The 90% confidence interval = 48.603 < μ < 55.397
Explanation:
Given:
Mean = 52
Standard deviation = 14.6
Sample size, n = 50
Confidence Interval, c = 90%
c = 0.9
Significance level, α = 1 - c
= 1 - 0.9
= 0.1
Critical value, z(α/2) = z(0.05) = 1.645
Critical value = ± 1.645
Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]
[tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]
Limits of 90% confidence interval are given by:
Lower limit = μ - E
= 52 - 3.397
= 48.603
Upper limit = μ + E
= 52 + 3.397
= 55.397
Thus, 90% confidence interval = 48.603 < μ < 55.397
Juan has $2,224.52 in his checking account that charges a $23 per check overdraft
protection fee. In the next 4 days, the following checks arrived from payment in the
following order: check 129 for $1,520.00, check 126 for $750.89, and check 127 for $185.00.
How much does Juan have in his account?
Answer: good luck
Step-by-step explanation:
PLEASE HELP
Circle A has circumference 2 2/3 m. Circle B has a diameter that is 1 1/2 times as long as Circle A’s diameter. What is the circumference of Circle B?
The circumference of Circle B is 4 meters.
Convert mixed number to fraction:
Circumference of Circle A = 2 2/3 m = 8/3 m
Find the diameter of Circle A:
Circumference = π * diameter
8/3 m = π * diameter_A
diameter_A = 8/3π m
Find the diameter of Circle B:
diameter_B = 1 1/2 * diameter_A = 3/2 * (8/3π) m
diameter_B = 4 / π m
Find the circumference of Circle B:
Circumference = π * diameter_B
Circumference of Circle B = π * (4 / π) m
Circumference of Circle B = 4 m
Therefore, the circumference of Circle B is 4 meters.
A jar pinto beans and black beans in a ratio of 1: 1, and 300 of the beans are pinto beans. How many beans in total are there in the jar?
Answer:
600 beans
Step-by-step explanation:
If there are 300 pinto beans and the ratio is 1:1 there would have to be 300 black beans making 600 total.
Simplify (32)2
A) 9
B) 18
C) 27
D) 81
Answer:
D)81
Step-by-step explanation:
HELPPPP!!!!
Need the answer ASAP!!
Given that the functions [tex]f(x)=x+4[/tex] and [tex]g(x)=x^{3}[/tex]
We need to determine the value of the function [tex](g \ {\circ} f)(-3)[/tex]
First, we shall determine the composition of the function [tex](g \circ f)(x)[/tex]
Function [tex](g \circ f)(x)[/tex]:
Let us determine the function [tex](g \circ f)(x)[/tex]
Thus, we have;
[tex](g \circ f)(x)=g[f(x)][/tex]
[tex]=g[x+4][/tex]
[tex]=(x+4)^3[/tex]
[tex](g \circ f)(x)=x^3+3x^2(4)+3x(4)^2+(4)^3[/tex]
[tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, the function is [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Value of the function [tex](g \ {\circ} f)(-3)[/tex]:
The value of the function can be determined by substituting x = -3 in the function [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, we have;
[tex](g \circ f)(-3)=(-3)^3+12(-3)^2+48(-3)+64[/tex]
Simplifying the terms, we get;
[tex](g \circ f)(-3)=-27+12(9)+48(-3)+64[/tex]
[tex](g \circ f)(-3)=-27+108-144+64[/tex]
[tex](g \circ f)(-3)=1[/tex]
Thus, the value of the function [tex](g \ {\circ} f)(-3)[/tex] is 1.
A toy company is considering a cube or sphere-shaped container for packaging a new product. The height of the cube would equal the diameter of the sphere . Compare the volume to surface area ratios of the containers. Which packaging will be more efficient? For a sphere, SA =4πr²
Answer:
Packaging with cube will be more efficient.
Step-by-step explanation:
Given:
A cube and a sphere where the diameter of the sphere is equal to the height of the cube.
Let the height of the cube "x"
Radius of the sphere = [tex](\frac{x}{2})[/tex]
Formula to be used:
Surface area of the cube = [tex]6x^2[/tex] and Surface area of the sphere = [tex]4\pi (r)^2[/tex]
Volume of the cube = [tex]x^3[/tex] and Volume of the sphere = [tex]\frac{4\pi r^3}{3}[/tex]
We have to compare the ratio of SA and Volumes.
