The cost of gasoline for 12 gallons is $22.18. What is the cost of 1 gallon?
Answer:
$1.85
Step-by-step explanation:
12 gallons = $22.18
1 gallon = $22.18 ÷ 12
1 gallon = $1.85
A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used
Answer:
Step-by-step explanation:
Using the sample size formula
n= (zs/e)²
z is the z score at 99% = 2.58
s is the standard deviation = 250
e is the sample mean = 50
Substitute
n = (2.58×250/50)²
n = (2.58×5)²
n = (12.9)²
n=166.41
hence the sample size is 166.41
Solve for the distance between the points (25, -41) and (31, -32).
Answer:
The distance should be [tex]3\sqrt{13[/tex]
Step-by-step explanation:
Distance formula
The graph below represents the unit rate for the cost c, in dollars, of b candy bars. Write an equation to represent the cost of candy bars. HELPP
Answer:
16
Step-by-step explanation:
i would try but not 100% sure
Simplify each expression (2a^4)^-3,a does not =0
Answer:
3rd option.) 1/8a^12
Step-by-step explanation:
(2a⁴)^-3
=1/(2a⁴)³
=1/8a^12
Answer: The next one is 3. 7/2v^2
Step-by-step explanation: In case you needed help with that
1) Joanie invested $4,500 into an account that pays 4,5% Interest compounded monthly for 10
years. What is the future value of the investment?
Answer:
$2025
Step-by-step explanation:
Hope that helps!
m∠11 = 11x
m∠13 = 10x + 12
Answer:m∠11 = 11x
m∠13 = 10x + 12
Step-by-step explanation:
m∠11 = 11x
m∠13 = 10x + 12
Find The slope of the line that passes through (3,15) and (6,10)
Answer:
-5/3
Step-by-step explanation:
10-15=-5
6-3=3
Answer:
-5/3
Step-by-step explanation:
m=y2-y1/x2-x1
10-15-(-5)
6-3=3
-5/3
hope this helped :3
sorry if it is wrong
a barangay has 1000 individuals and its population doubles every 60 years. Give an exponential model for the barangay's population
Answer:
P(t) = 1000e^(0.01155)t
Step-by-step explanation:
Let the population of barangay be expressed according to the exponential formula;
P(t) = P0e^kt
P(t) is the population of the country after t years
P0 is the initial population
t is the time
If barangay has 1000 initially, this means that P0 = 1000
If the population doubles after 60years then;
at t = 60, P(t) = 2P0
Substitute into the formula
2P0 = P0e^k(60)
2 = e^60k
Apply ln to both sides
ln2 = lne^60k
ln2 = 60k
k = ln2/60
k = 0.01155
Substitute k = 0.01155 and P0 into the expression
P(t) = 1000e^(0.01155)t
Hence an exponential model for barangay's population is
P(t) = 1000e^(0.01155)t
need help with the question in the image
Answer:
y=2
Step-by-step explanation:
the image and preimage are 6 units apart so thhe line of reflection is in the middle at 3 units and is a line that is paralel to the x-axis
y=2
Rebotar Inc. makes basketballs. Their fixed costs are $3,450. Variable costs are $12 per basketball. If the basketball is priced at $25 and 300 basketballs are sold, did Rebotar break even? How do you know? Show all work
Given:
Fixed cost = $3,450
Variable cost = $12 per basketball
Selling price = $25 per basketball
Number of basketball sold = 300
To find:
Whether Rebotar did break even.
Solution:
According to the question,
Cost of 1 basketball = $12
Cost of 300 basketball = $12×300
We know that,
Total cost = Fixed cost + Variable cost
[tex]TC=3450+12(300)[/tex]
[tex]TC=3450+3600[/tex]
[tex]TC=7050[/tex]
So, the total cost is $7050.
Now,
Selling price of a basketball = $25
Selling price of 300 basketball = $25×300
Total revenue is
[tex]TR=25\times 300[/tex]
[tex]TR=7500[/tex]
So, total revenue is $7500.
At break even situation the profit is zero. In other words, the total revenue is equal to total cost.
Since, [tex]TC\neq TR[/tex], therefore, Rebotar did not break even.
