Answer:
The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195
Step-by-step explanation:
The six measurements are:
202, 164, 157, 177, 113, 213
Sample mean:
Sum of all values divided by the number of values which is 6. So
[tex]S_m = \frac{202+164+157+177+113+213}{6} = 171[/tex]
Sample standard deviation:
Square root of the difference squared between each value and the mean, and divided by 1 subtracted by the sample size. So
[tex]s = \sqrt{\frac{(202-171)^2+(164-171)^2+(157-171)^2+(177-171)^2+(113-171)^2+(213-171)^2}{5}} = 35.69[/tex]
Confidence interval
We have the standard deviation for the sample, which means that the t-distribution will be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.365
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.365\frac{35.69}{\sqrt{6}} = 49[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 171 - 49 = 122 ppm
The upper end of the interval is the sample mean added to M. So it is 171 + 49 = 220 ppm
The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195
The equal sides of an isosceles triangle are 2 cm shorter than the length of the third side. If the perimeter of the triangle is 35 cm, find the length of the third side.
with the formula plsssss
• Equal sides of an isosceles triangle = 2cm shorter than the length of the third side.
To calculate :• Length of the third side.
Calculation :Let the third side be c.
Also, two equal sides be a and b.
According to the question,
[tex] \longmapsto [/tex] a = ( Third side - 2 ) cm
[tex] \longmapsto [/tex] a = ( c - 2 ) cm
Similarly, length of b(second side) will also be same as a and b are two equal sides of an isosceles triangle.
[tex] \longmapsto [/tex] b = ( c - 2 ) cm
Now, we know that :
★ Perimeter of ∆ = Sum of all sides
Perimeter = 35 cm.[tex] \longmapsto [/tex] 35 = a + b + c
[tex] \longmapsto [/tex] 35 = (c - 2) + (c - 2) + c
[tex] \longmapsto [/tex] 35 = c - 2 + c - 2 + c
[tex] \longmapsto [/tex] 35 = c + c + c - 2 - 2
[tex] \longmapsto [/tex] 35 = 3c - 4
[tex] \longmapsto [/tex] 35 + 4 = 3c
[tex] \longmapsto [/tex] 39 = 3c
[tex] \longmapsto [/tex] [tex] \sf \dfrac{39}{3} [/tex] = c
[tex] \longmapsto [/tex] 13 = c
So, third side of the triangle is 13 cm.
Lauren bought 20 oz of sliced ham. She used 3/4 of the ham to make sandwiches for her friends. She used 1/5 of the ham in an omelet. How many ounces of ham were left?
Answer:
19 oz
Step-by-step explanation:
Lauren bought 20 ounces of sliced ham, out of which she used three-fourth of the ham to make sandwiches for her friends and one fifth of the ham in an omelette. We are to find the ounces of ham that were left. So, total ounces of ham that were used = 15 + 4 = 19 ounces.
Hope this helped!
Please help asap!!!!
Answer:
[tex] m\widehat {MP} =46\degree [/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]
[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]
[tex] 23\degree \times 2= m\widehat {MP} [/tex]
[tex] m\widehat {MP} =46\degree [/tex]
The length of a rectangular garden is 8m greater than twice the width the area of the garden is 280m^2 what is the width of the garden
Step-by-step explanation:
Given :-
The length of the garden 8m greater than 2 times the width.
Area of the garden is 280 m²
Let us consider the length as x and width as y.
Sp, we can day length as :-
x = 8 + 2y ---(1)
Now, we know that:-
Area of Rectangle = Length × Breadth
280 = x * y
We can replace the value of x now,
280 = y × ( 8 + 2y)
280 = 8y + 2y²
2y² + 8y - 280 = 0
y² + 4y - 140 = 0
Factorise it.
(y -10)(y + 14)
Cancelling -ve value, we get the width as 10 metres.
Hope it helps :)
Answer:
Step-by-step explanation:
Width = w
Length = 2w + 8
Area of rectangular garden = 280 square meter
length * width = 280
(2w + 8 ) *w = 280
2w * w + 8*w = 280
2w² + 8w = 280
2w² + 8w - 280 = 0
Divide the whole equation by 2
w² + 4w - 140 = 0
w² + 14w - 10w - 14 *10 = 0
w(w + 14) - 10(w + 14) = 0
(w + 14)(w - 10)= 0
w - 10 = 0 {Ignore w + 14, as measurements will not be -ve}
w = 10 m
l = 2*10 +8
= 20 +8
l = 28 m
1.Write the expression in expanded form. The subscript number can be write in
normal form. E.g. X1 + X1Y1, do not forget the correct parenthesis and the correct
order. *
2.For the equation in above evaluate the notation using the values below. Please
enter the exact value.