Ratio of SA : Ratio of their volumes :
⇒ [tex]\frac{SA\ of\ cube\ (S_1)}{SA\ of\ sphere\ (S_2)}[/tex] ⇒ [tex]\frac{Volume \ of \ cube\ (V_1)}{Volume\ of\ sphere\ (V_2)}[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x}{2})^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi r^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x^2}{4})}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x}{2})^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{\pi x^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x^3}{8})}{3} }[/tex]
⇒ [tex]\frac{6}{\pi}[/tex] ⇒ [tex]\frac{6}{\pi}[/tex]
⇒ approx [tex]2[/tex] ⇒ approx [tex]2[/tex]
⇒ [tex]S_1=2S_2[/tex] ⇒ [tex]V_1=2V_2[/tex]
Packaging of the toy with the cube will be more efficient as it has more volume comparatively.
Solve the system of equations.
y = 1/2x + 3
x + y = 6
Consider the system of equations below. What could be the first step in solving the
system of equations using elimination?
2x + 3y = 8
2x + 6y = 12
Add the two equations.
Add 4 to both sides of the first equation.
Multiply the first equation by -1
Multiply the second equation by 2.
Answer:
(A) Add the two equations.
Step-by-step explanation:
Solved by addition/elimination method.
Let me know if I'm wrong.
<3
The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?
We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.
We are asked to find the percentage of students that are between 14 and 18 years old.
First of all, we will find z-score corresponding to 14 and 18 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{14-15}{2}[/tex]
[tex]z=\frac{-1}{2}[/tex]
[tex]z=-0.5[/tex]
Similarly, we will find the z-score corresponding to 18.
[tex]z=\frac{18-15}{2}[/tex]
[tex]z=\frac{3}{2}[/tex]
[tex]z=1.5[/tex]
Now we will find the probability of getting a z-score between [tex]-0.5[/tex] and [tex]1.5[/tex] that is [tex]P(-0.5<z<1.5)[/tex].
[tex]P(-0.5<z<1.5)=P(z<1.5)-P(z<-0.5)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.5<z<1.5)=0.93319-0.30854[/tex]
[tex]P(-0.5<z<1.5)=0.62465[/tex]
Let us convert [tex]0.62465[/tex] into percentage.
[tex]0.62465\times 100\%=62.465\%\approx 62.5\%[/tex]
Therefore, approximately [tex]62.5\%[/tex] of the students are between 14 and 18 years old.
Answer:
62.47%
Step-by-step explanation:
Frederick made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 3 1 2 in long, what is the area of the whole quilt?
Answer:
Step-by-step explanation:
Given that, .
Frederick make 7 × 7 quilt array
This shows that there are seven rows and there are seven columns.
So, the total quilt is
7 × 7 = 49 squares patches
We are told that each of this square patches are 3½ in long
Then, since it is a square patch, it's area is
A = S² = 3½ × 3½ = 12¼ in²
So, each square patch has an area of 12¼in²,
Then, for 49 square patches
The total area of 49 Square patches is
A = 49 × 12¼ = 600.25 in²
So, the area of the whole quilt is 600.25 in²
Answer:
The area of the whole quilt is 600.25 ft²
Step-by-step explanation:
Here we have the length of each patch given as [tex]3\frac{1}{2} in[/tex]
Therefore, whereby the quilt had 7 × 7 array of different color square patches, we have;
Length of each side of quilt = [tex]7 \times 3\frac{1}{2} = 7 \times \frac{7}{2} = \frac{49}{2} = 24\frac{1}{2}[/tex]
∴ Area of the whole quilt = [tex]24\frac{1}{2} \times 24\frac{1}{2} = \frac{2401}{4} = 600\frac{1}{4} \ ft^2[/tex]
The area of the whole quilt = 600.25 ft².
Tyler went to an electronics store with a gift card. After he spent 13/20 of the gift card's value on a video game, the card's value was less than $26.25. Which inequality describes x, the value of the gift card when Tyler entered the store?
Answer:
[tex]\frac{7}{20}x < 26.25[/tex]
Step-by-step explanation:
If $x is the value of the gift card when Tyler entered the store, then after spending [tex]\frac{13}{20}[/tex] of the gift card the card's value was less than $26.25.
So, we can write the inequality as
[tex]x - \frac{13}{20}x < 26.25[/tex]
⇒ [tex]\frac{7}{20}x < 26.25[/tex]
So, this is the required inequality that describes x, the value of the gift card when Tyler entered the store. (Answer)
Hector puts a principal of $5,600 in a savings account with a simple interest rate of 8%. After several years, he
withdraws the balance of $11,424. How many years did he leave his investment in this particular savings account?
Simple interest: I = Pirit
11 years
12 years
13 years
14 years
Done
Answer:
13 years
first calculate interest and use formula
SI=ptr/100.
Answer:
13
Step-by-step explanation:
Consider Jasper’s balance sheet. Which shows how to calculate Jasper’s net worth? $4,400 - $15,800 = -$11,340 $15,800 + $4,400 = $20,260 $15,800 - $4,400 = $11,400 $20,260 - $15,800 = $4,400
Answer:
15,800-4,400
Step-by-step explanation:
Add the assets column which equals to 15,800, then add the liability column which adds up to be 4,400 :)
Answer:$15,800 - $4,400 = $11,400
Step-by-step explanation:
yes
Jake made these miniature golf scores: 2, 3, 2, 4, 3, 3, 3, 4, 2, 3, 4, 2, 4, 4, 9, 3, 4, 4.
