Answer:
wat do u want me to do
Step-by-step explanation:
The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP
Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6 -----------------------------------1
second statement
sum of the next 4 terms inclusive
T₉ = ⁹/₂(2a + 8d ) = 69
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
divide through by 18 to reduce to lowest time
a + 4d = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
a + 2d = 6
a + 4d = 11
-2d = -5
d = ⁵/₂.
Now substitute for d to get a
a + 2(⁵/₂) = 6
a + 5 = 6
a = 6 - 5
a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............
The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
What is sequence?
An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
The sum of the first 5 terms of an AP is 30,
Write the equations as shown below,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6
T₉ = ⁹/₂(2a + 8d ) = 69 (sum of the next 4 terms inclusive)
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
a + 4d = 11
Solve the equation as shown below,
d = ⁵/₂, and a = 1.
Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
To know more about the sequence:
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If you have a piece of glass that is 12in X 12in - how many square feet is it?
Answer:
1 square foot is the answer
Answer:
1 ft^2
Step-by-step explanation:
We know 12 inches = 1 ft
12 inches by 12 inches
1 ft by 1 ft
The area is 1 * 1 = 1 ft^2
Calculate two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimal places.) f(x) = x2 − 5, x1 = 2n xn f(xn) f '(xn) f(xn)/f '(xn) xn − f(xn)/f '(xn)1 2
Answer:
Step-by-step explanation:
Given that:
[tex]\mathsf{f(x) = x^2 -5 } \\ \\ \mathsf{x_1 = 2}[/tex]
The derivative of the first function of (x) is:
[tex]\mathsf{f'(x) =2x }[/tex]
According to Newton's Raphson method for function formula:
[tex]{\mathrm{x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}}[/tex]
where;
[tex]\mathbf{x_1 =2}[/tex]
The first iteration is as follows:
[tex]\mathtt{f(x_1) = (2)^2 - 5} \\ \\ \mathbf{f(x_1) = -1}[/tex]
[tex]\mathtt{f'(x_1) = 2(2)} \\ \\ \mathbf{ = 4}[/tex]
[tex]\mathtt{\dfrac{f(x_1)}{f'(x_1)}} = \dfrac{-1}{4}}[/tex]
[tex]\mathbf{\dfrac{f(x_1)}{f'(x_1)} =-0.25}[/tex]
[tex]\mathtt{x_1 - \dfrac{f(x_1)}{f'(x_1)}} = \mathtt{2 - (-0.25)}}[/tex]
[tex]\mathbf{x_1 - \dfrac{f(x_1)}{f'(x_1)} = 2.25}[/tex]
Therefore;
[tex]\mathbf{x_2 = 2.25}[/tex]
For the second iteration;
[tex]\mathtt f(x_2) = (2.25)^2 -5}[/tex]
[tex]\mathtt f(x_2) = 5.0625-5}[/tex]
[tex]\mathbf{ f(x_2) =0.0625}[/tex]
[tex]\mathtt{f'(x_2)= 2(2.25)}[/tex]
[tex]\mathbf{f'(x_2)= 4.5}[/tex]
[tex]\mathtt{ \dfrac{f(x_2)}{f'(x_2)}} = \dfrac{0.0625}{4.5}}[/tex]
[tex]\mathbf{ \dfrac{f(x_2)}{f'(x_2)} = 0.01389}[/tex]
[tex]\mathtt{x_2 - \dfrac{f(x_2)}{f'(x_2)}} = \mathtt{2.25 -0.01389}}[/tex]
[tex]\mathbf{x_2 - \dfrac{f(x_2)}{f'(x_2)} = 2.2361}}[/tex]
Therefore, [tex]\mathbf{x_3 = 2.2361}[/tex]
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99% confidence if (a) he uses a previous estimate of 22%?
Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
Someone PLEASE help!