Write the slope intercept form of the equation of the line through the given point plz
Answer: [tex]y=-x-5[/tex]
Step-by-step explanation:
Slope intercept form is [tex]y=mx+b[/tex], so we have to find a way to substitute the given information into the equation. We have [tex]m[/tex] because it gives us the slope. The slope is -1, as the directions state. Now, we substitute it in and solve for b:
Substitute -1 in for m⇒ [tex]y=-x+b[/tex] Substitute in the point (-1, -4) in for [tex]x[/tex] and [tex]y[/tex] respectively to get [tex]-4=-(-1)+b[/tex] Solve the equation to get b= -5After getting the y-intercept, you have the full equation!
Solve for x.
Help ASAP please!!!
Answer:
The value of x is 4
Step-by-step explanation:
In a right triangle, if a segment is drawn from the right angle ⊥ to the hypotenuse like the given figure, then
∵ The length of one side of the right triangle = (x + 2)
∵ The length of the hypotenuse = x + 5
∴ (x + 2)² = x (x + 5)
∵ (x + 2)² = (x + 2)(x + 2)
∴ (x + 2)(x + 2) = x(x + 5)
→ Simplify the two sides
∵ (x)(x) + (x)(2) + (2)(x) + (2)(2) = (x)(x) + (x)(5)
∴ x² + 2x + 2x + 4 = x² + 5x
→ Add the like terms in the left side
∴ x² + 4x + 4 = x² + 5x
→ Subtract x² from both sides
∵ x² - x² + 4x + 4 = x² - x² + 5x
∴ 4x + 4 = 5x
→ Subtract 4x from both sides
∴ 4x - 4x + 4 = 5x - 4x
∴ 4 = x
∴ The value of x is 4
#11 The directions on a sewing pattern say to buy an extra 12.5% of fabric to account for error. Sam needs 2.75 yards of fabric to make a shirt, so he buys 2.4 yards. Choose the correct statement. *
A. Sam bought the correct amount of fabric because he bought what was suggested.
B. Sam bought the correct amount of fabric because he needs less than 2.4 yards.
C.Sam did not buy the correct amount of fabric because he needs less than 2.4 yards.
D.Sam did not buy the correct amount of fabric because he should have bought 3.09 yards.
Answer:
D
Step-by-step explanation:
Sam should have bought 3.09 yards of fabric instead of 2.4 yards
So, Option D is correct.
Step-by-step explanation:
Total fabric needed by Sam = 2.75
According to directions on a sewing pattern they say to buy an extra 12.5%
So, extra fabric would be: 12.5% of 2.75
Solving
Now adding 0.343 into 2.75 to get extra fabric quantity:
2.75+0.343
=3.09
Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards
So, Option D is correct.
someone pleaseeeeeee answer :)))
Answer:
You would have to rent 10 movies for the cost to be the same.
Step-by-step explanation:
20+1.5x=3.5x
-1.5x on both sides
20=2x
x=10
Answer:
You would have to rent 8 movies at the first store and 10 movies at the second
Step-by-step explanation:
Find the slope of each line.
Liam says the DOMAIN of the relationship shown here
is 0
Edit the inequality below to correct her mistake.
Submit
1(-2.0)
(1.0)
9 M
Answer:
Step-by-step explanation:
- 2 ≤ x ≤ 1
x ∈ [ - 2 , 1 ]
Answer:
How we will solve:
- 2 ≤ x ≤ 1
x ∈ [ - 2 , 1 ]
A train travels a distance of 862 miles. Then it travels another 312 miles. The train then travels another 403 miles. How many more miles does the train travel on the first part of the trip than on the second and third trips combined? *
Answer:
It travels 530 more miles on the first trip than the second trip and travels 469 more miles on the first trip than the third trip.
Step-by-step explanation:
Take 872-342=530 so then that's your answer to the first part of the question, now do the same thing just plug in the different numbers: 872-403=469
Jeri has 2/3 yard of fabric to use for making some puppets she needs 1/6 yard for each puppet how many puppets can jeri make with the fabric
Answer:4
Step-by-step explanation:
Write the sentence as an inequality 8 is less than 6 more than 3 times a number x
Answer:
Sometimes you have to think a little out of order to do this type of problem.... but here goes an explanation.
