution of the proportion of the students who prefer later start times for school
μₓ = p = 0.63
Step-by-step explanation:
Explanation:-
Given sample size 'n' =200
given data Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school
sample proportion
[tex]p = \frac{x}{n} = \frac{126}{200} = 0.63[/tex]
The mean of sampling distribution of the proportion of the students who prefer later start times for school
μₓ = p = 0.63
Standard deviation of the proportion
[tex]S.D = \sqrt{\frac{p(1-p)}{n} } = \sqrt{\frac{0.63(1-0.63)}{200} } = 0.034[/tex]
The number of hours that a nine month old baby sleeps at night are normally distributed with a population standard deviation of 1.5 hours and an unknown population mean. A random sample of 22 nine month old babies is taken and results in a sample mean of 12 hours. Find the margin of error for a confidence interval for the population mean with a 90% confidence level. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answer:
The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this quesstion:
[tex]\sigma = 1.5, n = 22[/tex]
So
[tex]M = 1.645*\frac{1.5}{\sqrt{22}} = 0.53[/tex]
The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.
Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: (a) What is the probability of getting one child of each sex?
Answer:
49.97% probability of getting one child of each sex
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution 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.
The probability that a couple’s first child is a boy is 0.512.
This means that [tex]p = 0.512[/tex]
The will have two children:
This means that [tex]n = 2[/tex]
(a) What is the probability of getting one child of each sex?
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997[/tex]
49.97% probability of getting one child of each sex
Bruce, a store owner, would like to determine if a new advertising initiative has increased his sales per day compared to last year. He gathers information on 14 random sales days and conducts a hypothesis test about the sales revenue during a day using a significance level of 0.5 %. The mean revenue per day prior to the initiative was 650 dollars. df t0.10 t0.05 t0.025 t0.01 t0.005 ... ... ... ... ... ...13 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.99715 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 Determine the critical value(s) using the partial t-table above. If entering two critical values, use +-.
Answer:
The critical value of t =3.012
Step-by-step explanation:
Solution
Recall that:
Bruce a store owner put together information on random sales of = 14 days
A significant level of =0.5%
The mean revenue per day = 65 dollars
Now,
We find he critical values using the partial t-table stated above
Thus,
The degree of freedom is given below:
n -1 = 14
14-1 =13
For a 0.005 level and right tailed test and with a 13 degree of freedom, the critical value of t =3.012.
A ball is thrown straight up from a cliff. The function f(x) = –4.9t2 + 17t + 19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is that height reached? Round your answers to 1 decimal place.
Maximum height:
__ meters
Time:
__ seconds
Answer:
Maximum height: 33.7 meters
Time: 1.7 seconds
Step-by-step explanation:
Suppose we have a quadratic equation in the following format:
[tex]f(t) = at^{2} + bt + c[/tex]
In a is negative, the maximum point of the function happens at the time of
[tex]t_{v} = -\frac{b}{2a}[/tex]
And it's value is: [tex]f(t_{v})[/tex]
In this question:
[tex]f(t) = -4.9t^{2} + 17t + 19[/tex]
So [tex]a = -4.9, b = 17, c = 19[/tex]
The time of the maximum height is:
[tex]t_{v} = -\frac{b}{2a} = -\frac{17}{2*(-4.9)} = 1.7[/tex]
The maximum height is:
[tex]f(1.7) = -4.9*(1.7)^{2} + 17*1.7 + 19 = 33.7[/tex]
Suppose that you record the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend. Would you expect to find a positive or negative association between these variables? Explain briefly.
Answer:
positive
Step-by-step explanation:
the higher the temp the higher the number of ice creams sold
The association would be positive between the variables.
Given that,
Recorded the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
As the temperature increases, people will love to eat the ice cream more, which increase the sales of the ice cream which implies that the association would be positive between the variable.
Thus, the association would be positive between the variables.
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4x + 5y = 7 3x – 2y = –12 Multiply each equation by a number that produces opposite coefficents for x or y
Answer:
Step-by-step explanation:
DO YOU MEAN :
[tex]4x + 5y = 7\\ 3x - 2y = -12\\Multiply-equation 1 -by -the-coefficient-of-x-in-equation-2\\multiply-equation-2 -by-the-co-efficient -of x -in-equation- 1\\\\3(4x + 5y = 7)\\4( 3x - 2y = -12)\\\\12x +15y=21\\12x -8y=-48[/tex]
Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable.