Step-by-step explanation:
[tex]f(f(x)) = f( {x}^{2} + 4)[/tex]
[tex] = {( {x}^{2} + 4) }^{2} + 4[/tex]
[tex] = {x}^{4} + 4 {x}^{2} + 16 + 4[/tex]
[tex] = {x}^{4} + 8 {x}^{2} + 20[/tex]
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
step by step
given length=6
so area of square is given by s2 i.e 6^2
=6×6
=36 (Ans)
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown
Answer:
The minimum sample size is [tex]n = 2123[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.028[/tex]
Given that the confidence level is 99% then the level of significance is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Now let assume that the sample proportion is [tex]\r p = 0.5[/tex]
hence [tex]\r q = 1 - \r p[/tex]
=> [tex]\r q = 0.50[/tex]
Generally the sample size is mathematically represented as
[tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]
[tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]
[tex]n = 2123[/tex]
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....
Simplify 10 - [14 = (3 + 4) · 2]+3
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
the principal p is borrowed at a simple interest rate r for a period of time t. find the loan's future value g P = 700, r = 8.25, t = 3 months
Answer:
Hey there!
Simple interest formula: I=PRT
I=700(8.25)(0.25)
I=1443.75
Hope this helps :)
Answer:
Step-by-step explanation:
I = PRT
I = 700(0.0825)(1/4) = 14.44
Because the interest is usually in percentage and it's impossible to have 825% as your interest rate. So the actual interest rate has to be 0.0825.
The formula above calculated the interest, if you want the total, you will need to add 700 to that number.
[img id="5156824"][/img]Here's a small quick example of the formula that should help.
What are two solutions of x
Answer:
Answer is attached below :)
find the slope of the line y = 4
Answer:
Brainleist!
Step-by-step explanation:
0
there is no y=mX+b
there is no x no XXXX
that means the slope must be 0 (bc theres a y)
Sorry if my explanation is bad... let me know in comments if u need more help
[PLEASE HELP] Consider this function, f(x) = 2X - 6.
Match each transformation of f (x) with its descriptions..
Answer:
Find answer below
Step-by-step explanation:
f(x)=2x-6
Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}
Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}
Parity of 2x-6: Neither even nor odd
Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)
inverse of 2x-6: x/2+6/2
slope of 2x-6: m=2
Plotting : y=2x-6
A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat
Answer:
2 servings of salad and 1 serving of soup
Step-by-step explanation:
In the given scenario the aim is to minimise the fat content of the food combination.
Fat content of soup is 3mg while fat content of salad is 2 mg.
Using Soup as 0 and Salad as 2 will not give the required vitamin content
The logical step will be to keep servings of soup to the minimum.
Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1
1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.
This will not work because amount of vitamin B complex is not up to 10 mg
2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat
This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.
Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving
in the diagram, POS and UOR are straight lines. OQ is the bisector of angle POR . angle POU and angle UOT are complementary angles.Find the values ofx abd y.
Answer:
x = 34° and y = 62°
Step-by-step explanation:
Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.
In high school, a teacher gave two sections of a class the same arithmetic test. The results were as follows:
Section I: Mean 45, Standard
Deviation 6.5
Section II: Mean 45,
Standard deviation 3.1
What conclusions is correct?
Answer:
Section I test scores are more dispersed that that of section II.
Step-by-step explanation:
Consider the data collected from the arithmetic test given to two sections of a school.
Section I: Mean = 45, Standard Deviation = 6.5
Section II: Mean = 45, Standard deviation = 3.1
The mean of both the sections are same, i.e. 45.
So there is no comparison that can be made from the center of the distribution.
The standard deviation for section I is 6.5 and the standard deviation for section II is 3.1.
The standard deviation is a measure of dispersion, i.e. it tells us how dispersed the data is from the mean or how much variability is present in the data.
The standard deviation for section I is higher than that of section II.
So, this implies that section I test scores are more dispersed that that of section II.