Step-by-step explanation:
8 is less than looks like this: 8 <
6 more than looks like this: +6
3 times a number x is: 3x
So
8 < 3x+6 meets the criteria
The inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The sentence as an inequality 8 is less than 6 more than 3 times a number x:
From the question:
Here x is any real number:
The inequality will be:
8 < 3x+6 which represents 8 is less than 6 more than 3 times a number x
Thus, the inequality will be 8 < 3x+6 if the 8 is less than 6 more than 3 times a number x; the answer is 8 < 3x+6.
Learn more about inequality here:
brainly.com/question/19491153
#SPJ2
A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. Twenty-five repetitions of the simulation were performed. The simulated number of makes in each set of 10 shots was recorded on the dot plot below.
What is the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts
Answer:
0.9 or 90%
Step-by-step explanation:
The probability of shot is 47%
The probability of no shot is 100 -47 = 53%
The dot plot is made from the 10 repeated shots which recorded 25 scores.
The number of dots on the fifth tick is 9 of 10 shots
therefore; 9/10 = 0.9, which 90 in percentage.
The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.
Given information:
A basketball player claims to make 47% of her shots from the field.
It s required to simulate the player taking sets of 10 shots, assuming that her claim is true. Twenty-five repetitions of the simulation were performed.
The dot plot shows the simulated number of makes in each set of 10 shots.
The dots in the 5 shot mark is 9, that in 6 shot mark is 2 and that in 7 shot mark is 1.
So, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated as,
[tex]P(x\geq5)=\dfrac{9+2+1}{30}\\=\dfrac{12}{25}[/tex]
Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.
For more details, refer to the link:
https://brainly.com/question/11740746
22 There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
Colour
blue
red
yellow
Probability
0.2
The number of red cubes in the box is the same as the number of yellow cubes in the box.
(a) Complete the table.
Answer:
Colour ---- Probability
Blue ----- 0.2
Red ------- 0.4
Yellow ------ 0.4
Step-by-step explanation:
Given
Colour ---- Probability
Blue ----- 0.2
Red -------
Yellow ------
Required
Complete the table
In probability, all probabilities add up to 1.
i.e.
[tex]P(Blue) + P(Red) + P(Yellow) = 1[/tex]
Substitute 0.2 for P(Blue)
[tex]0.2 + P(Red) + P(Yellow) = 1[/tex]
[tex]P(Red) + P(Yellow) = 1 - 0.2[/tex]
[tex]P(Red) + P(Yellow) = 0.8[/tex]
From the question, we understand that the frequency of yellow and red balls are the same.
Hence:
[tex]P(Red) = P(Yellow)[/tex]
[tex]P(Red) + P(Yellow) = 0.8[/tex] becomes
[tex]P(Red) + P(Red) = 0.8[/tex]
[tex]2P(Red) = 0.8[/tex]
Make P(Red) the subject
[tex]P(Red) = 0.4[/tex]
Recall that:
[tex]P(Red) = P(Yellow)[/tex]
Hence,
[tex]P(Yellow) = 0.4[/tex]
So, the complete table is:
Colour ---- Probability
Blue ----- 0.2
Red ------- 0.4
Yellow ------ 0.4
Determine the standard deviation (sigma)by filling in the table as part of your calculation. Consider the following data 6, 6, 10, 8, 10, 8 x x Overbar x minus x Overbar (x minus x Overbar) squared a. 1.63 c. 0.94 b. 0.47 d. 1.15
Answer:
A
Step-by-step explanation:
I got it right on the assignment 100%
Answer:here’s the answer for this question
Step-by-step explanation:edge2023
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $1,264 with a standard deviation of $150. What is a 90% confidence interval for the mean daily income this parking garage will generate
Answer:
$1226.78<x<$1301.22
Step-by-step explanation:
The formula for calculating confidence interval is expressed as;
CI = xbar ± z×(s/√n)
Given
Mean (xbar) = $1264
z is the z score at 90% CI = 1.645
s is the standard deviation = $150
n is the sample size = 44
Substitute
CI = 1264±1.645(150/√44)
CI = 1264±1.645(150/6.63)
CI = 1264±1.645(22.624)
CI = 1264±37.22
CI = (1264-37.22, 1264+37.22)
CI = (1226.78, 1301.22)
Hence the confidence interval of the mean is $1226.78<x<$1301.22
On a coordinate plane, the x-axis is labeled Turkey hot dogs and the y-axis is labeled dollars. Points (2, 1) and (4, 2) are plotted. Use equivalent ratios to decide which statements are true about the cost per hot dog. Check all that apply. The cost of 2 turkey hot dogs is $1. The cost of 1 turkey hot dog is $2. The cost of 4 turkey hot dogs is $2. The cost of 3 turkey hot dogs is $2. The cost of 6 turkey hot dogs is $3. The cost of 10 turkey hot dogs is $5.
