How many solutions to 15x+11=8x
Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}
Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?
Answer: Third graph represents the acceptable weights for the frozen yogurt options.
Step-by-step explanation:
Since we have given that
Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4
After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.
So, it means the weight should be lie between 4 ounces and 7 ounces.
So, it can be written as [4,7].
4≤ x ≤7, here, x is the weight of frozen yogurt.
So, third graph represents the acceptable weights for the frozen yogurt options.
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it be?
Find the area of the shaded region below. The units are in feet.
Use 3.14 for π. Round your answer to two decimal places.
for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value
Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?
Find the area of sector AOB. Express your answer in terms of pi and rounded to the nearest tenth.
To find the area of sector AOB, use the formula A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, the area is approximately 0.139 m², rounded to the nearest tenth.
Explanation:To find the area of sector AOB, we need to use the formula for the area of a sector: A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, we get A ≈ (1.11/360) * π * (4.5)^2.
Using a calculator, we can calculate the value to be approximately 0.139 m². Rounding to the nearest tenth, the area of sector AOB is 0.1 m².
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The areas of the sectors of circles 5 and 6 to the nearest tenth are 197.8 cm² and 6.3 ft² respectively.
What are the areas of the sectors?The area of the sector of a circle can be expressed as:
Area = ( θ/360º ) × πr²
Where θ is the sector angle in degrees, R is the radius of the circle, and π is constant pi.
For question5)
Angle θ = 70 degrees
Radius r = 18 cm
Area =?
Area = ( θ/360º ) × πr²
Plug in the values:
Area = ( 70/360º ) × π × 18²
Area = 63π cm²
Area = 197.8 cm²
For question 6)
Angle θ = 180 degrees
Diameter d = 4ft
Radius r = 4/2 = 2ft
Area =?
Area = ( θ/360º ) × πr²
Plug in the values:
Area = ( 180/360º ) × π × 2²
Area = 2π ft²
Area = 6.3 ft²
Therefore, the area of the sector is 6.3 ft².
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Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.
A. 30
B. 40
C.60
D. 80
The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.
The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.
Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.Which expression is the greatest common factor (GCF) of the terms of trinomial 12x^7y^9 + 6x^4y^7 - 10x^3y^5
Answer: 2. [tex]\mathbf{2x^3y^5}[/tex]
Step-by-step explanation:
Greatest common factor of any two or more expression is the largest common expression that divides them.The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]
Term 1 : [tex]12x^7y^9[/tex]
Term 2 : [tex]6x^4y^7[/tex]
Term 3: [tex]- 10x^3y^5[/tex]
Lowest power of x = 3
Thus , The highest common power of x = [tex]x^3[/tex] (i)
Lowest power of y = 5
The highest common power of y =[tex]y^5[/tex] (ii)
Greatest common factor of 12, 6 , -10= 2 [Because 2 is the largest number that divides all of them] (iii)
From (i) , (ii) , (iii) , we have
Greatest common expression : [tex]2x^3y^5[/tex]
Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]
find the solution x-4y=9 and x-y=-9
see picture for solution
An apartment has 1026 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
A basketball player makes 39% of her shots from the free throw line. suppose that each of her shots can be considered independent and that she takes 5 shots. let x = the number of shots that she makes. what is the standard deviation for x?
Answer: 1.09
Step-by-step explanation:
Given : A basketball player makes 39% of her shots from the free throw line.
i.e. Proportion of her shots from the free throw line: p= 0.39
We assume that each of her shots can be considered independent .
She takes 5 shots.
i.e. Number of trials : n= 5
Let x = the number of shots that she makes.
Then , the standard deviation for x will be :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]
Hence, the standard deviation for x= 1.09
Final answer:
The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.
Explanation:
To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.
Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.
The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).
Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.
Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.
Find the circumference and the area of a circle with diameter
2ft
The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².
Explanation:To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².
Final answer:
The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².
Explanation:
To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.
The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:
C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet
So the circumference is approximately 6.28 feet.
The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:
A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet
So the area of the circle is approximately 3.14 square feet.
answer this plz
14 students are surveyed about the clothes they are wearing.
8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.
How many students are wearing jeans, but not a t-shirt?
2
3
4
5
Answer:
its
Step-by-step explanation:
what is 475% of 9.2?
The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending? h(t) = 5t + 500 h(t) = 5t – 500 h(t) = –5t + 500 h(t) = –5t – 500
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. find the probability that the first card is an ace and that the second card is an ace?
4 aces in a deck
52 cards
you have a 4/52 reduced to 1/13 probability of picking an ace.
without replacing it there would be 51 cards left and 3 aces
so second probability of picking an ace is 3/51 reduced to 1/17
the probability of doing both = 1/13 x 1/17 = 1/221
Answer:
conf
Step-by-step explanation:
Explain how you can use place value patterns to describe how 50 and 5000 compare
Need help with this word problem
Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?
x = average of next 5 quizzes
4 * 73 = first 4 quizzes
There will be a total of 4 +5 = 9 quizzes
Average of all quizzes = 88 = (4*73+5x)/9
9*88 = 9*(292 +5x)/9
792 = 292 + 5x
500 = 5x
X = 500/5 = 100
Next 5 quizzes need to average 100
The histogram shows the duration, in minutes, of movies in theaters.
What relationship between the median and mean is shown by the histogram?
A) The mean is less than the median.
B) The median is less than the mean.
C) The mean is equal to the median.
D) The median and mean cannot be compared from a histogram.
Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour
The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.
$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.
Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
Of the books in a library, 1/3 came from Robbie's collection and 15 came from Marta's. Of the rest, 15 were Elena's 1/5 were Winfield's, and 5 were purchased from the bookstore. How many book are there in the library?
The total number of books in the library are 75.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What will be the equation for given scenario?Let the total number of books in the library be x.
The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]
Collect the like terms,
[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]
On solving the equation for x we get x=75.
Therefore, the total number of books in the library are 75.
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What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?
The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?
A turkey was cooked at 300 f in the oven for 5 hours. the internal temperature rose from 35 f to 150 f. what was the average rise in temperature per hour
HELP PLEASE
Evaluate the expression.
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
v ⋅ w
a) -41
b) <-20, -36, 15>
c) <-28, 18, -35>
d) -9
Answer:
v . w = <-20, -36, 15>
Step-by-step explanation:
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
To find the dot product of vectors we multiply the numbers
We need to multiply v and w
vectors is in the form of <x,y,z>
Multiply all the x values
4 times -5= -20
6 times -6 = -36
-5 times -3 = 15
So v . w = <-20, -36, 15>
Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero