Answer:
Xbar = 76.5
s = 24.70
(61.19 ; 91.81)
Step-by-step explanation:
Given that :
Confidence interval = (65, 88)
Recall:
Confidence interval = xbar ± margin of error
Margin of Error = (upper boundary - lower boundary) / 2
Margin of Error = (88 - 65) /2 = 11.5
Taking the lower boundary :
Lower boundary = xbar - margin of error
xbar = lower boundary + margin of error
Xbar = 65 + 11.5
Xbar = 76.5
Margin of Error = Tcritical * s/sqrt(n)
s = sample standard deviation
Tcritical at 90% confidence, df = 9-1= 8 = 1.397
11.5 = 1.397 * s/sqrt(9)
11.5 = 1.397 * s/3
34.5 = 1.397s
s = 34.5 / 1.397
s = 24.695
s = 24.70
C.) 95% confidence interval :
Tcritical at 95%, df = 8 = 1.860
Margin of Error = 1.860 * 24.70/sqrt(9) = 15.311
Confidence interval :
Lower boundary = 76.5 - 15.311
Upper boundary = 76.5 + 15.311
(61.19 ; 91.81)
5 shirts for $30.00
Rate: What go's here Unit Rate: What go's here?
Pls help!
Step-by-step explanation:
that each shirt is 6 dollars
When 10 b = 5 (StartRoot c EndRoot + 2) is solved for c, one equation is c = (2b minus 2) squared Which of the following is an equivalent equation to find c?
Answer:
I will show all the steps to lead to the solution.
1) 10b = 5 (√c + 2) <---- starting equation
2) divide by 5 => 2 b = √c + 2
3) subtract 2 => 2b - 2 = √c
4) raise to the power 2 => (2b - 2)^2 = c, which is the expression given.
Now these are two equivalent forms:
1) extract 2 from the parentheses: c = 4 (b -1)^2
2) expand the parentheses: c = 4b^2 - 8b + 4)
Step-by-step explanation:
Choice D
An equivalent equation to find c is [tex]4 (b-1)^{2}[/tex]
Here, given that
When 10 b = 5 ([tex]\sqrt{c}[/tex] + 2) is solved for c, one equation is c = (2b minus 2) squared.
What is equivalent equation?
Equivalent equations are algebraic equations that have identical solutions or roots.
Now,
For finding the solution, all steps are
⇒[tex]10 b = 5 (\sqrt{c} + 2)[/tex]
Divide both side by 5;
⇒[tex]2b = \sqrt{c} + 2[/tex]
subtract 2 from both sides,
⇒ [tex]2b - 2 = \sqrt{c}[/tex]
⇒ [tex](2b - 2)^2 = c[/tex]
⇒[tex]4 ( b-1 )^2 = c[/tex]
So, An equivalent equation to find c is [tex]4 (b-1)^{2}[/tex]
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What is the surface area of the cylinder? Use 3,14 for pi and round your answer to the nearest hundredth.
Answer:
B. 226.08 sq in
Step-by-step explanation:
Given data
r= 3 in
h= 9in
The expression for the surface area of a cylinder is
A=2πrh+2πr^2
Substitute
A= 2*3.142*3*9+ 2*3.142*3^2
A= 169.668+ 2*3.142*9
A= 169.668+ 56.556
A=226.224 sq in
solve the simultaneous equations
8x+3y=45 2x+3y=27
Answer:
x = 3 and y = 7
Step-by-step explanation:
Given that,
8x+3y=45 .......(1)
2x+3y=27 ........(2)
We need to solve equations (1) and (2)
Multiply equation (2) by 4.
8x+12y=108 .....(3)
Subtract equation (1) from (3).
8x+12y-(8x+3y)=108-45
12y-3y = 63
9y = 63
y = 7
Put the value of y in equation (1).
2x+3(7)=27
2x+21 = 27
2x = 27-21
2x = 6
x = 3
So, the values of x and y are 3 and 7 respectively.
What's the distance between –14 and –5 on a number line?
Question 3 options:
A)
9
B)
34
C)
68
D)
17
Answer:
9
Step-by-step explanation:
because 14-9=5
or 5+9=14
Hope this helped, plz give me brainiest.
if I have a 8 inch by 10 inch poster what is the area
Answer:
80 inches
Step-by-step explanation:
8x10=80
because, lxw
l= length
w= width
Answer:
80
Step-by-step explanation:
im not trying to copy the answer above, im just going to say why its 80
so firstly we have the known dimensions of 10 by 8, so in this case we have 10 rows that each contain 8 units
we can then multiply the 8 units of one row, by the amount of rows there are total (in this case 10) to get the total unit count, or area
8 * 10 = 80
(NOTE: you can use the Asterisk (*) as a multiplication mark as to not get it confused with x as in the variable, as with slash (/) for dividing)
hope this helps with this and other problems, credits to the answer above for doing the initial work :)
at the aminal sheter they use 84 ounces of dog food for each dog.They have 14 dogs to feed.How many ounces of dog food does each dog get.
a total of 1500 raffle tickets were collected during the school fair. if you have 30 raffle tickets, what is the probability that you will win?
