Answer:
-8
Step-by-step explanation:
The term-to-term rule is -8.
16 - 24= -8
8 - 16 = -8
0 - 8 = -8
The arithmetic sequence is a concept of algebra and in given sequence 24, 16, 8, 0 the next term is, -8
What is an arithmetic sequence?In the arithmetic sequence the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any [tex]n^{th}[/tex] term in AP,
T = a + (n-1)d
d = T₂-T₁
Where, a is first term , n is [tex]n^{th}[/tex] term and d is common difference
Given sequence,
24, 16, 8, 0
a = 24
n = 5
d = 16-24 = -8
T₅ = 24 +( (5-1)×(-8))
T₅ = -8
Hence, [tex]5^{th}[/tex] term of sequence is -8
To know more about arithmetic sequence check:
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how many are 5 x 5 ?
[tex](2 + 6)(2 + 3)[/tex]
Answer:
40 because (8)(5)=40 when you add the numbers inside the parenthesis
Step-by-step explanation:
Look at my picture for the written work for ANOTHER method
To solve this problem, you use the method called FOIL.
F= multiply the FIRST terms
O= multiply the OUTTER terms
I= multiply the INNER terms
L= multiply the LAST terms
Please rate this the brainlist if this helped, thanks!
Answer:
[tex]40[/tex]
Step-by-step explanation:
[tex](2+6)(2+3)[/tex]
Solve brackets.
[tex](8)(5)[/tex]
Multiply.
[tex]=40[/tex]
[tex](\sqrt{5})(\sqrt[3]{5})[/tex] answers [tex]6\frac{5}{6}\\5\frac{1}{6}\\5\frac{2}{3}\\5\frac{7}{6}[/tex]
Answer:
A : [tex]5^{\frac{5}{6} }[/tex]
Step-by-step explanation:
Because you're multiplying two numbers with the same base, you can add their exponents:
[tex]\sqrt{5} = 5^{\frac{1}{2} } = 5^{\frac{3}{6} } \\\sqrt[3]{5} =5^{\frac{1}{3} } = 5^{\frac{2}{6} }[/tex]
[tex]5^{\frac{3}{6} } * 5^{\frac{2}{6} } = 5^{\frac{5}{6} }[/tex]
If x ∥ y and y ∥ z, then _____
Answer:
x ║ z
Step-by-step explanation:
Lines parallel to the same line are parallel to each other.
x and z are both parallel to y, so are parallel to each other:
x ║ z
What steps would you take to determine if these figures are similar? Check all that apply. Use a scale factor of 2. Multiply the vertices of polygon ABCD by One-half. Translate the intermediate image 4 units down. Perform two different dilations. Reflect the intermediate image.
Answer:
Well I took it"s Reflect the intermediate image. and Multiply the vertices of polygon ABCD by One-half.
Step-by-step explanation:
Answer:
2 and 5 or B and E
Step-by-step explanation:
i did it on edge! ; )
need answer asap!!! pls help ?
Answer:
what is your problem
Step-by-step explanation:
What will happen (other things being equal) if you increase the sample size used to construct a given confidence interval?
Answer:
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
Step-by-step explanation:
The sample size is important to find the margin of errror of a confidence interval.
The margin of error is given by a formula in the following format:
[tex]M = \frac{c*s}{\sqrt{n}}[/tex]
In which c is the critical value(depends on the distribution used, can be T or Z), s is the standard deviation(of the sample or the population) and n is the size of the sample.
As n increases, M decreases, which leads to a lower margin of error.
The lower the margin of error, the more precise the interval is.
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
2. Write an equation of a line in slope-intercept form
that passes through a point (4,-6) and has a slope of -3.
Answer:
y = -3x+6
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = -3x +b
Substitute the point into the equation
-6 = -3*4+b
-6 =-12+b
Add 12 to each side
-6+12 =-12+12+b
6=b
y = -3x+6
Which expression is equivalent to 8 - (6r + 2)? A. -6r + 6 B. 2r + 2 C. 6r + 10 D. -6r + 10
Answer:
6 -6r
Step-by-step explanation:
8 - (6r + 2)
Distribute the minus sign
8 - 6r -2
Combine like terms
6 -6r
Answer:
A. -6r+6
Step-by-step explanation:
We are given the expression:
8-(6r+2)
First, let's distribute the negative sign. Multiply each term inside the parentheses by -1.
8+ (-1*6r) + (-1*2)
8-6r-2
Now, combine like terms. Add the constants, or terms without a variable.
