Answer:
A
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
B
[tex]t = -3.34[/tex]
C
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
D
reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 8300[/tex]
The sample mean is [tex]\ = x = 8000[/tex]
The standard deviation is [tex]s = 440[/tex]
The sample size is [tex]n = 24[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
The test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]
=> [tex]t = -3.34[/tex]
The p-value is obtained from the z -table ( reference calculator dot net ) , the value is
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
Looking at the values of [tex]p-value and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis
I need help badly best answer gets BRAINLIEST:)
Answer:
a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°
Step-by-step explanation:
Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.
Find X so that m is parallel to n. Identify the postulate or theorem you used. Please help with these 3 problems, I don’t understand it at all
the corresponding angles should be equal
so, [tex] 5x+15=90 \implies 5x=75\implies x=15^{\circ}[/tex]
PLEASE HELP ASAP RN!!!!!!
Answer:
3sqrt(2)
Step-by-step explanation:
sqrt(32) - sqrt(2)
rewriting sqrt(32)
sqrt(16*2) - sqrt(2)
sqrt(16) * sqrt(2) - sqrt(2)
4 sqrt(2) - sqrt(2)
3sqrt(2)
A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.
Answer:
[tex]\large \boxed{\$10000.00}[/tex]
Step-by-step explanation:
We can use the formula for continuously compounded interest.
[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]
Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
3
BO
Evaluate the function f(x) = x2 + 4x + 1 at the given values of the independent variable and simplify.
a. f(6)
b. f(x +9)
c. f(-x)
Answer:
a) f(6)=(6)^2+4(6)+1=65
b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117
f (-x)=(-x)^2-4x+1
If a state issued license plates using the scheme of 3 letters followed by 3 digits, how many plates could it issue?
Answer:
17,576,000
Step-by-step explanation:
there are 26 english letters (A-Z) and 10 digits(0-9).
there are 3 spaces for letters. therefore Any of the 26 letters can be combined with any 26 other letters and any of those can be combined with any of another 26 letters.
26*26*26= 17576
similarly 10 digits can combined in 1000 ways
10*10*10=1000
17576 letter combination can combine with 1000 digits combination.
so 17,576 x 1000 = 17,576,000 different plates could issue.
jana has 3 banana muffins, 3 poppy seed muffins, 3 spice muffins and 3 blurry muffins she put 1/2 of the muffins on a late how many muffins did janna put on the plate
Answer:
6
Step-by-step explanation:
Jana had a total of 3+3+3+3 = 12 muffins. Half that number is 3+3 = 6 muffins.
Jana put 6 muffins on the plate.
Tonya and Leo each bought a cell phone at the same time. The trade-in values, in dollars, of the cell phones are modeled by the given functions, where x is the number of months that each person has owned the phone.
Answer:
The answer is: Leo's phone had the greater initial trade-in value. Tonya's phone decreases at an average rate slower than the trade in value of Leo's phone.
Step-by-step explanation:
I got it right. Hope this helps.
The initial trade-in value of Tonia's phone is greater when compared with Leo's
There is a decrease in the trade-in value of Leo's phone at an average slower rate
[tex]f(x) = 490\times 0.88[/tex]
[tex](x)[/tex] ⇒ [tex]g(x)[/tex]
[tex]0[/tex] ⇒ [tex]480[/tex]
[tex]2[/tex] ⇒ [tex]360[/tex]
[tex]4[/tex] ⇒ [tex]470[/tex]
Now we will solve with the greater initial value
The initial value is when x = 0. So, we have
[tex]f(x) = 490 \times o.88^x\\\ f(o) = 490 \times 0.88 ^0\\f(0 =490 \times 1 \\f(o) = 490[/tex]
From leos table
[tex]g(0) = 480\\f(0) > g(o)\\i.e \\490 > 480[/tex]
So Tonia had a greater initial value
Solving (b): The phone with a lesser rate
y [tex]y = a b ^ x[/tex]
An exponential function is:
where [tex]b \rightarrow rate[/tex]
For Tonia
[tex]b = o.88[/tex]
For Leo we have
[tex](x_{1} , y_{1} )= (0,480)\\(x_{1}, y_{1} ) = (2, 360)[/tex]
So the equation becomes
[tex]y = ab ^x \\480 = ab ^0 \\and \\360 = ab ^2[/tex]
On solving
[tex]480 = a \times 1\\a = 480[/tex]
[tex]360 = ab ^ 2[/tex]
so it becomes
[tex]480 = 360 \times b ^2 \\[/tex]
On dividing both sides by [tex]480[/tex] we get
[tex]b ^ 2 = 0.87[/tex]
[tex]b ^ 2 = 0.75[/tex]
On taking square root we get
[tex]b = 0.87[/tex]
In comparison, we get Leo's rate is slower.