X1 =0
Y1 = 5
Z1 = 0
X2 = 1
Y2 = 26
Z2 = -2
X3 = 12
Y3 = -2
Z3 = 3
X4 = -1
Y4 = 25
Z4 = 24
Answer:
(a) Expanded form:
[tex]((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)[/tex]
(b) The value of the expression: -21
Step-by-step explanation:
Given
[tex]\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)[/tex]
Solving (a): The expanded form:
This means that we substitute the values of i from 1 to 4 in the above expression.
So, the expression becomes:
[tex]((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)[/tex]
Solving (b): The value of the expression
To do this, we simply substitute the given values of X1, X2....... in the expression.
This gives:
So, the expression becomes:
[tex]((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)[/tex]
Simplify each bracket
[tex]((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)[/tex]
[tex]0 + 29 -48 -2[/tex]
[tex]-21[/tex]
Hence, the result of the expression is -21
What is the range of the function on the graph?
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
Jan’s family has 3/4 of a cake left. How many members of her family can get 1/4 of what is left?
Answer:
3
Step-by-step explanation:
3/4 divided by 1/4 equals 3
Answer:
3
Step-by-step explanation:
3/4 is currently left
Subtract 1/4 by 3/4 until nothing is left
The number you get is 3 therefore the answer is 3
Alexandra invested $610 in an account paying an interest rate of 7 3/8% compounded
daily. Madeline invested $610 in an account paying an interest rate of 7 7/8%
compounded continuously. After 16 years, how much more money would Madeline
have in her account than Alexandra, to the nearest dollar?
Exact answer: 165.5754
Rounded to the nearest dollar: 166
Alex's pig weighs under 220 pounds.
Let p = the weight of the pig
Answer:
p > 220
Explanation:
This inequality says, "p (the weight of the pig) is less than 220." This describes the situation shown. So, the answer is p > 220.
Good luck ^^
PLEASE HURRY! FIRST PERSON GETS BRAINLIST!!!!!!
Hank is throwing a surprise party. The party costs $20 per person. Create an equation and graph to represent the relationship between the cost of the party and the number of friends attending.
The independent variable is ____.
A. Number of friends (f)
B. Cost of party (c)
Answer:
B
Step-by-step explanation:
A pair of shoes that normally sells for $85.00 goes on sale for 35% off. Season thinks that the sale price should be $50.00 but Melanie disagrees and says the price should be $55.25. Aiyanna says they are both wrong and decides the price should be $29.75. Who is correct and why?
Answer:
Melanie is correct
Step-by-step explanation:
35% of 85 is 29.75 so take that away from the original price and you get 55.25
This means the price will be 55.25$
Answer:
Melanie is correct since 65% of $85.00 is $55.25.
Step-by-step explanation:
The original price of the shoes is $85.00. That is 100% of the price of the shoes since 100% is a whole amount.
The discount on the shoes is 35%.
100% - 35% = 65%
That means the sale price is 65% of the original price. Now we calculate 65% of $85.00.
65% of $85.00 =
= 0.65 * $85.00
= $55.25
Answer: Melanie is correct since 65% of $85.00 is 55.25.
Two people share proceeds of a business venture in the ratio 2:3 If the proceeds came to GHS 2,350,000 how much does each get?
Answer:
GHS 940,000 and GHS 1,410,000
Step-by-step explanation:
Total Ratio, thus 2+3 = 5 = 2,350,000
2/5 × 2,350,000 = 940,000
3/5 × 2,350,000 = 1,410,000
In conclusion, the money was shared at GHS 940,000 and GHS 1,410,000 among the two.
Students in a school are asked to pick either football, rugby or tennis to play in their lesson.
The number of students who picked football and rugby are in the ratio of 5:4
The number of students who picked rugby and tennis are in the ratio of 12:25
125 students picked tennis.Work out how many students picked football.
Step-by-step explanation:
let x be rubgy liked let y football liked
x/125=12/25
ansx=60
again
y/60=5/4
ans y=75
football liked students are 75
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
BRAINLIEST AND ACED+ PLEASE HELP ME :c
Answer:
1 1/2 x 4 1/2 x 5 = 33 3/4
If g(x) = 3^Vx-123, find g( - 2).
Answer:
g(-2) = -5
Step-by-step explanation:
We are given the following function:
[tex]g(x) = \sqrt[3]{x - 123}[/tex]
Find g( - 2).
This means that we find g when [tex]x = -2[/tex]. So
[tex]g(-2) = \sqrt[3]{-2 - 123} = \sqrt[3]{-125} = \sqrt[3]{-5^3} = -5[/tex]
So
g(-2) = -5
You have a poster that is 5 feet by 3 feet. You want to put a
frame, with a uniform width, around the picture. The poster
and the frame must have an area of 24 square feet. Find
the width of the frame.