-6r + (8+-2)
-6r + (8-2)
-6r + (6)
-6r+6
The answer is A. -6r+6
Evaluate the expression ( 1 + 2 i ) ( − 2 − 1 i ) and write the result in the form a + b i .
Answer:
- 5i.
Step-by-step explanation:
( 1 + 2 i ) ( − 2 − 1 i )
= 1 * -2 + 1*-1i + 2i*-2 - 2i*1i
= -2 - i - 4i - 2i^2 i^2 = -1 so we have:
-2 - 5i +2
= 0 - 5i
= -5i.
a lorry is travelling at 13.5 m/s along a road whereto speed limit is 50km/h. She that the lorry is travelling below the speed limit
Answer:
First, convert 13.5 m/s to km/hr
13.5 x 3.6 = 48.6 km/hr
This is below the speed limit of 50 km/hr
Answer:
48600/hour × 1/1000= 48.6km/h
Step-by-step explanation:
Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant. Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state).
A. State the null and alternative hypotheses.
B. Find the value of the test statistic.
C. What is the p-value?
D. What is your conclusion?
1. Reject H0. There is a significant difference in drug resistance between the two states.
2. Do not reject H0. There is a significant difference in drug resistance between the two states.
3. Reject H0. There is not a significant difference in drug resistance between the two states.
4. Do not reject H0. There is not a significant difference in drug resistance between the two states.
Answer:
A)
Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states
Alternative Hypothesis :H₁:
There is significant difference between in drug resistance between the two states
B)
The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance
Rejected H₀
There is a significant difference in drug resistance between the two states.
C)
P - value = 0.0066
P - value = 0.0066 < 0.02
D)
1) Reject H₀
There is a significant difference in drug resistance between the two states.
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 174
Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.
First sample proportion
[tex]p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632[/tex]
Given second sample size n₂ = 375
Given data Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant
Second sample proportion
[tex]p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186[/tex]
Step(ii):-
Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states
Alternative Hypothesis :H₁:
There is significant difference between in drug resistance between the two states
Test statistic
[tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]
Where
[tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }[/tex]
[tex]P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } = \frac{17.9718}{549} = 0.0327[/tex]
Q = 1 - P = 1 - 0.0327 = 0.9673
Step(iii):-
Test statistic
[tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]
[tex]Z = \frac{0.0632-0.0186 }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }[/tex]
Z = 2.7261
Level of significance = 0.02 or 0.98
The z-value = 2.054
The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance
Reject H₀
There is a significant difference in drug resistance between the two states.
P- value
P( Z > 2.7261) = 1 - P( Z < 2.726)
= 1 - ( 0.5 + A (2.72))
= 0.5 - 0.4967
= 0.0033
we will use two tailed test
2 P( Z > 2.7261) = 2 × 0.0033
= 0.0066
P - value = 0.0066 < 0.02
Reject H₀
There is a significant difference in drug resistance between the two states.
Consider country Z with a GDP level of 210000 and a growth rate of 5% in 2019 (ie calculated at the end of year 2019). The experts predict that the growth of the economy of country Z will gradually slowdown in the coming year. More precisely, they foresee the following growth rate for the future: 2019-2022 (5%), 2022-2025 (3%).
a. Assuming that the prediction of the experts listed above are accurate, when in the future will country Z's GDP double compared to the GDP level of 2019??
b. What would country Z's GDP growth rate be from 2025 and so on at 1%. Explain your reasoning carefully
Answer:
a. Country Z's GDP will double in 23 years' time, given the experts prediction of 5% growth for 3 and 3% thereafter.
b. Z's GDP 's growth rate would be 39%.
This growth rate is calculated by determining Z's GDP from the end of 2025 as 292,000. So, (292,000 - 210,000)/210,000 x 100 = 39% from the 2019 base year.
Step-by-step explanation:
a) 2019 Country Z's GDP = 210,000
2019 Growth rate = 5%
Future growth rate:
2019 - 2022 = 5%
2022- 2025 = 3%
2025 - so on = 1%
Let Country Z's GDP in 2019 = G₀ = 210,000
n = number of years from 2019
g = growth rate = 5%
(1 + g)ⁿ = increase in GDP as a result of the growth rate and number of years
Gⁿ = GDP in n years
Therefore, Gⁿ = G₀(1 + g)ⁿ
b) With GDP growth of 5% from 2019 to 2022, the GDP will be
= 210,000 (1 + 5%)³
= 210,000 x 1.158
= 243,000 approx.
c) From 2022 to 2025 at 3%, the GDP will be
= 243,000 (1 + 3%)∧20
= 243,000 x 1.817
= 441,531
d) Z's GDP from 2025 with 1% growth and so on, will become double at:
Gⁿ = 265,600(1 + 1%)∧48
= 265,600 x 1.61
= 428,000
48 + 6 = 54 years.