Learn more about Equation here:
https://brainly.com/question/14686792
# SPJ2
51: Y = 3: 5 value of Y
Answer:Y=25:3
Step-by-step explanation:
Answer:
51 : 85 = 3 : 5Step-by-step explanation:
51 : Y = 3 : 551 ÷ 17 = 3•To find the Y we should multiply 5 by 17 5 × 17 = 8551 : 85 = 3 : 5•Checking51 ÷ 17 = 3 ; 85 ÷ 17 = 5[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
What is nine thousandths as a decimal
Answer:
Nine thousandths = 0.009
Step-by-step explanation:
thousandths = 1/1000 = 0.001
nine thousandths = 9/1000 = 0.009
Answer:
.009
Step-by-step explanation:
9 thousandths as a decimal is 9/1000. Which is the same 0.009
What is the product of 8.0425 x 2.6?
Answer:
20.9105
Step-by-step explanation:
8.0425
2.6
80425*26=2091050
there is 5 decimals so you move the decimal over to the left 5 times
20.9105 :)
nishan bought 7 marbles Rs.x per each. if he gave Rs.100 to the shop keeper. what is the balance he would receive?
1) (1) The selling price (ii) The cost price (iii) Profit The marked price of an article is 15% above its selling price and the cost price is 25% less tha its marked price. Find the discount percent and gain percent.
Answer: (iii) Profit The marked price of an article is 15% above its selling price and the cost price is 25% less tha its marked price. Find the discount percent and gain percent.
Step-by-step explanation:
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
What is the complete factorization of the polynomial below?
x3 + 4x2 + 16x + 64
Answer: (x+4) ( x-4i)(x+4i)
Discussion:
Factor the polynomial:
x^3+4x^2+16x+64 = (x +4 ) ( x^2 + 16) (*)
Factor x^2 +1 6 over the complex numbers:
x^2 + 16 = (x -4i)(x+4i) (**)
Combing (*) and (**) gives the full factorization
(x+4) ( x-4i)(x+4i)
Select the correct answer.
Answer:
B
Step-by-step explanation:
With limits, the first thing one should always try is direct substitution. Therefore, let's try that.
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) \\= (\frac{(1)^2+1}{(1)+1}+(1)^2+3) \\=\frac{2}{2}+1+3\\ =1+4=5[/tex]
Therefore:
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) =5[/tex]
What is the three hundred and twenty six to the nearest ten
Hi there!
»»————- ★ ————-««
I believe your answer is:
330
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
We are rounding the number 326 to the nearest tens.
The '2' is in the tens place, and the '6' is to the right of the digit.
Since the '6' is greater than or equal to 5, then we would round up.
326 ≈ 330
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
1+2x=6x+11 PLS HELP URGENT
Answer:
x = -5/2
Step-by-step explanation:
1+2x=6x+11
Subtract 2x from each side
1+2x-2x=6x-2x+11
1 = 4x+11
Subtract 11 from each side
1-11 = 4x
-10 =4x
Divide by 4
-10/4 = 4x/4
-5/2 =x
Answer:
[tex]\boxed{x=-\frac{5}{2}}\\[/tex]
Step-by-step explanation:
To begin, get the variable on one side of the equation - preferably the left for standard solution notation (for this equation, it is easier to place it on the right side to avoid negative values). Do this by subtracting 2x from both sides of the equation. Then, subtract 11. Finally, divide by 4 and get the answer in terms of x.