Match the measure to the corresponding value for these scores.
mode
median
range
mean
7
3.5
4
3
Answer:
Mode is 4 median is 3 range 7 mean 3.5
Step-by-step explanation:
Brent biked 800 meters on Friday. On Saturday, he biked 3 kilometers. On Sunday, he biked 2 kilometers, 600 meters. How many kilometers did Brent bike over the three days
Answer:
333
Step-by-step explanation:
Question: here is a spinner with 6 pink shaded areas and 6 white shaded areas. If you spin the spinner ONCE, What is the probability (P) your spinner will land on a pink shaded area?
—-I NEED HELP ASAP!!
Answer: 6/12
Step-by-step explanation:
You have a 50% percent chance of landing on the shaded area
Sadie is making punch for her soccer team picnic. She uses 8 quarts of lemon lime soda, 4 pints of vanilla ice cream and 8 cups of orange juice. How many gallons of punch will she have.
Answer:
[tex]3\text{ gallons}[/tex]
Step-by-step explanation:
GIVEN: Sadie is making punch for her soccer team picnic. She uses [tex]8[/tex] quarts of lemon lime soda, [tex]4[/tex] pints of vanilla ice cream and [tex]8[/tex] cups of orange juice.
TO FIND: How many gallons of punch will she have.
SOLUTION:
Amount of lemon lime soda punch [tex]=8\text{ quarts}[/tex]
Amount of vanilla ice cream punch [tex]=4\text{ pints}[/tex]
Amount of orange juice punch [tex]=8\text{ cups}[/tex]
Now,
[tex]1\text{ gallon}=4\text{ quarts}[/tex]
total lemon lime soda punch [tex]=2\text{ gallon}[/tex]
[tex]1\text{ gallon}=8\text{ pint}[/tex]
total vanilla ice cream punch [tex]=0.5 \text{gallon}[/tex]
[tex]1\text{ gallon}=15.77\text{ cups}[/tex]
total orange juice punch [tex]=0.51\text{ gallon}[/tex]
Hence total gallon of punch [tex]=2+0.5+0.51[/tex]
[tex]\approx3\text{ gallon}[/tex]
Hence sadie has total [tex]3\text{ gallons}[/tex] of punches
What is the volume of this cylinder if its circumference is 125.7 feet
(the height is 80 ft) use 3.14 for pi
A) 100,681.06
B) 100,053.1
C) 10048
D) 32,032
To find the volume of a cylinder given its circumference and height, divide the given circumference by 2π to find the radius then use the formula for the volume of a cylinder πr²h. In this case, the volume of the cylinder is approximately 100,530.4 cubic feet.
Explanation:The volume of a cylinder can be calculated using the formula V = πr²h where V is the volume, r is the radius of the base, h is the height, and π is a constant that is approximately 3.14. Firstly, we need to find the radius. The circumference of the circle, which is the base of the cylinder, is given by the formula C = 2πr where C is the circumference and r is the radius. Given the circumference as 125.7 feet, we can calculate the radius (r) by dividing the circumference by 2π. Therefore, r = 125.7/(2*3.14) = 20 feet. Once we have the radius, we can calculate the volume of the cylinder using the formula V = πr²h. Substituting r = 20 feet and h = 80 feet, we get V = 3.14 * (20)^2 * 80 which equals 100,530.4 cubic feet. Hence, the closest answer would be option (B) 100,053.1.
Learn more about Volume of a Cylinder here:https://brainly.com/question/16788902
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The volume of a cone is cubic inches. Its height is 12 inches. What is the radius of the cone?
Answer: 4.22
Step-by-step explanation:
Un grupo de turistas gasta $ 153 para alquilar tubos y aletas. Se alquilan un total de 12 snorkels y 15 pares de aletas. Alquilar un snorkel cuesta tres veces más que alquilar un par de aletas. ¿Cuánto cuesta alquilar un snorkel? Cuesta $ alquilar un snorkel.
Answer:
The cost to rent a snorkel is 9$
(espanol) el costo de un snorkel es de 9$
Step-by-step explanation:
(English)Given that the group of tourists have spent $153 in renting snorkels and fins and there are 12 snorkels and 15 pairs of fins being rented, allow x to be the amount paid for the rent of the snorkels and y to be the rent for pairs of fins then 12x + 15y = 153. Given also that the rent for a snorkel is three times the rent of a pair of fins then x = 3y then, 12(3y) + 15y = 153. Simplify the equation, 36y + 15y = 153. 51y = 153. Solve for y by dividing both sides of the equation by 51 then, y = 153/51 = 3. Therefore, renting a pair of fins costs $3. To compute for the rent of a snorkel, use the equation x = 3y then, x = 3($3) = $9.
