Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
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hey one more for my friend :)
Answer:
Third graph from the top
Step-by-step explanation:
A proportional relationship is a straight line that goes through the point (0,0)
Answer:
The third graphStep-by-step explanation:
The third straight graph, since a proportion is a relationship in which a second variable is changed by a same value all the time (linear).
Hope this helps, if not, tell me and I shall try again
HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
Approximately, what was the rate of change for the number of the websites for this time period??
=============================================================
How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
----------
You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
Find the critical value z Subscript alpha divided by 2 that corresponds to the given confidence level. 80%
Answer:
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Step-by-step explanation:
For this problem we have the confidence level given
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Express it in slope-Intercept form
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
How many meters are in 18,200 milliliter
Answer:
18.2 :)
Have a great day!!!
The Demon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three other were sprayed with Action. When the grape ripened, 400 of the vines treated with Pernod 5 and 400 of the vines treated with Action were checked for infestation. The number of infested vines treated with Pernod 5 and Action are 24 and 40 respectively.
At 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answer:
At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Then, the null and alternative hypothesis are:
H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0
The significance level is 0.05.
The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.
[tex]p_1=X_1/n_1=24/400=0.06[/tex]
The sample 2, of size n2=400 has a proportion of p2=0.1.
[tex]p_2=X_2/n_2=40/400=0.1[/tex]
The difference between proportions is (p1-p2)=-0.04.
[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/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{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]
As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (beforeminusafter) in their levels of LDL cholesterol (in mg/dL) have a mean of 2.7 and a standard deviation of 17.8. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
We have,
To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = X ± (Z * (σ/√n))
where:
CI is the confidence interval
X is the sample mean
Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)
σ is the population standard deviation
n is the sample size
Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:
CI = 2.7 ± (1.645 * (17.8/√47))
Calculating the standard error (SE):
SE = σ/√n = 17.8/√47 ≈ 2.587
Substituting the values into the confidence interval formula:
CI = 2.7 ± (1.645 * 2.587)
Calculating the upper and lower bounds of the confidence interval:
Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199
Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799
Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.
Interpreting the confidence interval:
Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).
However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.
Thus,
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.
What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = mean ± (Z * (standard deviation / √n))
Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.
Plugging in the values:
CI = 2.7 ± (1.645 * (17.8 / √47))
CI = 2.7 ± (1.645 * (17.8 / 6.856))
CI = 2.7 ± (1.645 * (2.596))
CI = 2.7 ± 4.270
CI = 2.7 + 4.270 ; CI = 2.7 - 4.270
CI = 6.97 ; CI = -1.57
Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).
The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.
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Is (0,-2) a solution of 3x - y = 2?
Answer:
yes, (0,-2) is the answer when graphing this equation.
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
For each ordered pair, determine whether it is a solution to the system of equations. y=6x-7 9x-2y=8
Answer:
x = 2, y = 5
Step-by-step explanation:
Hello,
y=6x-7
9x-2y=8
can be written as
(1) 6x - y = 7
(2) 9x -2y = 8
(2)-2*(1) gives
9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6
<=> -3x=-6
<=> x = 6/3=2
and we replace it in (1)
y = 6*2-7=12-7=5
hope this helps
Which of the following are exterior angles? Check all that apply.
Answer:<5 and <4 are exterior angles
Step-by-step explanation:
Because they are the only ones outside it they are the only ones that are exterior angles!
<!> Brainliest is appreciated! <!>
Answer:
for AL Its 3 and 4
Not sure of how to solve this
Answer:
undefined
Step-by-step explanation:
Using the slope formula
m = (y2-y1)/ (x2-x1)
and the given points
m = ( 8 - -1)/( 2-2)
= (8+1) / 0
We cannot divide by 0 so the slope is undefined
help help help help pls
Hi !!
For f(x) = 3/x + 4 , B is correct.
• f(-3) = 3/(-3) + 4
f(-3) = - 1 + 4
f(-3) = 3
• f(-2) = 3/(-2) + 4
f(-2) = -1,5 + 4
f(-2) = 2,5
• f(1) = 3/(1) + 4
f(1) = 3 + 4
f(1) = 7
• f(2) = 3/(2) + 4
f(2) = 1,5 + 4
f(2) = 5,5
• f(3) = 3/(3) + 4
f(3) = 1 + 4
f(3) = 5
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
I NEED HELP PLEASE, THANKS! :)
A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)
Answer: 136
Step-by-step explanation:
An= A1+(n-1)d
A1=16, d=8, and n=16
A16= 16 +(16-1)(8)
A16= 16(15)(8)
A16= 16+120
A16=136
Hey there! :)
Answer:
f(16) = 136 seats.