Answer:
A C E F
Step-by-step explanation:
Answer:
A, C, E, and F.
Approximate the root by using a linearization centered at an approximate nearby number
√101
Linearization is the idea in calculus where if you zoom in really close onto a section of the graph, the curve and the tangent line will be extremely similar to each other.
We can use this idea and approximate nearby values to the tangent line.
The parent graph of a square root function is [tex]f(x)=\sqrt{x}[/tex].
There are two methods in which we can calculate the approximate value of [tex]\sqrt{101}[/tex] by using linearization techniques.
Method 1:Write equation of tangent line.Find the value of y at x = 101.Let's use the nearest perfect square to [tex]\sqrt{101}[/tex], which is [tex]\sqrt{100}[/tex]. When drawing the graph of the square root function, we use the point (100, 10) because where x = 100, y = 10 on a square root function.
Now, we have a point that the tangent line passes through, and we want to find the slope.
We can do so by taking the derivative of [tex]f(x) =\sqrt{x}[/tex].
[tex]f'(x)=x^\frac{1}{2}[/tex] [tex]f'(x)=\frac{1}{2} x^-^\frac{1}{2}[/tex] [tex]f'(x)=\frac{1}{2x^\frac{1}{2} }[/tex] [tex]}f'(x)=\frac{1}{2\sqrt{x} }[/tex]Plug in x = 100 to find the slope of the tangent line here.
[tex]f'(100)=\frac{1}{2\sqrt{100} }[/tex] [tex]f'(100)=\frac{1}{2(10)}=\frac{1}{20}[/tex]The slope of the tangent line at x = 100 is 1/20. Now, we can use the point and the slope of the tangent line to determine the equation for the tangent line.
(100, 10), m = 1/20
Point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex] [tex]y-(10)=\frac{1}{20}(x-(100))[/tex] [tex]y=\frac{1}{20}x-5+10[/tex] [tex]y=\frac{1}{20}x+5[/tex]To find the value of y at x = 101, plug this into the tangent line equation.
[tex]y=\frac{1}{20}(101)+5[/tex] [tex]y=\frac{101}{20}+5[/tex] [tex]y=\frac{101}{20} +\frac{100}{20} = \frac{201}{20}[/tex]201/20 is equal to 10.05. Let's estimate the error of this calculation to the actual value of [tex]\sqrt{101}[/tex], inputted into a calculator.
We get [tex]\sqrt{101}=10.04987562[/tex], which is extremely close to 10.05. Our estimate using linearization only has an error of 0.00012.
Method 2:You may have noticed that the first method uses little calculus, apart from taking the derivative of f(x).
The more "calculus-y" method involves finding the change in y in terms of the change of x.
We know that dy/dx is the the change in y due to a change in x, so we can use this to find the change in y when x = 101.
[tex]\frac{dy}{dx} =\frac{1}{2\sqrt{x} }[/tex]Solve for dy by mutliplying dx to both sides of the equation.
[tex]dy=\frac{1}{2\sqrt{x} } \cdot dx[/tex]The change in x is 1, because 101 - 100 = 1.
We want to find the change in y when x = 100, and has a change of 1. Therefore, we have:
[tex]dx=1[/tex] [tex]x=100[/tex]Plug these values into the equation [tex]dy=\frac{1}{2\sqrt{x} } \cdot dx[/tex] and solve for dy.