The frame will be 3
units wide.
Answer:
x=[tex]\frac{1}{2}[/tex] ft
Step-by-step explanation:
Please see the attached image
(5+2x)(3+2x)=24 - solve for x
15+10x+6x+4x^2=24
4x^2+16x+15=24
4x^2+16x-9=0
Use quadratic formula
[tex]x=\frac{1}{2} , x=-\frac{9}{2}[/tex]
x cannot be negative, so we can rule [tex]-\frac{9}{2}[/tex] out.
x=[tex]\frac{1}{2}[/tex] ft.
Marvin earns $9.75 per hour at his summer job. He wants to buy a video game system that costs $263.25
Enter an equation to model the relationship between the number of hours worked h and the amount earned e
The equation is:
Answer:
$9.75h=e-$263.25
Step-by-step explanation:
A box of cherries weighs 2 1/4 pounds.
If you bought 5 boxes, what is the total
weight of the purchased cherries?
Answer:
The total weight of the purchased cherries is [tex]11\frac{1}{4}[/tex] pounds.
Step-by-step explanation:
Multiply [tex]2\frac{1}{4}[/tex] by 5.
[tex]2\frac{1}{4} * 5 = 11 \frac{1}{4}[/tex]
Answer:
11.25 or 45/4
Step-by-step explanation:
2 1/4 times 5
Solve each equation 24 = 5k - 8k
Answer:
k = -8
Step-by-step explanation:
24 = 5k - 8k
24 = -3k
k = 24/(-3)
k = -8
Answer:
k = -8
Step-by-step explanation:
Solve for k
First we re arrange our equation so that it look simple to calculate.
24=5k-8k
5k-8k = 24
-3k = 24
Divide -3 both side to get the value of k
k = -8
To prove substitute k into formula:
5k-8k = 24
5 (-8) - 8 (-8) = 24
-40 + 64 = 24
24 = 24
let us have -2 and 1 what will be the answer ??
Answer:
[tex] - 2 + 1 \\ = - 1[/tex]
Assuming this is what you asked since your question is not clear.
It is not clear what operation should be performed on -2 and 1. Please provide more information or context so that a specific answer can be provided.
It is unclear what operation you want to perform with -2 and 1. Please specify the operation (addition, subtraction, multiplication, or division) so I can provide the correct answer.
Learn more about addition, subtraction, multiplication, or division here;
https://brainly.com/question/11609653
#SPJ11
A fashion designer wants to know how many new dresses women buy each year. A sample of 208 women was taken to study their purchasing habits. Construct the 85% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 6.2. Assume that the population standard deviation is 1.1.
Answer:
The 85% confidence interval for the mean number of dresses purchased each year is (6.1, 6.3).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{1.1}{\sqrt{208}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 6.2 - 0.1 = 6.1
The upper end of the interval is the sample mean added to M. So it is 6.2 + 0.1 = 6.3
The 85% confidence interval for the mean number of dresses purchased each year is (6.1, 6.3).
17% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who
favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight
(a) P(3)=(Round to three decimal places as needed)
(b) P(x24) =(Round to three decimal places as needed.)
(c) P(x<8)=(Round to three decimal places as needed.)
Answer:
Following are the solution to these question:
Step-by-step explanation:
Following are the binomial distribution with parameters:
[tex]n = 12\\\\p = 0.24[/tex]
For point a:
[tex]\to P(X = 3) = binom.dist(3, 12, 0.24, False) = 0.2573[/tex]
For point b:
[tex]\to P(X > 4) = 1 - P(X < 3) = 1 - binom.dist(3, 12, 0.24, True) = 0.3205[/tex]
For point c:
[tex]\to P(<8) = binom.dist(7, 12, 0.24, True) = 0.9979[/tex]
Determine the equation of a circle with center at (8, 10) and radius is 6
OMG PLS HELP!!!!!!!!!!!!!! A rectangular prism has a height of 20 cm, length of 7 cm and width of 5 cm. Use the volume formula to find the volume of this prism. A. 140 cm3 B. 500 cm3 C. 700 cm3 D. 900 cm3
Answer:
The correct answer is C: 700 cm³
Step-by-step explanation:
V = l × w × h
V = 7 × 5 × 20
V = 7 × 100
V = 700
125 a la octava potencia?
please lo necesito
Please help, brainliest for correct answer
Answer:
11494.04 units
Step-by-step explanation:
V = 4/3 [tex]\pi[/tex] r³ = 4/3 · [tex]\pi[/tex] · 14³ ≈ 11494.04032
Plzz help will mark brainleast
A small pond contains 8 catfish and two bluegill. If eight fish are caught at random what is the probability that all of them are catfish
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.