1 + 2x = 6x + 11
1 = 4x + 11
-10 = 4x
[tex]\boxed{x=-\frac{5}{2}}[/tex]
the product of two consecutive positive integer is 306
Answer:
[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]
Step-by-step explanation:
The product means multiplication.
There are two positive consecutive integers.
Let the first positive consecutive integer be x.
Let the second positive consecutive integer be x+1.
[tex](x) \times (x+1) =306[/tex]
Solve for x.
Expand brackets.
[tex]x^2 +x =306[/tex]
Subtract 306 from both sides.
[tex]x^2 +x -306=306-306[/tex]
[tex]x^2 +x -306=0[/tex]
Factor left side of the equation.
[tex](x-17)(x+18)=0[/tex]
Set factors equal to 0.
[tex]x-17=0[/tex]
[tex]x=17[/tex]
[tex]x+18=0[/tex]
[tex]x=-18[/tex]
The value of x cannot be negative.
Substitute x=17 for the second consecutive positive integer.
[tex](17)+1[/tex]
[tex]18[/tex]
The two integers are 17 and 18.
The product of two consecutive positive integers is 306.
We need to find the integers
solution : Let two consecutive numbers are x and (x + 1)
A/C to question,
product of x and (x + 1) = 306
⇒x(x + 1) = 306
⇒x² + x - 306 = 0
⇒ x² + 18x - 17x - 306 = 0
⇒x(x + 18) - 17(x + 18) = 0
⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
so x = 17 and (x +1) = 18
Therefore the numbers are 17 and 18.
Hope it helped u if yes mark me BRAINLIEST
TYSM!
Write a rational number in fraction form that is equivalent to -1.\overline{5}
Answer:
[tex]\dfrac{-14}{9}[/tex].
Step-by-step explanation:
The given number is [tex]-1.\overline{5}[/tex].
We need to find a rational number in fraction form that is equivalent to given number.
Let [tex]x=-1.\overline{5}[/tex]
[tex]x=-1.555...[/tex] ...(1)
Multiply both sides by 10.
[tex]10x=-15.555...[/tex] ...(2)
Subtracting (1) from (2), we get
[tex]10x-x=-15.555...-(-1.555...)[/tex]
[tex]9x=-14[/tex]
Divide both sides by 9.
[tex]x=\dfrac{-14}{9}[/tex]
Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].
e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean
Answer:
Step-by-step explanation:
[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]
On the maturity date of a $10,800, 6-month, 8% note, the borrower sends a check that includes the principal and all of the interest due on the note. What is the amount of the borrower's check?
Answer: $ 11,232.00
Step-by-step explanation:
Given: Amount = $ 10,800
Interest Rate = 8% =0.08
Time in Months= 6.00
Formula :
Interest on Note = (Amount)× (Interest Rate) × ((Time in Months) /12)
= (10800)× (0.08)× (6/12)
= $432
The amount of the borrower's check =(Amount + Interest on Note)
= $ (10,800+432)
= $ 11,232.00
Hence, The amount of the borrower's check = $ 11,232.00
Anand needs to hire a plumber. He's considering a plumber that charges an initia
hourly rate of $28. The plumber only charges for a whole number of hours. Anar
more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
28 - 65H <250
Complete question :
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an
hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
A. 28 + 65H < 250
B. 28 + 65H > 250
C. 65 + 28H < 250
D. 65 +28H > 250
2) What is the largest whole number of hours that Anand can afford?