Step-by-step explanation:
This situation can be expressed as an explicit function where 'n' is the row number.
The question also states that the number of seats increases by 8. Use this in the equation:
f(n) = 16 + 8(n-1)
Solve for the number of seats in the 16th row by plugging in 16 for n:
f(16) = 16 + 8(16-1)
f(16) = 16 + 8(15)
f(16) = 16 + 120
f(16) = 136 seats.
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
Consider the matrices. A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢−27−35−12⎤⎦⎥ What is the result of A−B? Enter your answer by filling in the boxes.
hello
[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
hope this helps
Using matrices A and B, the result of A-B is
[tex]A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
Given :
Two matrices A and B. We need to subtract both matrix
Lets find out A-B
Given matrices A and B are
[tex]A=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] \\B=\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right][/tex]
When we subtract A-B we need to subtract the corresponding elements in that matrix
[tex]A-B=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] -\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right]=\left[\begin{array}{ccc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
The above is the resultant matrix .
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You want to put a 2 inch thick layer of topsoil for a new 14 ft by 26 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:
2 1/4
Step-by-step explanation:
The volume of soil needed is ...
(14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³
The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.
You need to order 2 1/4 cubic yards.
___
There are 3 ft or 36 inches to a yard.
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
1. Which of these is a Pythagorean triple?
(a) (3, 4, 5)
(b) (5, 6, 7)
(c) (10, 11, 12)
(d) (15, 16, 17)
2. If y2 = 172 – 82. What is the value of y?
(a) 10
(b) 25
(c) 15
(d) 16
3. How many kilograms are there in 5 tonnes?
(a) 500 kg
(b) 50 000 kg
(c) 5, 000 kg
(d) 50 kg
4. If the probability that a girl win a race is 0.6. What is the probability that that the girl loses the race?
(a) 0.4
(b) 1
(c) 4
(d) 6
5. The distance from Lagos to Ibadan can be measured using which of the following units of measurement?
(a) centimeter
(b) Millimeter
(c) Kilograms
(d) Kilometer
6. The longest side of a right-angled triangle is called?
(a) right side
(b) Opposite
(c) Hypotenuse
(d) None of the above
7. The mass/weight of your pen can be measured using………
(a) Grams
(b) Kilometer
(c) Centimetre
(d) Tonne
8. There 5 blue balls, 8 red balls and 2 black balls in a basket. One ball is picked at random. Find the probability that the ball picked is red.
(a) 58
(b) 815
(c) 215
(d) 13
9. The mass of a lorry can be measured using which of the following?
(a) liter
(b) Kilometer
(c) Tonne
(d) Milligram
10. How many tonnes are there in 15 000 kg?
(a) 150 tonnes
(b) 15 tonnes
(c) 1500 tonnes
(d) 1.5 tonnes
11. What is 20% of #38 000?
(a) #7 600
(b) #3 800
(c) #2 800
(d) #760
12. Express 17:30 hours as a.m. or p.m. time.
(a) 7:30 pm
(b) 7:30 a.m.
(c) 5:30 p.m.
(d) 5:30 a.m.
13. Angle 900 is also called?
(a) left angle
(b) quarter angle
(c) right angle
(d) middle angle
14. “Kilo” is a Greek word from the word “khilioi” meaning what?
(a) Million
(b) Thousand
C) Billion
D) Hundred
15. Which is the most widely used system of measurement in the world?
(a) tape rule system
(b) counter system
(c) metric system
(d) none of the above
PART B
ANSWER ALL QUESTIONS
1. The largest unit of measurement for distance/length is kilometer. True or false …………………….
2. The probability that a student fails an examination is 0.2. What is the probability that the student passes the examination? .................
The members of a village cooperative agree to contribute time and money towards a one year village improvement programme (VIP). Below is the table of activities of the programme.
Activity
Time (hour)
Money(#)
Planting/ watering trees
300
20 000
Collecting/burning rubbish
200
0
Clearing storm ditches
80
5 000
Making speed bumps
20
5 000
3. How much is the total money pledged? …………..
4. Which activity takes more money? ………………..
5. Which activity cost no money? ……………………….
Answer
1. (a) (3,4,5)--3^2 +4^2=9+16=25=5^2
2. (b) 25--172-82=50/2=25
3. (c) 5,000 kg--1,000 kg in 1 tonne
4. (a) 0.4--1-0.6=0.4
5. (d) kilometer
6. (c) hypotenuse
7. (a) grams
8. i think it is (a) 58--5+8+2=15~~8/15 =0.53~closest answer is 58
9. (c) tonne
10. (b) 15 tonnes--1000 kg in 1 tonne
11. (a) #7,600--38000*20%, or 0.20, =7,600
12. (a) 7:30 pm
13. (c) right angle
(c) metric system
Part B
1. True
2. 0.8
3. 30,000 dollars--20,000 +0+5,000+5,000=30,000
4. Planting/watering trees--20 dollars
5. Collecting/burning rubbish--0 dollars
How many ways can a 4-person subcommittee be selected from a committee of 6 people? (B) How many ways can a president comma vice dash president comma secretary comma and treasurer be chosen from a committee of 6 people?
Answer:
A) 360
B) 360
Step-by-step explanation:
Part A)
Given that there are a total of 6 people and 4 person subcommittee is to be selected.
Number of ways to select 1st person = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select 2nd person = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select 3rd person = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select 4th person = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
Part B)
Given that there are a total of 6 people in the committee
Number of ways to select president = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select vice president = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select secretary = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select treasurer = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
which expression defies the arithmetic series 10 + 7 + 4 ... for six terms?
Answer:
[tex]a_n = 10-3(n - 1)[/tex]
10 + 7 + 4 + 1 + -2 + -5
Step-by-step explanation:
Explicit Arithmetic Formula: [tex]a_n = a_1 + d(n-1)[/tex]
To find d, take the common difference between 2 numbers.
To find the other terms of the sequence, plug them into the explicit formula or subtract 3 from the given numbers.
Find the circumference of a circle with a radius of 15 centimeters. Round your answer to the nearest centimeter
Answer:
94 cm
Step-by-step explanation:
The formula for finding the circumference of a circle is;
Circumference = 2πr
where π = [tex]\frac{22}{7}[/tex] or 3.14 and
r = radius
Here radius is 15 cm so;
Circumference = [tex]2 * \frac{22}{7} * 15[/tex]
= [tex]\frac{660}{7}[/tex]cm
= 94.28cm
= 94 cm ( rounded to the nearest centimetre )
How do you write 0.0683 in scientific notation? ____× 10^____
Answer:
It's written as
[tex]6.83 \times {10}^{ - 2} [/tex]
Hope this helps you
Answer:
6.83 × 10 -2
hopefully this helped :3
Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?
Answer:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
Step-by-step explanation:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.
What is the equation of the graphed line written in
standard form?
O 2x - y = -4
O 2x - y = 4
O y = 2x – 4
O y=x-4
Answer:
2x-y=4
Step-by-step explanation:
Standard form of a line: Ax+by=c
Use slope intercept form: y=mx+b
slope= 2
y=2x-4
Add 4 to both sides.
y+4=2x
subtract y from both sides.
4=2x-y
Rotate the equation
2x-y=4
Answer:
2x-y=4
Step-by-step explanation:
y=2x-4 is the slope intercept.
y-2x=-4
-2x+y=-4
2x-y=4
Show all work to solve 3x^2 – 5x – 2 = 0.
Answer:
Step-by-step explanation:
3x2−5x−2=0
For this equation: a=3, b=-5, c=-2
3x2+−5x+−2=0
Step 1: Use quadratic formula with a=3, b=-5, c=-2.
x= (−b±√b2−4ac )2a
x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)
x= (5±√49 )/6
x=2 or x= −1 /3
Answer:
x=2 or x= −1/ 3
The solutions to the equation are x = -1/3 and x = 2.
Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:
First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Next, we set each factor equal to 0 and solve for x.
(3x + 1)(x - 2) = 0
3x + 1 = 0
3x = -1
x = -1/3
x - 2 = 0
x = 2
Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.
Here is the explanation for each of the steps:
Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.
Learn more about equation here: brainly.com/question/29657983
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