(Espanol) Dado que el grupo de turistas han gastado $153 en el alquiler de snorkels y aletas y hay 12 snorkels y 15 pares de aletas que se alquilan, permitir x para ser la cantidad pagada por el alquiler de los snorkels y y para ser el alquiler para pares de aletas entonces 12x + 15y 153. Dado también que el alquiler para un snorkel es tres veces el alquiler de un par de aletas y luego x a 3y, entonces, 12 (3y) + 15y a 153. Simplifique la ecuación, 36y + 15y a 153. 51y a 153. Resuelva para y dividiendo ambos lados de la ecuación por 51 entonces, y á 153/51 a 3. Por lo tanto, alquilar un par de aletas cuesta $3. Para calcular el alquiler de un snorkel, utilice la ecuación x á 3y, a continuación, x a 3($3) a $9.
A farmer has 45 acres of land and plants 17 apple trees on each acre. How many trees in total did the farmer plant?
765 trees
775 trees
865 trees
875 trees
Answer:
765
Step-by-step explanation:
17 * 45 = 765
Answer:
765
Step-by-step explanation:
1. Approximate the length of the hypotenuse to
the nearest tenth using a calculator.
Answer:
What is the answer?
Step-by-step explanation:
what’s the area of the trapezoid
Answer:
i will give you the steps to find out how
Step-by-step explanation:
Explanation: To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
Answer:
The equation to find the area of a Trapezoid is A=h·([tex]\frac{b1+b2}{2}[/tex])
Step-by-step explanation:
c3 if c = 2 need help
Answer:
6
Step-by-step explanation:
If c is 2 then that means you would multiply 2 and 3 to get 6
Ever since he broke his wrist last summer, Carlos never skateboards without his safety equipment. In the Reply box below, copy and paste these headers to identify your answers: 1. Risk the person is taking or the steps he or she is taking to avoid a risk: 2. Reason why:
Answer:
Carlos is risking breaking another bone or getting hurt because he doesn't use any safety equipment to prevent it from happening.
Step-by-step explanation:
Please help me I understand everything else but I don’t know what to do
The cost of 4 ice cream cones from the snack bar was $10.40. If each ice cream cone costs the same amount, which model correctly illustrates the relationship? Check all that apply.HELPPPP
y = 10.4 x
y = 2.6 x
y = 4 x
Cost of Ice Cream Cones
A 2-column table with 3 rows. Column 1 is labeled number of ice cream cones with entries 13, 26, 39. Column 2 is labeled Total cost (in dollars) with entries 5, 10, 15.
Cost of Ice Cream Cones
A 2-column table with 3 rows. Column 1 is labeled number of ice cream cones with entries 5, 10, 15. Column 2 is labeled Total cost (in dollars) with entries 13, 26, 39.
Cost of Ice Cream Cones
On a coordinate plane, the x-axis is labeled number of ice cream cones and the y-axis is labeled total cost (in dollars). A line goes through points (0, 0) and (5, 13).
Cost of Ice Cream Cones
On a coordinate plane, the x-axis is labeled number of ice cream cones and the y-axis is labeled total cost (in dollars). A line goes through points (3, 1) and (18, 7).
Answer:The answer is B,E and F
Step-by-step explanation:
I'm not sure how to explain but divided 10.40 by 4 and the answer is 2.6 and after that you can figure the rest out. Hope this helps!
Jackson purchases a new car for 48,000 The cars value is modlee by the expression 48000(0.76)^t where y represents the cars value and t represents time in years what is the decay rate expressed at a percentage
Answer:
i think 48,000
Step-by-step explanation:
Answer:
me to
Step-by-step explanation:
A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 140 feet. How long will it take to move from one end to the other?
Answer:
The answer is : 20 seconds
Step-by-step explanation:
First, we are told that it takes the person 8 seconds to travel 56 feet, hence, we will find the time it takes to travel one foot.
56 feet = 8 seconds
∴ 1 foot = 8/56 seconds
Next, we are told that the length of the sidewalk is 140 feet, therefore walking from one end of the sidewalk to the other is the the same as walking 140 feet, and this is calculated thus:
1 foot = 8/56 seconds (calculated above)
∴ 140 feet = 8/56 × 140 = 20 seconds
If the vertex of a parabola is (8,10) , what is the axis of symmetry?
Answer:
x = 8
Step-by-step explanation:
The axis of symmetry for graph is always set up as "x="
So, if the x in this ordered pair is 8, then the axis of symmetry is also 8.
(I have posted a picture below as proof...)