Answer: 1/50 or 0.02
Step-by-step explanation:
30 / 1500 = 1/50
1/50 or 0.02
Please find the VOLUME . Will mark the brainliest be geniune no links
Answer:
Pyramid formula: V= LWH/3
224
Step-by-step explanation:
Answer:
336
Step-by-step explanation:
The figure shown is a triangular prism
The volume of a triangular prism can be calculated by using this formula
[tex]V=ah[/tex]
where a = area of base and h = height
we are already given the height ( 8 ft ) so all we need to find is the area of the base
Because this is triangular prism the base will be a triangle
The area of a triangle can be calculated using this formula
[tex]A=\frac{bh}{2}[/tex] where b = base length and h = height
The base length of this particular triangular prism is 12 ft and the height of the base is 7 ft
That being said we plug in the values into the formula
[tex]A=\frac{12*7}{2} \\12*7=84\\\frac{84}{2} =42[/tex]
So we can conclude that the area of the base is 42 ft²
Now to find the volume
Using the formula V = ah
* plug in the values *
V = 42 * 8
42 * 8 = 336
Therefore the volume of the triangular prism is 336ft³
Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 520 grams, write a function showing the mass of the sample remaining after tt years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth of a percent.
Answer:
The percentage rate of decay per year is of 5.19%.
The function showing the mass of the sample remaining after t is [tex]A(t) = 520(0.9481)^t[/tex]
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Every 13 years, its mass decreases by half.
This means that [tex]A(13) = 0.5A(0)[/tex]. We use this to find r. So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.5A(0) = A(0)(1-r)^{13}[/tex]
[tex](1-r)^{13} = 0.5[/tex]
[tex]\sqrt[13]{(1-r)^{13}} = \sqrt[13]{0.5}[/tex]
[tex]1 - r = (0.5)^\frac{1}{13}[/tex]
[tex]1 - r = 0.9481[/tex]
[tex]r = 1 - 0.9481[/tex]
[tex]r = 0.0519[/tex]
The percentage rate of decay per year is of 5.19%.
The initial mass of a sample of Element X is 520 grams
This means that [tex]A(0) = 520[/tex]. So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 520(1-0.0519)^t[/tex]
[tex]A(t) = 520(0.9481)^t[/tex]
The function showing the mass of the sample remaining after t is [tex]A(t) = 520(0.9481)^t[/tex]
Which statement is correct?
A. Cosecant is the reciprocal of tangent.
O B. Sine is the reciprocal of secant.
C. Secant is the reciprocal of cosine.
D. Cotangent is the reciprocal of cosecant.
If your answer is right I’ll mark you!
Answer:
D
Step-by-step explanation:
5 1/2= 5 2/4
5 2/4 - 1 3/4 = 3 3/4
Answer:
3 3/4
Step-by-step explanation:
5 1/2 - 1 3/4
5 2/4 - 1 3/4
22/4 - 7/4
15/4
3 3/4
Which expression is equivalent to  when ?    
Answer:
[tex]5(w + 4) \\ = 5(9 + 4) \\ = 5 \times 13 \\ = 65[/tex]
How many times greater is the value of the 4 in 900,400 than the value of the 4 in 900,040 please help me faster!
Answer:
10 times plz mark brainliest
Answer:
10
Step-by-step explanation:
10×10=100. TRUST ME I DID THE MATH
Use the graph to answer the question.
On a coordinate plane, a line goes from (negative 5, 7) to (3, 3).
Which parametric equations describe the curve?
x = –t + 1 and y = 0.5t + 4 when –2 ≤ t ≤ 6
x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3
x = 0.5t + 4 and y = –t + 1 when –2 ≤ t ≤ 6
x = 0.5t + 4 and y = –t + 1 when –5 ≤ t ≤ 3
The answer for this question is A:
A = x = –t + 1 and y = 0.5t + 4 when –2 ≤ t ≤ 6
The parametric equations of the curve are:
x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3
Parametric equation of the line:The parametric equation of the line is, [tex]x=x_0+at,y=y_0+bt[/tex] where [tex](x_0,y_0)[/tex] is the point on the line and [tex]\frac{b}{a}[/tex] is the slope of the line with a, b are real numbers.
Slope of the line:If (a, b) and (c, d) are any two points on the line then, slope of the line is:
m = (d - b)/(c - a)
For given situation,
a line goes from (-5, 7) to (3, 3).
Using the formula of slope, the value of m i.e., slope of the line would be,
⇒ m = (7 - 3)/(-5 - 3)
⇒ m = 4/(-8)
⇒ m = 1/(-2)
⇒ m= 0.5/(-1)
Comparing with m = b/a,
b = 0.5 and a = -1.
From the graph of the line given below,
A point (1, 4) is also on the line.