If f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction, what is the value of (StartFraction f Over g EndFraction) (5)?
Answer:
270
Step-by-step explanation:
f(5) = 7 +4·5 = 27
g(5) = 1/(2·5) = 1/10
The ratio of functions is the ratio of their individual values:
(f/g)(5) = f(5)/g(5) = 27/(1/10)
(f/g)(5) = 270
pls help me pls pls pls
Answer: 1x + 2y = 4
Step-by-step explanation:
The equation of the line is y = -1/2x + 2.
First, let's make 4 on one side of the equation. First, bring x to the left. y + 1/2x = 2. Then multiply the whole equation by two. Thus, 1x + 2y = 4.
Hope it helps <3
Fill in the missing information. Tim Worker is doing his budget. He discovers that the average miscellaneous expense is $45.00 with a standard deviation of $16.00. What percent of his expense in this category would he expect to fall between $38.60 and $57.80?
Answer:
[tex] P(38.6 <X <57.8)[/tex]
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]
[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]
We can find the probability of interest using the normal standard table and with the following difference:
[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]
Step-by-step explanation:
Let X the random variable who represent the expense and we assume the following parameters:
[tex]\mu = 45, \sigma 16[/tex]
And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:
[tex] P(38.6 <X <57.8)[/tex]
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]
[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]
We can find the probability of interest using the normal standard table and with the following difference:
[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]
What is the explicit rule for the following sequence? 48, 24, 12, 6, ……
4(x+1)=16 HELP MEEEEEE
Answer:
4(x + 1) = 16
x + 1 = 4 (Divide equation by 4)
x = 3 (subtract 1)
Answer:
x = 3
Step-by-step explanation:
4(x + 1)=16
Expand the brackets.
4x + 4 = 16
Subtract 4 on both sides.
4x + 4 - 4 = 16 - 4
4x = 12
Divide both sides by 4.
4x/4 = 12/4
x = 3
the class mean was 72 with a standard deviation of 4.2. Calculate the z-score (to 2 decimal places) for a person who received score of 59. Is it usual or unusual?
lllluvyvyvyvtctctvtvtctvtctctctctctctctvtvyvyvyvyvyvyvtvtv
Plz answer what is in the screen shot!
Answer:
([tex]\sqrt{15}[/tex])/7
Step-by-step explanation:
Let b be the tird side of the triangle
tanθ= b/c
using the pythagorian theorem we get :
a²+b²= c² ⇒ b²= c²-a²= 8²-7²=15 ⇒b=√15
so: tanθ= √15/7
what is the answer to the problem i need help with?
Answer:
C
Step-by-step explanation:
Recall the equation for a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where the center is (h,k) and the radius is r.
The given equation is:
[tex](x+5)^2+(y+7)^2=21^2[/tex]
Another way to write this is:
[tex](x-(-5))^2+(y-(-7))^2=21^2[/tex]
Thus, we can see that h=-5 and k=-7.
The center is at (-5, -7).
Will give brainliest, can somebody help me with this question
Answer:
A = 5x + 5
Step-by-step explanation:
Area of Parallelogram Formula: A = bh
Since we are given b = 5 and h = x + 1, simply plug it into the formula:
A = 5(x + 1)
A = 5x + 5
━━━━━━━☆☆━━━━━━━
▹ Answer
A = 5x + 5
▹ Step-by-Step Explanation
A = bh
A = 5(x + 1)
A = 5x + 5
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
What is the inverse of the function f(x) = 2x + 1?
1
1
h(x) =
X-
2
2
1
1
Oh(x) =
- x +
O h(x) =
3x-2
Oh(x) =
= {x+2
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x+1[/tex]
Replace it with y
[tex]y = 2x+1[/tex]
Exchange the values of x and y
[tex]x = 2y+1[/tex]
Solve for y
[tex]x = 2y+1[/tex]
Subtracting 1 from both sides
[tex]2y = x-1[/tex]
Dividing both sides by 2
[tex]y = \frac{x-1}{2}[/tex]
Replace it by [tex]f^{-1}[/tex]
So,
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Answer:
[tex]\displaystyle f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
Step-by-step explanation:
f(x) = 2x + 1
f(x) = y (output)
y = 2x + 1
Solve for x.
y - 1 = 2x
Divide 2 on both sides.
y/2 - 1/2 = x
1/2y - 1/2 = x
Switch variables.
