Answer:
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at least 64%, that is:
[tex]H_0: p \geq 0.64[/tex]
At the alternative hypothesis, we test if the proportion is of less than 64%, that is:
[tex]H_1: p < 0.64[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
64% is tested at the null hypothesis:
This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.
This means that [tex]n = 900, X = 0.61[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]
[tex]z = -1.88[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.
Looking at the z-table, z = -1.88 has a p-value of 0.0301.
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
look at the image for the question?
Answer:
396 in ^3
Step-by-step explanation:
The volume of a rectangular prism is
V = l*w*h where l is the length, w is the width, and h is the height
V = 12 * 3 * 11
V = 396 in ^3
How would you find the coefficient of the third term in (x+5)^7?
Answer:
The answer is option B
Step-by-step explanation:
To find the coefficient of the third term in
[tex](x + 5)^{7} [/tex]
Rewrite the expansion in the form
[tex](a + x)^{n} [/tex]
where n is the index
So we have
[tex] ({5 + x})^{7} [/tex]
After that we use the formula
[tex]nCr( {a}^{n - r} ) {x}^{r} [/tex]
where r is the term we are looking for
For the third term we are looking for the term containing x²
that's
r + 1 = 3
r = 2
So to find the coefficient of the third term
We have
[tex]7C2[/tex]
Hope this helps you
first of all, the notation is wrong it should be [tex] {}^nC_r \text{ and more usual notation is } {n \choose k} [/tex]
second, the
[tex](r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r[/tex]
here [tex] a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 [/tex]
so the coefficient of third term is, [tex]{7 \choose 2}={7\choose 5}[/tex]
an important property of binomial coefficient you should know:
[tex] {n \choose k}={n \choose {n-k}}[/tex]
and if you interchange [tex] x \text{ and } a[/tex]
only the "order" will get reversed. i.e. the series will start from back.
another thing, the [tex] k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}[/tex]
[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]
In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.
The number of times that each prime divides the original integer becomes its exponent in the final result.
In here, Prime number 2 to the power of 2 equals 4.
[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]
First, We need to add fractions-
Rule:-
[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]
LCD = [tex]7 \cdot 2^{2}[/tex]
[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]
[tex]x=2[/tex]
OAmalOHopeO
Ax + By = C for x. plz sove
Answer:
[tex]\boxed{\boxed{ x=\frac{C-By}{A}; A\neq 0}}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\\\\Ax+By-By=C-By\\\\Ax=C-By\\\\\frac{Ax=C-By}{A}\\\\\boxed{ x=\frac{C-By}{A}; A\neq 0}[/tex]
Hope this helps.
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.
a) Conduct the appropriate hypothesis test using a 0.1 level of significance.
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
i. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
ii. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
iii. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
iv. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
Answer:
Step-by-step explanation:
99% =2.58
xbar / Point Est. 50.67
µ 50
σ 3.9
n 36
Confidence Interval
50-> (48.9,52.44) -> Fail to Reject H0
Test Statistic 1.0308
P-Value 0.1549
Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$179.80
Step-by-step explanation:
799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.
The sum of three numbers is 72 the second number is three times the third the third number is eight more than the first what are the numbers
Answer:
Our three numbers are 8, 48, and 16.
Step-by-step explanation:
Let the first, second, and third numbers be x, y, and z, respectively.
The sum of them is 72. In other words:
[tex]x + y + z = 72[/tex]
The second number y is three times the third number z. So:
[tex]y = 3z[/tex]
And the third number z is eight more than the first number x. So:
[tex]z = x + 8[/tex]
To find the numbers, solve for the system. We can substitute the last two equations into the first:
[tex]x + (3z) + ( x + 8) = 72[/tex]
Substitute again:
[tex]\displaystyle x + 3(x+8) + x+8 = 72[/tex]
Solve for x. Distribute:
[tex]x+3x+24+x+8=72[/tex]
Combine like term:
[tex]5x + 32 = 72[/tex]
Subtract:
[tex]5x = 40[/tex]
And divide:
[tex]x=8[/tex]
Thus, the first number is eight.