Let [tex]\bold{(x_0,y_0)=(1,4)}[/tex]
Using the parametric equation of the line,
[tex]x=x_0+at[/tex]
⇒ x = 1 + (-1)t
⇒ x = -t + 1
and [tex]y = y_0+bt[/tex]
⇒ y = 4 + (0.5)t
⇒ y = 0.5t + 4
Therefore, the parametric equations of the curve are:
x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3
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is -92 a rational number
Answer: Yes
Step-by-step explanation: A rational number is a number that can be described as a fraction. -92 can be a fraction, therefor it's rational.
No
A rational number is any number that can be expressed as a ratio of two integers. For example, 1.5 is rational since it can be written as 3/2, 6/4, 9/6 or another fraction or two integers. Pi is irrational since it cannot be written as a fraction.
A department store buys 100 shirts at a cost of $600 and sells them at a selling price of $10 each
Find the percent markup.
The percent markup is%.
Answer
66.5%
Step-by-step explanation:
The markup percent is 66.7%
The first step is to calculate the unit cost
= Cost of the shirt/quantity of shirt
= 600/100
= 66
The percent mark up can be calculated as follows
= 100 × (new price-old price/old price)
= 100 × (10-6)/6
= 100 × 4/6
= 100 × 0.666
= 66.7
Hence the markup percent is 66.7%
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7. Write 300 as a product of prime factors.
How do you work out Experimental and Theorical Probability.
pls help,
theoretical probability is based on logic as in:
there's a spinner with five equal sections. There would be a theoretical probability of 20% for each section
Experimental probability is based on results of previous experiments such as:
Damien spun that same spinner 10 times and landed on the red section 3 of ten times
Please help, will mark Brainly and if you need help with anything I’ll help with any work you send
Don’t tell me to go to a website, it doesn’t work at all. Stop spamming that.(will be reporting anyone who does)
Answer:
The first one is missing (d - 9) so it would be 5(d -9) or when you factor it out 5d - 45
In the second one (d + 7) is missing so it will be 8d(d + 7) so if you factor that out you will receive 8d^2 + 56
Step-by-step explanation:
3d^2 + 18d -21 =(3d -3)( d + 7)
3d^2 -30d +27 =(3d -3)(d - 9)
Write the standard form of the equation of the circle with center (4,7) that passes through the point (−7,9).
Answer:
[tex](x-4)^2+(y-7)^2=125[/tex]
Step-by-step explanation:
1) Find the radius
To find the radius of the circle, use the distance formula for the points (4,7) and (-7,9)
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (4,7) and (-7,9)
[tex]d=\sqrt{(-7-4)^2+(9-7)^2}\\d=\sqrt{(-11)^2+(2)^2}\\d=\sqrt{121+4}\\d=\sqrt{125}[/tex]
Therefore, the radius of the circle is [tex]\sqrt{125}[/tex] units.
2) Plug all data into the circle equation
Equation of a circle (not centred at the origin):
[tex](x-h)^2+(y-k)^2=r^2[/tex] where the centre is [tex](h,k)[/tex]
Plug in the point (4,7) as (h,k)
[tex](x-4)^2+(y-7)^2=r^2[/tex]
Plug in the radius [tex]\sqrt{125}[/tex]
[tex](x-4)^2+(y-7)^2=(\sqrt{125}) ^2\\(x-4)^2+(y-7)^2=125[/tex]
I hope this helps!
The area of sector AOB is
9/4pi and MZAOB = 40°. Find the
radius of circle O.
Radius:
Answer:
i ma rhhy
Step-by-step explanation:
i am right
PLZ HELP ME HELP WITH THIS
9514 1404 393
Answer:
yes
Step-by-step explanation:
A negative exponent in the numerator is the same as a positive exponent in the denominator (and vice versa). So, the first two expressions are equivalent.
An exponent is an indication of repeated multiplication. So, the 2nd and 3rd expressions are equivalent.
Any product can be decomposed to a product of its factors. So, the last two expressions are equivalent.
All of the expressions are equivalent.
Find the measure of 7
Answer:
its 96 because it is corresponding to both the 96 degrees in the fig
Find the value of x in the triangle below.
Answer:
Can't be Solved
Step-by-step explanation:
tan x = opp/adj
tan x = 23/11
tan x = 2.09090909 which is about
tan x = 2.09
x = 64.4 degrees which is the tangent of 2.09 in degrees.
x = 64.4 degrees
This is the only way to solve, since no answer is equivalent it can't be solved.
HELPPPP PLS this is my last question
Answer:
-6
Step-by-step explanation:
Absolute value for positive numbers is just that number
Negative numbers are the opposite when doing absolute value
Absolute value of -6 is 6
Helpp plzz will mark brainleast
Answer:
median is the middle value so i think its 54
A rectangle's length is 6 feet shorter than twice its width. If we use w to represent the rectangle's width, use a polynomial to represent the rectangle's area in expanded form.
9514 1404 393
Answer:
area = 2w² -6w
Step-by-step explanation:
For width w, the length is ...
L = 2w -6
and the area is ...
A = LW = (2w -6)(w) = 2w² -6w . . . area of the rectangle
With the spinner shown, the theoretical probability of landing on 2 is 0.25. Which number of
spins would most likely result in a relative frequency that is closest to the theoretical
probability? SP7. HELP! Due in 45 min
Need help with this