1/2x - 1/2 = y
[tex]f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
Evaluate the following integral using trigonometric substitution.
Integral from 7 StartRoot 49 - x2 EndRoot dx
1. What substitution will be the most helpful for evaluating thisintegral?
2. Find dx?
3. Rewrite the given integral using substitution.
Answer:
Step-by-step explanation:
1. Given the integral function [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex], using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as [tex]asin \theta[/tex] i.e [tex]x = a sin\theta[/tex].
All integrals in the form [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex] are always evaluated using the substitute given where 'a' is any constant.
From the given integral, [tex]\int\limits {7\sqrt{49-x^{2} } } \, dx = \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx[/tex] where a = 7 in this case.
The substitute will therefore be [tex]x = 7 sin\theta[/tex]
2.) Given [tex]x = 7 sin\theta[/tex]
[tex]\frac{dx}{d \theta} = 7cos \theta[/tex]
cross multiplying
[tex]dx = 7cos\theta d\theta[/tex]
3.) Rewriting the given integral using the substiution will result into;
[tex]\int\limits {7\sqrt{49-x^{2} } } \, dx \\= \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -(7sin\theta)^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -49sin^{2}\theta } } \, dx\\= \int\limits {7\sqrt{49(1-sin^{2}\theta)} } } \, dx\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, dx\\since\ dx = 7cos\theta d\theta\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, 7cos\theta d\theta\\= \int\limits {7\{7(cos\theta)} }}} \, 7cos\theta d\theta\\[/tex]
[tex]= \int\limits343 cos^{2} \theta \, d\theta[/tex]
Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one. The asymptote is x = -3
Answer:
[tex]y=\log_3{(x+3)}[/tex]
Step-by-step explanation:
The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.
The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.
The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.
The function is ...
[tex]\boxed{y=\log_3{(x+3)}}[/tex]
I NEED HELP PLEASE, THANKS! :)
Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)
Answer:
-17.67 +3.43i
Step-by-step explanation:
Carry out the indicated math:
18 cis 169° = (18·cos(169°) +i·18·sin(169°)) = (18·(-0.9816) +i·18·0.1908)
= -17.67 +i·3.43
Answer:
The rectangular form is z = -17.67 + i 3.43
Step-by-step explanation:
Which of the following are examples of statistical questions?
a
How many pairs of shoes do you own?
b
What types of music does the 6th grade like?
c
How many sodas do Jack and his friends drink in a week?
d
How many cats does Jack have?
The correct answers are B. What types of music does the 6th grade like? and C. How many sodas do Jack and his friends drink in a week?
Explanation:
Statistical questions are those that can only be answered by collecting and analyzing numerical data. This often implies gathering data from a group of individuals and using this to answer the question. Additionally, statistics questions are complex and do not have a direct or unique answer. In this context, the question "What types of music does the 6th grade like?" is statistical because to answer this, it is necessary to collect data from all students in 6th grade and analyze it. This occurs in "How many sodas do Jack and his friends drink in a week?" because it is necessary to know the number of sodas each person drinks in a week.
On the other hand, the questions "How many pairs of shoes do you own?" or "How many cats does Jack have?" are not statistical because it is not necessary to collect a lot of data to know the answer and they can be answered through only one number.
What is the length of AC?
Answer:
16Option A is the right option
Step-by-step explanation:
BO is bisector of line AC
so,
AB=BC
AC=AB+BC
=8+8
= 16
Hope this helps...
Good luck on your assignment....
Answer:
16
Step-by-step explanation
BD is perpendicular bisector of AC so BC is 8.
8+8=16
Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answer:
She would spend $52.50.
Step-by-step explanation:
c = 3.5t
c = 3.5(15)
c = $52.50
Hope this helped! :)
Answer:
328.48
Step-by-step explanation:
someone please help me!!!
Explanation:
Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)
r = radius
h = height of cone
In this case,
r = 8 is the radius
h = 41
So,
SA = surface area
SA = pi*r^2 + pi*r*sqrt(r^2+h^2)
SA = pi*8^2 + pi*8*sqrt(8^2+41^2)
SA = 1250.936884057 use a calculator for this step
SA = 1251 square meters approximately