Answer:
[tex][0,Z_n][/tex]
Step-by-step explanation:
Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentages for online purchases
Since Amazon is an online purchase, The set of possible values for the variable is a positive real number. It is a positive real number that must be within [tex]Z_n[/tex]. It cannot exceed the tax percentage for online purchases that can be found in Amazon. [tex]Z_n[/tex] is a set of online purchases that can be found on Amazon, therefore the set of possible values for the variable is [tex][0,Z_n][/tex]
Which phrase best describe the translation from the graphy y=(x+2)² to the graph of y=x²+3
Answer:
2 units right
3 units up
Step-by-step explanation:
the graph y=(x+2)² is the parent function y=x^2 translated 2 units left
the graph y=x²+3 is the parent function y=x^2 translated 3 units up
so, the translation from y=(x+2)² to y=x²+3 is:
2 units right (to get to zero)
3 units up
(you can change the order if you want, it doesn't really matter here)
2. The average score Josie had in 6 subjects is 72 and her average score after 2 additional
subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the
8
th subject correct to the nearest whole number?
Answer:
6(72)= 432 & 8(74.25)=594
594-432=162==> 162-80=82
Find the mode of the following data set.
Stem Leaves
4
8
5 0,1,6
6
2,2,4
7 3,5
Answer:
2 or 6
Step-by-step explanation:
The mode is always the number that repeats or is shown more than once. But there is no number that repeats. So your answer is No mode.
once again i need help with my 8th grade hw [tex]-9\leq 7-8x[/tex] ... thnx
Step-by-step explanation:
-9 ≤ 7 − 8x
8x ≤ 16
x ≤ 2
What is the solution of the equation x2 + 8x = 4?
Answer:
hope this is correct
In an isosceles triangle, the equal sides are 2/3 if the length of the base. Determine the measure if the base angles.
Please help me with good explanation, I have a trig exam soon!
Answer:
41.41°
Step-by-step explanation:
In ∆ABC below, the legs are 4 and the base is 6.
So, the legs are ⅔ the length of the base.
In ∆CBD,
cosB = BD/BC = 3/4 = 0.75
B = arccos 0.75 = 41.41°
The base angles are each 41.41°
The measure should be 41.41°
Calculation of the measure:Since In ∆ABC , the legs should be 4 and the base should be 6.
Now
the legs are two-third the length of the base.
Also,
In ∆CBD,
cosB [tex]= BD\div BC = 3\div 4 = 0.75[/tex]
So,
B = arccos 0.75 = 41.41°
Therefore, we can concluded that The base angles are each 41.41°
Learn more about length here: https://brainly.com/question/3385843
The volume of a stock is the number of shares traded for a given day. Several years ago, a certain company's stock had a mean daily volume of 7.52 million shares, according to a reputable financial news outlet. A random sample of 40 trading days in a recent year was obtained and the volume of shares traded on those days was recorded, with the accompanying results.
Required:
a. Find the test statistic:
b. Find the P-value
c. The level of significance is .05. what can be concluded from the hypothesis?
Volume (millions of shares)
4.1531 2.8893
4.6228 6.0203
5.6386 6.2774
4.5822 3.968
5.6903 4.0065
4.4313 11.2343
7.3941 2.6991
9.0557 3.2285
7 9800 4.2762
10.1556 3.2913
3.4189 5.8544
4.5624 2.6153
7.3287 8.1435
9.1723 5.3304
3.6798 4.1807
4.2868 5.3668
5.5448 1.7945
3.7656 5.0502
4.0201 3.1832
3 .798 5.4563
Answer:
a) test statistic, [tex]t_{s} = -4.20[/tex]
b) P-value = 0.0001
c) It can be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years
Step-by-step explanation:
There are 40 trading days, therefore, sample size, n = 40
Calculate the Sample mean:
[tex]\bar x = \frac{\sum x}{n} \\\bar x = \frac{4.153 +4.6228 + ...+...+5.4563}{40}\\\bar x = 5.5945[/tex]
Get the null and alternative hypothesis:
Null hypothesis, [tex]H_{0} : \mu = 7.52[/tex]
Alternative hypothesis, [tex]H_{a} : \mu \neq 7.52[/tex]
Calculate the sample standard deviation:
[tex]SD = \sqrt{\frac{\sum (x - \bar x)^{2} }{n - 1} } \\SD = \sqrt{\frac{(4.1531-5.5945)^{2} + (4.6228-5.5945)^{2}+...+ (5.4563-5.5945)^{2}}{39} } \\SD = \sqrt{\frac{327.6161}{39} } \\SD = 2.8983[/tex]
a) Calculate the test statistic:
[tex]t_{s} = \frac{\bar{x} - \mu}{SD/\sqrt{n} } \\t_{s} = \frac{5.5945 -7.52}{2.8983/\sqrt{40} }\\t_{s} = -4.20[/tex]
b) Calculate the P-value
Getting the P-value using the excel function:
P-value = (=T.DIST.2T(|ts|, df))
P-value = (=T.DIST.2T(4.20, 39))
P-value = 0.0001
c) If the level of significance, [tex]\alpha = 0.05[/tex]
The P-value (0.0001) < α(0.05), the null hypothesis is rejected.
It can therefore be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years