The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.
Explanation:The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]
In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]
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The sales tax in mike's state is 6%. mike bought a jetta having a sales tax of $820. what was the cost of the vehicle? round to the nearest dollar.
What happens to the force of gravity between two maser if they are moved father apart A. It increases. B. It decreases. C. It stays the same D. It fluctuates. ( Question two ) Earths path around the sun is ____. A elliptical. B circular. C . random. D. Triangular. (Question three). The asteroid belt separates what ? A. Sun and stars B. Earth in moon C. Inner and outer planets D. Milky Way from other galaxies ( Questikn four ) the tilt of the earth its axis causes ____. A. Day in night. B. The seasons. C. A year D. A month umm it right will mark brilliant
A farmer wants to build a rectangular garden 10ft long and 6ft wide. How many feet of fencing should he buy?
The goal of an optimization problem is to find the maximum or minimum value of the
An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.
The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.
Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.
The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week. ©
Answer:
2.28%
Step-by-step explanation:
Let X be the number of books borrowed from a library each week
Given that X is normal with mean = 190 and std dev = 30
Thus Z score would be
Z=[tex]\frac{x-190}{30}[/tex]
Required probability or chance = P(X>250)
=P([tex]z>\frac{250-190}{30}[/tex]
=P(Z>2)
=0.5-0.4772
=0.0228
=2.28%
Answer:
2.5 for plato
Step-by-step explanation:
#platolivesmatter
Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer. How does one arrive at the answer? Are all the ingredients added? Is anything multiplied?
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is
The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.
To find the expected number of books a customer will purchase,
use the formula for the expected value (also known as the mean) of a random variable:
Expected Value (μ) = Σ (x × P(x))
Where:
μ is the expected value.
x represents the possible values of the random variable (in this case, 0, 1, and 2).
P(x) is the probability associated with each value of x.
Probability of purchasing 0 books (P(0)) = 0.2
Probability of purchasing 1 book (P(1)) = 0.4
Probability of purchasing 2 books (P(2)) = 0.4
Now, calculate the expected value:
μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)
μ = 0 + 0.4 + 0.8
μ = 1.2
To find the standard deviation (σ) of the customer's book purchases,
use the formula for the standard deviation of a discrete random variable:
Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]
Where:
σ is the standard deviation.
x represents the possible values of the random variable.
μ is the expected value.
P(x) is the probability associated with each value of x.
In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).
Now, calculate the standard deviation:
σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]
σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]
σ = √[0.288 + 0.064 + 0.256]
σ = √0.608
σ ≈ 0.78
Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.
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Derive the equation of the parabola with the focus
is (-7,5) and the directrix of y=-11
Brody calculated the area of a square to be16/36 square foot. Which shows the side length of the square?
given right triangle XYZ what is the value of tan 60°
Answer:
√3
Step-by-step explanation:
got 100%
Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price.
a stereo with a cash price of $1,200 at $119.00 per month for 12 months
Answer:
(a) $1428
(b) $228
(c) 11 months
Step-by-step explanation:
(a) Total installment price = 119 × 12 = $ 1428
(b) The carrying charges = amount paid - cash price
= 1428 - 1200 = $ 228
(c) No. of needed to save the money = 1200 ÷ 119 = 10.08 ≈ 11 months
Answer: A=1428.00
B=228.00
C=11
The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder.
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose the height of cylinder is h and radius of base is r.
The volume of cylinder will be : [tex]\pi r^2h[/tex]
The cone is of same height means h and same base means radius will be r.
The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]
It means the volume of cone is one third of the volume of cylinder.
The volume of cylinder is given as π.
So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex] : Answer
Hope it will help :)
How many triangles are with two sides each 6 inches long and one angle measure of 90°.
The description relates to an isosceles right triangle.
An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.
In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.
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A cable hangs between two poles of equal height and 30 feet apart. set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. the height (in feet) of the cable at position x i
The length of the cable is the number of units on it.
The cable is 35.26 feet long
How to determine the cable lengthThe function is given as:
[tex]h(x) = 15\cos(x/15)[/tex]
For all the lengths, we have the following differential equation
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]
So, we have:
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]
Evaluate
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]
This gives
[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]
Evaluate the exponents
[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]
The above function is an even function.
So, we have:
[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]
Integrate
[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]
Simplify
[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]
Expand
[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]
Solve
[tex]Length = 35.26[/tex]
Hence, the length of the cable is 35.26 feet
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Form a seven-letter word by mixing up the letters in the word FIXTURE.