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $15.59$ and $15.6$ so each division is $\frac{15.60-15.59}{10}=0.001$
A is 5 division from $15.59$, so, A is $15.59+5\times 0.001=15.595$
similarly, C is 4 division behind $15.59$ so it is $15.590-4\times0.001=15.586$
and B is $15.601$
A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2
Answer:
fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb
Step-by-step explanation:
t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh
3(x–6)=18 help plese
Answer:
x = 12
Step-by-step explanation:
3(x–6)=18
x-6 = 18:3
x-6 = 6
x = 6+6
x = 12
Answer:
x=12
Step-by-step explanation:
PLEASE HELP ASAP Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable d represents Madelyn's distance driven, in miles. The variable t represents the number of hours since the other drivers began to race. Which equation can be used to determine the distance Madelyn drove t hours into the race? d=55t−0.5 d=55(t+0.5) d=55(t−0.5) d = 55t + 0.5
Answer:
d=55(t+0.5)
Step-by-step explanation:
d=55(t+0.5)
Answer:
27.5
Step-by-step explanation:
Find the measure of c.
Answer:
149 degrees
Step-by-step explanation:
This shape is a cyclic, so opposite angles add up to 180 degrees.
180-31 = 149
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answer:
Question 18: B. 104
Question 19: [tex] x = \frac{3}{2} [/tex]
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
[tex] y = \frac{k}{x^2} [/tex] ,
where k is constant
y = 26 when x = 4,
Constant, k, = [tex] y*x^2 = k [/tex]
[tex] k = 26*4^2 = 416 [/tex]
The equation would be [tex] y*x^2 = 416 [/tex]
Step 2: use the equation to find y when X = 2.
[tex] y*x^2 = 416 [/tex]
[tex] y*2^2 = 416 [/tex]
[tex] y*4 = 416 [/tex]
Divide both sides by 4
[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]
[tex] y = 104 [/tex]
Question 19:
[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]
Cross multiply
[tex] x(7) = 3(x + 2) [/tex]
[tex] 7x = 3x + 6 [/tex]
Subtract 3x from both sides
[tex] 7x - 3x = 3x + 6 - 3x [/tex]
[tex] 4x = 6 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{6}{4} [/tex]
[tex] x = \frac{3}{2} [/tex]
Answer: D.) 52
Explanation: I guessed and got it right lol
A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?
Answer:
34 grams
Step-by-step explanation:
If the remaining sample has 30.26 grams of radioactive substance, and 11% of it decayed, that means that 30.26 grams is 89% of the original. Let the original be x.
30.26=0.89x
Multiply both by one hundred
3026=89x
Divide both by 89
34=x
x=original, so the original was 34 grams.
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
Which of the following represents the largest number?
A. 1.75 * 10^6
B .1.25 * 10^6
C. 2.75 * 10^5
D. 3.82 * 10^5
Answer:
A
Step-by-step explanation:
A 1.75 * 10^6 = 1750000
B 1.25 * 10^6 = 1250000
C 2.75*10^5 = 275000
D 3.82*10^5 = 82000
option A (1.75 * 10⁶) represents the largest number among the given options.
To determine which of the given numbers represents the largest number, we can compare the exponents of 10 in each option.
A. 1.75 * 10⁶
B. 1.25 * 10⁶
C. 2.75 * 10⁵
D. 3.82 * 10⁵
Comparing the exponents:
A: 10⁶
B: 10⁶
C: 10⁵
D: 10⁵
Since both options A and B have an exponent of 10⁶, we need to compare the coefficients.
1.75 is greater than 1.25, so option A (1.75 * 10⁶) represents the largest number among the given options.
Therefore, the answer is A. 1.75 * 10⁶.
Learn more about exponents here
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If you invest $ 30 , 700 with an annual interest rate of 8.9 % , compounded daily, how much would you have at the end of 4 years?
Answer: $43,823.37
Step-by-step explanation:
Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
As per given , we have
P= $ 30,700
r= 8.9 % = 0.089
t= 4 years
[tex]A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37[/tex]
Hence, the amount at the end of 4 years would be $43,823.37 .
how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
i need help will rate you branliest
Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p
Hello, please consider the following.
We know that
[tex]a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}[/tex]
And we can write that.
[tex](p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})[/tex]
It means that, by replacing p by [tex]p^{1/3}[/tex]
[tex](p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