[tex]dy=\frac{1}{2\sqrt{200} } \cdot 1[/tex] [tex]dy=\frac{1}{2(10)}[/tex] [tex]dy=\frac{1}{20}[/tex]The change in y when x = 100 with a change of 1 is 1/20. We know when x = 100 the y-value is 10. Therefore, when x = 101, the change in y is 1/20, so y = [tex]10\frac{1}{20} = \frac{201}{20} = 10.05[/tex].
You can see that we get the same answer with either method.
A road rises 20 feet for every 100 feet in horizontal distance. What is the slope?
Answer:
Slope, [tex]m=\dfrac{1}{5}[/tex]
Step-by-step explanation:
It is given that,
A road rises 20 feet for every 100 feet in horizontal distance.
Rise (vertical distance) = 20 feet
Run (horizontal distance) = 100 feet
Slope of the road is given by the ratio of rise to the run. It can be calculated as :
[tex]m=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex]
So, the slope is [tex]\dfrac{1}{5}[/tex].
Which number line represents the solutions to lx - 5| = 1?
Answer:
The answer is B, or the second one
Step-by-step explanation:
Families with 5 children are randomly selected find the expected number of boys a family might have
Answer:
The expected number of boys a family might have is 2.5.
Step-by-step explanation:
Let X denote the number of boys in a family with 5 children.
The probability of a boy is, p = 0.50.
The child can either be a by or a girl independently.
The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.
The probability mass function is:
[tex]p_{X}(x)={5\choose x}(0.50)^{x}(1-0.50)^{5-x};\ x=0,1,2...5[/tex]
Compute the expected number of boys a family might have as follows:
[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]
x p (x) x · p (x)
0 [tex]p(0)={5\choose 0}(0.50)^{0}(1-0.50)^{5-0}=0.03125[/tex] [tex]0\times 0.03125=0[/tex]
1 [tex]p(1)={5\choose 1}(0.50)^{1}(1-0.50)^{5-1}=0.15625[/tex] [tex]1\times 0.15625=0.15625[/tex]
2 [tex]p(2)={5\choose 2}(0.50)^{2}(1-0.50)^{5-2}=0.3125[/tex] [tex]2\times 0.3125=0.625[/tex]
3 [tex]p(3)={5\choose 3}(0.50)^{3}(1-0.50)^{5-3}=0.3125[/tex] [tex]3\times 0.3125=0.9375[/tex]
4 [tex]p(4)={5\choose 4}(0.50)^{4}(1-0.50)^{5-4}=0.15625[/tex] [tex]4\times 0.15625=0.625[/tex]
5 [tex]p(5)={5\choose 5}(0.50)^{5}(1-0.50)^{5-5}=0.03125[/tex] [tex]5\times 0.03125=0.15625[/tex]
Then,
[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]
[tex]=0+0.15625+0.625+0.9375+0.625+0.15625\\\\=2.5[/tex]
Thus, the expected number of boys a family might have is 2.5.
The value of y varies directly with x, and y = 5 when x = -20. Find y when x = 35.
Please help! Thanks!!!!
Answer:
Step-by-step explanation:
If y= -5 when x= -20 that means x is 4 times y
y= 8.75 when x= 35
Answer:
Our equation is:
[tex]\displaystyle y=-\frac{1}{4}x[/tex]
When x=35, y=-35/4 or -8.75.
Step-by-step explanation:
We know that y varies directly with x.
The standard equation is:
[tex]y=kx[/tex]
We know that y is 5 when x is -20.
So, let’s substitute 5 for y and -20 for x and solve for k, our constant of variation. So:
[tex]5=k(-20)[/tex]
Divide both sides by -20:
[tex]\displaystyle k=-\frac{1}{4}[/tex]
Therefore, our constant of variation is -1/4.
Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{4}x[/tex]
To find y when x=35, let’s substitute 35 for x. So:
[tex]\displaystyle y=-\frac{1}{4}(35)=-\frac{35}{4}=-8.75[/tex]
So, when x=35, y=-8.75.