And since the third number is eight more than the first, the third number z is 16.
The second number is three times the third. Thus, the second number y is 3(16) or 48.
Our three numbers are 8, 48, and 16.
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answer:
[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]
Step-by-step explanation:
Given that:
1) x ∝ √y
2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]
Combining the proportionality
=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
Where k is the constant of proportionality.
Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A
Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
Find the area of the shape shown below.
2
2
nd
2
Need help Plz hurry and answer!!!
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
Which of the following is equivalent to –2i(6 – 7i)?
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
plz someone help me with this question
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
help asap!! will get branliest.
Answer:
5/2
Step-by-step explanation:
5^(-3). 2^2.5^6 / (2^3.5^2)
By the law of indices,
=5^(-3+6-2).2^(2-3)
=5^1.2^(-1)
=5. 2^-1
=5/2
If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4
Answer:
The correct answer is c
Step-by-step explanation:
Answer:
C.) 3/2
Explanation:
PLATO
The graph below represents which of the following functions?
Answer:
D
Step-by-step explanation:
The correct answer is D, try graphing them on desmos.
Bianca took a job that paid $150 the first week. She was guaranteed a raise of 6% each week. How much money will she make in all over 8 weeks? Round the answer to the nearest cent. please answer with the reasoning, I want to learn how to solve this and not just get the answer. Thank you.
Answer:
$225.54 (hope it help)
Step-by-step explanation:
for 2nd week
$150 for the first week and a raise of 6% each week
which means 150+6%
6% of 150 is 9 (150x0.06)
150+9=159
and it repeats
for 3rd week
6% of 159 is 9.54 (159x0.06)
159+9.54=168.54
for 4th week
6% of 168.54 is 10.1124 (168.54x0.06)
168.54+10.1124=178.652
for 5th week
6% of 178.652 is 10.71912 (178.652x0.06)
178.652+10.71912=189.37112
an easier to do it is to just do 178.652 + 6% on your calculater
and I'll skip all the way to the 8th since you know the formula
212.777390432+6%=225.544033858
225.544033858≈225.54
Complete the table for the given rule. Rule: y = x + 3. X ? Y 4. X ? Y 8. X ? Y 5
Answer:
X 1 for Y 4
X 5 for Y 8
X 2 for Y 5
Step-by-step explanation:
We can substitute the values of Y in the formula and then subtract three from both sides.
Lori wants to buy a radio for 60 dollars.
She can pay $60 now, or she can pay $12
a month for 6 months. How much more will
she pay for the radio if she makes monthly
payments?
Answer:
Lori will pay $12 more if she makes monthly payments
Step-by-step explanation:
to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72
subtracting the amount she would pay as a down payment
$72 - $60 is $12
Lori will pay $12 more if she makes monthly payments
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.). lim h → 0 1 + h − 1 h
Answer:
1Step-by-step explanation:
Given the limit of a function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h}[/tex], to evaluate the limit, the following steps must be taken.
Step 1: Substitute h = 0 into the function given.