Answer:
65 + 28H < 250
Number of hours Anand can afford = 6 hours
Step-by-step explanation:
Given the following information :
Initial hourly rate = $65
Hourly rate = $28
Number of hours worked (whole number) = H
Maximum budgeted amount to spend = $250
Therefore ;
(Initial charge + total charge in hours) should not be more than $250
$65 + ($28*H) < $250
65 + 28H < 250
Number of hours Anand can afford :
65 + 28H < 250
28H < 250 - 65
28H < 185
H < (185 / 28)
H < 6.61
Sinve H is a whole number, the number of hours he can afford is 6 hours
Answer:
65 + 28H < 250
6
Step-by-step explanation:
tried it, it worked.
the other answer is correct but hard to understand so give them thanks and 4 star :)
The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is
Answer:
Step-by-step explanation:
Formula for area of a triangle:
Height x Base /2
Base (b) = h +4
Height = h
h + 4 x h /2 = 30cm
=> h +4 x h = 60
=> h+4h =60
=> 5h = 60
=> h = 12
Height = 12
Base = 12 +4 = 16
Write the equation in slope-intercept form, y = 4(x - 5) + 7x
Answer:
y = 11x - 20
Step-by-step explanation:
y = 4(x - 5) + 7x
y = 4x - 20 + 7x
y = 11x - 20
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
Choose all options that apply. Which of the following are antiviral medications commonly used to treat the flu? | a) Azelastine Oxymetazoline c) Zanamivir O d) Oseltamivir
M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Color Purple Yellow Red Orange Green Blue Brown Percentage 22% 20% 23% 10% 6% 6% 13% Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy). Are these outcomes mutually exclusive? Why? Yes. Choosing a green and blue M&M is possible. Yes. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is possible. (b) Find P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? Yes. Choosing a yellow and red M&M is possible. No. Choosing a yellow and red M&M is not possible. Yes. Choosing a yellow and red M&M is not possible. No. Choosing a yellow and red M&M is possible. (c) Find P(not purple candy).
Answer:
A) 0.12. Yes. Choosing a green and blue M&M is possible
B) 0.43. Yes. Choosing a yellow and red M&M is possible
C) 0.78
Step-by-step explanation:
First of all, the summation of the distribution of all colours is;
Σ(all colors ) = 22% + 20% + 23% + 10% + 6% + 6% + 13% = 100%, or 1.
Thus;
a) P(green candy or blue candy) is;
P(GREEN ∪ BLUE) = P(G) + P(BL)
P(GREEN ∪ BLUE) = 6%+6%
P(GREEN ∪ BLUE) = 12% or 0.12
Now, due to the fact that we have to choose ONE candy and only ONE candy at random, then they are mutually exclusive: Yes. Choosing a green and blue M&M is possible
b)P(yellow candy or red candy is;
P(YELLOW ∪ RED) = P(Y) + P(R)
P(YELLOW ∪ RED) = 20% + 23% = 43% or 0.43
Yes. Choosing a yellow and red M&M is possible
c) P(NOT PURPLE)
the probability of having a purple is;
P(PURPLE) = 22% or 0.22
So, the Probability of NOT having a PURPLE is 1 - 0.22 = 0.78
a rectangular plot has 17m length and 14m width. What will be the cost of fencing at a rate of Rs.25 per meter
The fence would be the perimeter of the shape.
Perimeter = 17 + 17 + 14 + 14 = 62 meters.
Multiply the price per meter by total meters:
25 x 62 = 1550
For fencing , we have to find the perimeter of rectangle.
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Formula \: \: Using \: = \: 2 \: ( \: L + B \: )}}}}}\end{gathered}[/tex]
L denotes length of rectangleB denotes breadth of rectangleL = 17 mB = 14 mSubstuting the valuesPerimeter of rectangle = 2 ( L + B )
Perimeter of rectangle = 2 ( 17 m + 14 m )
Perimeter of rectangle = 2 ( 31 m )
Perimeter of rectangle = 62 m.
Hence, the perimeter of rectangle is 62 m.
For Fencing Cost = perimeter × rate of fencing per metre
Fencing Cost = 62 × 25
Fencing cost = 1,550
Hence, the cost of fencing of a rectangular plot is 1,550