How many ways can you do this if no vowel is isolated between two consonants?
You have the main rule: no vowel is isolated between two consonants.
The word FIXTURE consists of 4 consonants and 3 vowels.
There are such possible cases:
1. Formed word begins with three vowels and ends with 4 consonants.
The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]
2. Formed word begins with two vowels and ends with one vowel (between them stand all consonants).
The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]
3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).
The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]
4. Formed word begins with with 4 consonants and ends with 3 vowels.
The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]
5. In total 144+144+144+144=576 different words.
Solve for C. See photo
Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.
The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.
Explanation:Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.
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Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard
Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?
Solve the inequality and graph its solution: 2t + 1 > 9 or –18 > 5t – 3
To solve the inequality and graph its solution, solve the two separate inequalities: 2t + 1 > 9 and -18 > 5t - 3. The solution is t > 4 or t < -3.6. Graph the solution by plotting the points 4 and -3.6 on a number line, and shading the area to the right of 4 and the left of -3.6.
Explanation:To solve the inequality and graph its solution, we need to solve the two separate inequalities:
1) 2t + 1 > 9
2) -18 > 5t - 3
For the first inequality, we can subtract 1 from both sides and divide by 2 to obtain t > 4.
For the second inequality, we can add 3 to both sides and divide by 5 to obtain t < -3.6.
Thus, the solution to the original inequality is t > 4 or t < -3.6.
To graph the solution, we would plot the points 4 and -3.6 on a number line, and shade the area to the right of 4 and the left of -3.6.
To solve the inequalities 2t + 1 > 9 and –18 > 5t – 3, we must solve each separately, and since it's an 'or' inequality, we combine the solution sets. The solutions are t > 4 and t < -3. Graphically, these solutions represent non-overlapping shaded regions on a number line.
Explanation:To solve the inequality 2t + 1 > 9 or –18 > 5t – 3, we need to consider them separately as each inequality represents a different solution set.
For the first inequality:
Subtract 1 from both sides to obtain 2t > 8.Divide by 2 to isolate t, yielding t > 4.For the second inequality:
Add 3 to both sides to get –15 > 5t.Divide by 5, which flips the inequality because we are dividing by a positive number, resulting in t < –3.We interpret these results as two separate conditions:
t > 4: This suggests that t is any value greater than 4.t < –3: This suggests that t is any value less than -3.Since the original statement uses 'or', the solution set includes all the values that satisfy either inequality. Therefore, graphically, we would show these on a number line with a shaded region to the right of 4 and another shaded region to the left of -3. The areas do not overlap because there are no t values that can simultaneously be greater than 4 and less than -3.
Find the equation of the tangent plane to the surface z=e−x/17ln(y) at the point (3,3,0.920883)
ONLY ANSWER IF YOU KNOW THE ANSWER Which shows a correct order to solve this story problem? The Johnson Chair Factory used 165.6 pounds of nails in 6 weeks. The Martinez Table Factory used 154.2 pounds of nails in 6 weeks. How many pounds of nails did the two factories use altogether in one week? A. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. B. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. Step 4: Multiply the sum by 2. C. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Divide the two amounts by 6. D. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Multiply the two amounts by 6.
Answer:
A if you look close at the story you will learn alot! hope this helps!
Pietro buys 20 candy bars for $6 he plans to sell all 20 candy bars in 1 day he need to make a profit of $10 per day to meet his fundraising goal how much must he charge for each candy bar?
A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm
Try this option:
[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]
answer: B
B) 3 cm
Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]
Vcone =
1
3
πr2h
36π =
1
3
π(6)2h
36π = 12πh
h = 3
Thus, the height is 3 cm.
Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.
Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?
The price of the gas is $3.96.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Gas prices in Cook-County are at $3.30 per gallon.
If a market scientist predicts a 20% increase in the price of gas in the coming month,
that means,
100 + 20% = 120% increase = 1.2 in decimals.
The price of gas,
= 3.30 + 3.30 x 1.2
= 3.96
Therefore, the new price is $3.96.
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Select two rations that are equivalent to 3: 12.
can someone help me with number 4
what is the x intercept of the equation that passes through (1,-6) and is perpendicular to y=1/3x +1
Mr. lee drove his car 297.6 miles while using 16 gallons of gas . How many miles does he get to the gallon ?
The gift shop at Manatee mall was having a clearance sale everything was marked down 30% off the original price of a manatee that was $18 what is the clearance price