[tex]= \lim_{h \to 0} \frac{(1+h)-1}{h}\\\\[/tex]
[tex]= \frac{(1+0)-1}{0}\\\\= \frac{1-1}{0} \\\\= \frac{0}{0} (indeterminate)\\[/tex]
Step 2: Apply l'hospital rule
[tex]\lim_{h \to 0} \frac{\frac{d}{dh}[(1+h)-1] } {\frac{d}{dh}(h) } \\\\= \frac{0+1-0}{1}\\ \\= \frac{1}{1} \\ \\= 1[/tex]
Hence the limit of the function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h} \ is \ 1[/tex]
Find the zeros of the function in the interval (-2 pie, 2 pie). f(x) = 3 cos x
Answer:
Roots are -π/2 and π/2
Step-by-step explanation:
[tex]{ \bf{f(x) = 3 \cos(x) }}[/tex]
when x is -2π:
[tex]{ \sf{f( - 2\pi) = 3 \cos( - 2\pi) }} \\ { \sf{ = 3}}[/tex]
hence -2π is not a zero of the function
when x is 2π:
[tex]{ \sf{f(2\pi) = 3 \cos(2\pi) }} \\ { \sf{ = 3}}[/tex]
hence 2π is not a zero of the function
when x is π/2:
[tex]{ \sf{f( \frac{\pi}{2}) = 3 \cos( \frac{\pi}{2} ) }} \\ { \sf{ = 0}}[/tex]
Hence ±π/2 is the zero of the function.
A line is an undefined termi because it
Answer:
Goes on forever.
Step-by-step explanation:
Do numbers below 0 make sense outside of the context of temperature? If you think so, give some examples to show how they make sense. If you don’t think so, give some examples to show otherwise.
Answer:
Yes, they make sense outside the context of temperature.
Step-by-step explanation:
If you are standing in a line, and mark your current position as 0 then if you take two steps ahead it can be counted as positive and if you take two steps back from your current position it can be counted as negative. The positive and negative can denote your forward and backward movement respectively.
If we denote the growth in companies revenue as positive and dip as negative then it would also make sense. A positive number would mean profit for the company while a negative sign would show loss.
A ball thrown upwards hits a roof and returns back to the ground.
The upward movement is modeled by a function [tex]s=-t^2+3t+4[/tex]
s= −(t^2)+3t+4
and the downward movement is modeled by [tex]s=-t^2+3t+4[/tex]
s= −2(t^2)+t+7, where s is the distance (in metres) from the ground and t is the time in seconds.
Find the height of the roof from the ground.
Answer: 6 m
A ball thrown upwards from the altitude 4 m,
hits a roof and returns back to the ground.
upward movement: s= −t²+3t+4
downward movement: s=-2t²+t+7
Step-by-step explanation:
Let's calculate the intersection:
[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]
Sorry, i have forgotten the picture.
-3(y-5)+6y-2 simplify using distributive property and then combine like terms ANOTHER ONE PLEASE
Answer:
3y+13
Step-by-step explanation:
-3(y-5)+6y-2
Distribute
-3y +15 +6y-2
Combine like terms
-3y+6y +15-2
3y +13
[tex]\bf \large{\purple{ \implies}} \tt \: - 3(y - 5) \: + \: 6y \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 15 \: + \: 6y \: - 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 6y \: + \: 15 \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: 3y \: + \: 13[/tex]
An angle is 100° angle. how many degrees will you add it to make it a linear pair ?
Answer:
80
Step-by-step explanation:
linear pair = 180
Now,
100 + 80 = 180
If the area of a circle is 16π, the circumference of the circle is:
A. 8π
B. 16π
C. 2π
D. 4π
Laura made $273 for 13 hours of work.
At the same rate, how much would she make for 17 hours of work?
sl
X
$
?
I
The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 3 minutes. What cutoff value would separate the 2.5% of orders that take the most time to process?
A) 4.76 minutes
B) 3.52 minutes
C) 10.01 minutes
D) 11.00 minutes
E) 12.00 minutes
Find a • b. a = 5i + 7j, b = -4i + 3j
Answer:
[tex]a \cdot b = 1[/tex]
Step-by-step explanation:
[tex] a = 5i + 7j [/tex]
[tex] b = -4i + 3j [/tex]
[tex] a = a_xi + a_yj [/tex]
[tex]b = b_xi + b_yj[/tex]
[tex] a \cdot b = a_xb_x + a_yb_y [/tex]
[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]
[tex] a \cdot b = -20 + 21 [/tex]
[tex]a \cdot b = 1[/tex]
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?
The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.
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